Research ArticleVibration Frequencies Extraction of the Forth Road BridgeUsing High Sampling GPS Data

Jian Wang12 Xiaolin Meng23 Changbiao Qin1 and Jiaohong Yi1

1School of Environment Science and Spatial Informatics China University of Mining and Technology Xuzhou 221116 China2Sino-UK Geospatial Engineering Centre The University of Nottingham Nottingham NG7 2TU UK3Nottingham Geospatial Institute The University of Nottingham Nottingham NG7 2TU UK

Correspondence should be addressed to Jian Wang wjianhuance163com

Received 3 July 2015 Accepted 8 September 2015

Academic Editor Salvatore Russo

Copyright copy 2016 Jian Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes a scheme for vibration frequencies extraction of the Forth Road Bridge in Scotland from high sampling GPSdata The interaction between the dynamic response and the ambient loadings is carefully analysed A bilinear Chebyshev high-pass filter is designed to isolate the quasistatic movements the FFT algorithm and peak-picking approach are applied to extract thevibration frequencies and a GPS data accumulation counter is suggested for real-time monitoring applications To understand thechange in the structural characteristics under different loadings the deformation results from three different loading conditionsare presented that is the ambient circulation loading the strong wind under abrupt wind speed change and the specific trial withtwo 40 t lorries passing the bridge The results show that GPS not only can capture absolute 3D deflections reliably but also can beused to extract the frequency response accurately It is evident that the frequencies detected using the filtered deflection time seriesin different direction show quite different characteristics and more stable results can be obtained from the height displacementtime series The frequency responses of 0105 and 0269Hz extracted from the lateral displacement time series correlate well withthe data using height displacement time series

1 Introduction

The Global Navigation Satellite Systems (GNSS) positioningtechnology has been widely used in monitoring dynamicresponses of civil structures such as high-rise building andcable-stayed bridges for more than twenty years In order toobtain the deflection and the vibration frequencies of bridgesmany efforts have been made by the academic to developmonitoring systems and data processing algorithms

By using theGlobal Positioning System (GPS) Leach et alproposed a monitoring system of a cable-stayed suspensionbridge to obtain the deformation and the vibration [1] In1995 the capability of GPS for monitoring the structuralvibrations was verified with an experiment that was per-formed in the Calgary Tower a vibration frequency of 03Hzin both north-south and east-west directions was extracted[2] Two experiments were performed for the extraction ofthe short-term deformations of the suspension bridge atTulln in Austria and the results show that the precision of

a GPS monitoring system is about 2mm for the horizontalcoordinates and 4mm for the height component [3] Tomonitor the high frequency characteristic of a bridge aLeica SR510 receiver of 10Hz sampling rate and a JNS100receiver measured at 50Hz were used and the trials werecarried out in a controlled environment the real bridgemonitoring has proved the effectiveness of high samplingGPS [4] To improve the reliability of a system for bridgedeflectionmonitoring an integrated GPSPseudolites systemwas proposed and its geometric characteristic was analysed[5] The vertical natural frequency of the Pierre-LaporteBridge in Canada was extracted using different algorithmsand programs based on GPS monitoring data [6] A motionsimulation table was designed to simulate 2D motion ofhigh-rise building in a horizontal plane and motion of longspan bridges in a vertical plane then a GPS antenna wasinstalled on the table for collecting the data of a simulatedmotion It demonstrated that GPS data is accurate enoughfor monitoring the dynamic response of civil structures [7]

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 9807861 18 pageshttpdxdoiorg10115520169807861

2 Shock and Vibration

2515m

1258mA2

A1South North

Ref1Ref2

B C D E

F2515m

1258m

BCS of the bridgeS

W

N

E

X

Y

GPS reference GPS receiver GPS receiverGPS monitoring site F

Figure 1 The devices used to monitor the dynamic responses of the Forth Road Bridge (only the data from site F will be analysed)

0

05

1

15

Lat

(m)

minus01

0

01

Long

(m

)

63

64

65

66

Hei

ght (

m)

500 9 Feb23001700 1100 1700 2300 500 10 Feb1100 8 Feb

500 9 Feb 500 10 Feb1700 1100 1700 23001100 8 Feb 2300

1700 2300 500 10 Feb500 9 Feb23001700 11001100 8 FebTime (hrsdatemonth)

Figure 2 Lateral longitudinal and vertical deflection in BCS during the 46 h trial

A statistical analysis on the outlier level and the accuracy ofthe real-time kinematic (RTK) and postprocessing kinematicmodes were given by Nickitopoulou through using the datacollected via a rotating GPS receiver antenna [8] It can beconcluded that GPS is viable to record the responses of forcedvibration decayed free vibration and ambient vibration of

the Wilford Bridge over the River Trent in Nottingham anda triaxial accelerometer can be used to validate the dynam-ics estimated from GPS measurements [9] The structuraldeflection of a cable-stayed bridge over the River Tamar innorthern Tasmania Australia has been successfully detectedusing GPS monitoring data and the predicted deflection

Shock and Vibration 3

TemperatureHeight displacementMean height displacement

Tem

pera

ture

(∘C)

23456789101112

230

0

170

0

110

0 8

Feb

110

0

170

0

230

0

500

10

Feb

500

9 F

eb

Cross correlation minus055

64

642

644

646

648

65

652

Hei

ght (

m)

Figure 3 Relation between the air temperature and height deflec-tion at site F

calculated using the SPACEGASS structural analysis softwaresuite was used to verify the GPS results [10] The spectraldensity of deflections monitored via a RTK GPS installedon the Dalian Beida Bridge is in coincidence with that of afinite element model (FEM) [11] The study also reveals thepotential of GPS to measure the deflections and the modalfrequencies of rather stiff bridges far exceeding current limitsof the method assumed so far which was verified via anexample by monitoring the oscillations of a 40m long steelfootbridge [12] GPS was also suitable for the identificationof relatively rigid bridges with modal frequencies up to 4Hz[13] The mean amplitude of oscillations was calculated withmillimetre accuracy via a computer based algorithm usingGPS andRoboticTheodolites (RTS) and themethodwas usedto two short span bridges for the structural health monitor-ing [14] Im et al reviewed GPS technology for structuralhealth monitoring [15] GPS is a viable and promising toolfor vibration extraction considering the rapid advancementof GPS devices and algorithms Modal frequencies of theWilford Bridge are accurately identified using GPS mea-surements with a proposed Multimode Adaptive Filtering(MAF) algorithm and validated by accelerometer data Thefundamental frequency 1690Hz of the bridge was detectedwhich is slightly lower than the estimated frequency 1740Hzby the structural analysis [16]

Wind loading and multipath effects mainly contributeto low frequency components of bridge dynamics which aredifficult to separate and affect early alarming The amplitudeof multipath effect can reach a few centimetres in extremeenvironment and an adaptive filtering method can mitigatethe multipath effect for structural deflection monitoring [1718] Dynamic multipath induced by a passing vehicle forbridges was studied for the first time and certain strategies formodelling were proposed [19] Actually monitoring stationshave varying circumstance that produces different multipatheffects that will be considered in this paper

This paper proposes an innovative scheme for extractingthe vibration frequencies from high sampling GPS data ofthe Forth Road Bridge In order to extract the deflection aChebyshev high-pass digital filter is designed to eliminatemultipath effects and then an FFT is used to extract thefrequencies information The field experiment for the ForthRoad Bridge is introduced in detail and the data set of amiddle site on the west side of the bridge deck is chosen foranalysing the frequency responses The frequency responsein different situations is analysed and compared to obtain thenatural frequencies of the bridge

2 Field Experiment

21 The Forth Road Bridge in Scotland The Forth RoadBridge opened to traffic in 1964 links the north of Scotlandwith Edinburgh and the south carrying the A90 road ofUnited Kingdom (UK) It has an overall length of 25 km anda main span length of 1006m The road bridge runs at 3∘from north The traffic has increased from 4 million vehiclesin 1964 to over 23 million in 2002 In order to investigatethe dynamic responses of the Forth Road Bridge an overallexperiment was carried out in 2005 by a research groupof the University of Nottingham and the work on the dataprocessing of the deflection and frequency monitoring of theForth Road Bridge has been reported in 2012 [20]

22 Description of the Experiment During a 46 h observationperiod from 8 to 10 February 2005 the data sets werecollected by the staff from the former Institute of EngineeringSurveying and Space Geodesy (IESSG) at the University ofNottingham a part of the field data sets is used in this paper toextract the vibration frequencies in various ambient loadingsFive GPS receivers marked as B C D E and F were fixedto the bridge handrail and two GPS receivers marked as A1and A2 were located on top of the southern support tower asillustrated in Figure 1 [20]

More details of the receiversrsquo locations and their spec-ifications are found in [20] and an overall analysis andcomparisons of the observations of the GPS receivers weredemonstrated in [20] Data collected at station F is applied totest the proposed scheme as the weather station was installedexactly adjacent to F at the midspan on the western footwayA Leica GX1230 dual-frequency GPS receiver equipped witha Leica AT504 choke-ring antenna was used to collect data atthe rate of 10Hz

The raw GPS displacement measurements are first trans-formed into the local bridge coordinate system (BCS) usingthe rotation matrix the vertical component is representedas the height variations above the mean sea level and thehorizontal displacements are obtained by taking a specificposition as the datum

The lateral longitudinal and vertical movements of thebridge in BCS during the 46 h trial are illustrated in Figure 2It can be noted that the lateral direction contains morefrequency information than the other two directions as it ismore vulnerable to ambient loadings

4 Shock and Vibration

10minus10

10minus5

100

Mag

nitu

de

100

101

10minus1

10minus2

Frequency (rads)

minus200

minus100

0

100

200

Phas

e (de

g)

100

101

10minus1

10minus2

Frequency (rads)

minus150

minus100

minus50

0

Mag

nitu

de (d

B)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

minus400

minus300

minus200

minus100

0

Phas

e (de

g)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

Figure 4 The corresponding analogue and digit filter

Yes

No

Low frequencyinterferenceselimination

GPS sensors GPS data accumulation

High-pass digital filter

FFT transform

Vibrationextraction

Counter = 0

counter = counter + 1

Counter ge T

Figure 5 Flowchart for vibration frequencies extraction for the Forth Road Bridge

Lat displacementLat wind speed

Cross correlation minus007

minus003

minus002

minus001

0

001

002

003

Lat

(m)

242500 243000 243500 244000242000GPS time (s)

minus5

0

5

10

15

20

25

Win

d sp

eed

(km

h)

Figure 6 Lateral displacement and wind speed

Obvious systematic variations are shown in three direc-tions that are affected by the temperature and wind accordingto the analysis in literature [20] It is evident that lateralmovements are most significant which reach an order of twometers this is mainly caused by the ambient wind loadings

and the largest deflections occur in the second night due tothe existence of high wind speeds The height component ofthe bridge moves by an order of decimetres and there existsa close relationship between the height response and ambienttemperature variations and traffic loadings in Figure 3 wecan clearly see that a temperature change of about 55∘C canbe observed during the trial and it evidently changes thevertical position of the bridge deck especially the long-termdynamics As expected the longitudinal deflections are quitesmall and the peak to peak movements are at the order ofseveral centimetres Three different deformation situationsare considered to extract the vibration frequencies of thebridge in this paper which will be discussed in detail in latersections

3 Data Processing Scheme

31 Description of the Bridge Vibration Signal The vibrationsignal of a bridge monitored by GPS can be expressed by

119910 (119899) = 119872 (119899) + 119863 (119899) + 119873 (119899) (1)

where119872(119899) represents the low frequency interferences suchas multipath error atmospheric error or clock error at 119899thobservation epoch among which multipath error is the main

Shock and Vibration 5

minus0015

minus001

minus0005

0

0005

001

0015La

t di

spla

cem

ent (

m)

244000 242500 243000 243500242000GPS time (s)

(a)

times10minus3

10minus1

10minus2

100

Frequency (Hz)

0

02

04

06

08

1

12

14

16

18

2

Am

plitu

de(b)

times10minus4

0

1

2

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 7 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

part 119863(119899) is the actual dynamic vibrations of the bridge and119873(119899) is the noise [16] To obtain the vibration frequenciesof the bridge low frequency deflections can be isolatedusing high-pass digital filter that can be designed accordingto the characteristics of the specific vibration signal andChebyshev high-pass digital filter is designed for the vibrationfrequencies extraction of the Forth Road Bridge in this paper

32 Design of Chebyshev High-Pass Digital Filter For Type IChebyshev filter the gain response as a function of angular

frequency 120596 of 119899th-order low-pass filter is equal to theabsolute value of the transfer function119867

119899(119895120596)

119866119899(120596) =1003816100381610038161003816119867119899 (119895120596)

1003816100381610038161003816 =1

radic1 + 12057621198792119899

(1205961205960)

(2)

where 120576 is the ripple factor 1205960is the cut-off frequency and

119879119899is a Chebyshev polynomial of 119899th order The order of

6 Shock and Vibration

Long displacementLong wind speed

Cross correlation 011

242500 243000 243500 244000242000GPS time (s)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

Win

d sp

eed

(km

h)

Figure 8 Longitudinal displacement and wind speed

a Chebyshev filter is equal to the number of reactive compo-nents needed to realize the filter using analogue electronics[21]

The ripple is often given in dB Ripple in dB =20log10

radic1 + 1205762 so that a ripple amplitude of 3 dB results from120576 = 1 The transfer function is then given by

119867119886(119904) =

1

2119899 minus 1

119899

prod

119898=1

1

(119904 minus 119904minus119901119898

) (3)

where 119904minus119901119898

are only those poles with a negative sign in frontof the real term for the poles

The bilinear transform is used to convert a transferfunction 119867

119886(119904) in the continuous-time domain to a transfer

function119867119889(119911) in the discrete-timedomain Itmaps positions

on 119895120596 axis Re[119904] = 0 in 119904-plane to the unit circle |119911| = 1in 119911-plane The bilinear transform essentially uses this first-order approximation and substitutes into the continuous-time transfer function [22]119867

119886(119904)

119904 larr9978882

119879

119911 minus 1

119911 + 1 (4)

That is

119867119889(119911) = 119867

119886(119904)1003816100381610038161003816119904=(2119879)((119911minus1)(119911+1)) = 119867119886 (

2

119879

119911 minus 1

119911 + 1) (5)

The low-pass Type I Chebyshev filter is transferred fromanalogue filter to digital filter by using the above bilineartransformation Subsequently the low-pass digital Type IChebyshev filter is transferred into high pass by the followingequation [23]

Vminus1 = minus119911minus1

+ 120572

1 + 120572119911minus1 (6)

where

120572 =cos ((120596

0+ 1205790) 2)

cos ((1205960minus 1205790) 2) (7)

Equation (5) maps 119911-plane (low pass) to V-plane (highpass) and 120596

0and 120579

0are cut-off frequencies in 119911-plane and

V-plane respectively The loads of the bridge are varyingwith different factors such as wind speeds traffic flow andtemperature variation the optimal filter parameters can bedetermined considering the real deformation By testingdifferent data sets the high-pass digital Type I Chebyshevfilter with a sampling frequency of 20Hz is good enoughfor the data processing of the bridge In a real applicationthe filter is sampled into 10Hz The critical frequency forpass band is 05 pass band attenuation is less than 08 dBthe critical frequency for stopband is 0025Hz stopbandattenuation is greater than 20 dB A high-pass digital TypeI Chebyshev filter is designed with the above parameters(Figure 4)

33 The Scheme for Vibration Frequencies Extraction Theflowchart for vibration frequencies extraction is summarizedin Figure 5 The real-time GPS displacement data sets areinput into the designed high-pass digital filter introduced inSection 32 to eliminate the low frequency interferences As ahigh-pass digital filter cannot be used in a real-time scenarioa GPS data accumulation counter is used to form a time seriesover a sliding window with a predefined length to considerthe different deformation situations such as deformationduring quiet period or busy period a varied window length119879 can be used that is 2000 s or 1000 s used in this paperFinally the vibration frequencies are obtained using the fastFourier transform (FFT) algorithm

4 Vibration Frequencies Extraction

41 Vibration Frequencies Extraction under Ambient Circula-tion Loading Conditions In order to evaluate the safety ofthe large structures such as long span bridges and high-rise buildings it is popular to extract the structural modalparameters such as natural frequencies mode shapes anddamping ratios from GNSS measurements by using theambient loadingsThe Forth Road Bridge was operated undera heavy traffic flow in the daytime especially at rush hour thebridge deck was expected to move under the traffic loads Inthis section we are expected to extract the bridge dynamicsunder ambient circulation loading conditions that is thetraffic flow and wind speed are not high

In the following figure data set of 2000 seconds (242001ndash244000 s) for site F was used to characterize the bridgedynamics and extract the vibration frequencies Figure 6shows the lateral deflection time series and the correspondingwind speed data during the specific period it is evident thatthe peak to peak deflection with the amplitude of about 4 cmis relatively small this is due to existence of low wind speedsthe mean wind speed is 730 kmh during the observationperiod it shows low correlation with the wind speed Wecan also see that very slow movements form a part of thelateral displacement time series while the very slow vibrationcannot indicate the natural frequencies of the bridge In ourpaper the high-pass filter introduced in Section 32 will beapplied to the original displacement time series at 10Hz

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

2 Shock and Vibration

2515m

1258mA2

A1South North

Ref1Ref2

B C D E

F2515m

1258m

BCS of the bridgeS

W

N

E

X

Y

GPS reference GPS receiver GPS receiverGPS monitoring site F

Figure 1 The devices used to monitor the dynamic responses of the Forth Road Bridge (only the data from site F will be analysed)

0

05

1

15

Lat

(m)

minus01

0

01

Long

(m

)

63

64

65

66

Hei

ght (

m)

500 9 Feb23001700 1100 1700 2300 500 10 Feb1100 8 Feb

500 9 Feb 500 10 Feb1700 1100 1700 23001100 8 Feb 2300

1700 2300 500 10 Feb500 9 Feb23001700 11001100 8 FebTime (hrsdatemonth)

Figure 2 Lateral longitudinal and vertical deflection in BCS during the 46 h trial

A statistical analysis on the outlier level and the accuracy ofthe real-time kinematic (RTK) and postprocessing kinematicmodes were given by Nickitopoulou through using the datacollected via a rotating GPS receiver antenna [8] It can beconcluded that GPS is viable to record the responses of forcedvibration decayed free vibration and ambient vibration of

the Wilford Bridge over the River Trent in Nottingham anda triaxial accelerometer can be used to validate the dynam-ics estimated from GPS measurements [9] The structuraldeflection of a cable-stayed bridge over the River Tamar innorthern Tasmania Australia has been successfully detectedusing GPS monitoring data and the predicted deflection

Shock and Vibration 3

TemperatureHeight displacementMean height displacement

Tem

pera

ture

(∘C)

23456789101112

230

0

170

0

110

0 8

Feb

110

0

170

0

230

0

500

10

Feb

500

9 F

eb

Cross correlation minus055

64

642

644

646

648

65

652

Hei

ght (

m)

Figure 3 Relation between the air temperature and height deflec-tion at site F

calculated using the SPACEGASS structural analysis softwaresuite was used to verify the GPS results [10] The spectraldensity of deflections monitored via a RTK GPS installedon the Dalian Beida Bridge is in coincidence with that of afinite element model (FEM) [11] The study also reveals thepotential of GPS to measure the deflections and the modalfrequencies of rather stiff bridges far exceeding current limitsof the method assumed so far which was verified via anexample by monitoring the oscillations of a 40m long steelfootbridge [12] GPS was also suitable for the identificationof relatively rigid bridges with modal frequencies up to 4Hz[13] The mean amplitude of oscillations was calculated withmillimetre accuracy via a computer based algorithm usingGPS andRoboticTheodolites (RTS) and themethodwas usedto two short span bridges for the structural health monitor-ing [14] Im et al reviewed GPS technology for structuralhealth monitoring [15] GPS is a viable and promising toolfor vibration extraction considering the rapid advancementof GPS devices and algorithms Modal frequencies of theWilford Bridge are accurately identified using GPS mea-surements with a proposed Multimode Adaptive Filtering(MAF) algorithm and validated by accelerometer data Thefundamental frequency 1690Hz of the bridge was detectedwhich is slightly lower than the estimated frequency 1740Hzby the structural analysis [16]

Wind loading and multipath effects mainly contributeto low frequency components of bridge dynamics which aredifficult to separate and affect early alarming The amplitudeof multipath effect can reach a few centimetres in extremeenvironment and an adaptive filtering method can mitigatethe multipath effect for structural deflection monitoring [1718] Dynamic multipath induced by a passing vehicle forbridges was studied for the first time and certain strategies formodelling were proposed [19] Actually monitoring stationshave varying circumstance that produces different multipatheffects that will be considered in this paper

This paper proposes an innovative scheme for extractingthe vibration frequencies from high sampling GPS data ofthe Forth Road Bridge In order to extract the deflection aChebyshev high-pass digital filter is designed to eliminatemultipath effects and then an FFT is used to extract thefrequencies information The field experiment for the ForthRoad Bridge is introduced in detail and the data set of amiddle site on the west side of the bridge deck is chosen foranalysing the frequency responses The frequency responsein different situations is analysed and compared to obtain thenatural frequencies of the bridge

2 Field Experiment

21 The Forth Road Bridge in Scotland The Forth RoadBridge opened to traffic in 1964 links the north of Scotlandwith Edinburgh and the south carrying the A90 road ofUnited Kingdom (UK) It has an overall length of 25 km anda main span length of 1006m The road bridge runs at 3∘from north The traffic has increased from 4 million vehiclesin 1964 to over 23 million in 2002 In order to investigatethe dynamic responses of the Forth Road Bridge an overallexperiment was carried out in 2005 by a research groupof the University of Nottingham and the work on the dataprocessing of the deflection and frequency monitoring of theForth Road Bridge has been reported in 2012 [20]

22 Description of the Experiment During a 46 h observationperiod from 8 to 10 February 2005 the data sets werecollected by the staff from the former Institute of EngineeringSurveying and Space Geodesy (IESSG) at the University ofNottingham a part of the field data sets is used in this paper toextract the vibration frequencies in various ambient loadingsFive GPS receivers marked as B C D E and F were fixedto the bridge handrail and two GPS receivers marked as A1and A2 were located on top of the southern support tower asillustrated in Figure 1 [20]

More details of the receiversrsquo locations and their spec-ifications are found in [20] and an overall analysis andcomparisons of the observations of the GPS receivers weredemonstrated in [20] Data collected at station F is applied totest the proposed scheme as the weather station was installedexactly adjacent to F at the midspan on the western footwayA Leica GX1230 dual-frequency GPS receiver equipped witha Leica AT504 choke-ring antenna was used to collect data atthe rate of 10Hz

The raw GPS displacement measurements are first trans-formed into the local bridge coordinate system (BCS) usingthe rotation matrix the vertical component is representedas the height variations above the mean sea level and thehorizontal displacements are obtained by taking a specificposition as the datum

The lateral longitudinal and vertical movements of thebridge in BCS during the 46 h trial are illustrated in Figure 2It can be noted that the lateral direction contains morefrequency information than the other two directions as it ismore vulnerable to ambient loadings

4 Shock and Vibration

10minus10

10minus5

100

Mag

nitu

de

100

101

10minus1

10minus2

Frequency (rads)

minus200

minus100

0

100

200

Phas

e (de

g)

100

101

10minus1

10minus2

Frequency (rads)

minus150

minus100

minus50

0

Mag

nitu

de (d

B)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

minus400

minus300

minus200

minus100

0

Phas

e (de

g)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

Figure 4 The corresponding analogue and digit filter

Yes

No

Low frequencyinterferenceselimination

GPS sensors GPS data accumulation

High-pass digital filter

FFT transform

Vibrationextraction

Counter = 0

counter = counter + 1

Counter ge T

Figure 5 Flowchart for vibration frequencies extraction for the Forth Road Bridge

Lat displacementLat wind speed

Cross correlation minus007

minus003

minus002

minus001

0

001

002

003

Lat

(m)

242500 243000 243500 244000242000GPS time (s)

minus5

0

5

10

15

20

25

Win

d sp

eed

(km

h)

Figure 6 Lateral displacement and wind speed

Obvious systematic variations are shown in three direc-tions that are affected by the temperature and wind accordingto the analysis in literature [20] It is evident that lateralmovements are most significant which reach an order of twometers this is mainly caused by the ambient wind loadings

and the largest deflections occur in the second night due tothe existence of high wind speeds The height component ofthe bridge moves by an order of decimetres and there existsa close relationship between the height response and ambienttemperature variations and traffic loadings in Figure 3 wecan clearly see that a temperature change of about 55∘C canbe observed during the trial and it evidently changes thevertical position of the bridge deck especially the long-termdynamics As expected the longitudinal deflections are quitesmall and the peak to peak movements are at the order ofseveral centimetres Three different deformation situationsare considered to extract the vibration frequencies of thebridge in this paper which will be discussed in detail in latersections

3 Data Processing Scheme

31 Description of the Bridge Vibration Signal The vibrationsignal of a bridge monitored by GPS can be expressed by

119910 (119899) = 119872 (119899) + 119863 (119899) + 119873 (119899) (1)

where119872(119899) represents the low frequency interferences suchas multipath error atmospheric error or clock error at 119899thobservation epoch among which multipath error is the main

Shock and Vibration 5

minus0015

minus001

minus0005

0

0005

001

0015La

t di

spla

cem

ent (

m)

244000 242500 243000 243500242000GPS time (s)

(a)

times10minus3

10minus1

10minus2

100

Frequency (Hz)

0

02

04

06

08

1

12

14

16

18

2

Am

plitu

de(b)

times10minus4

0

1

2

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 7 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

part 119863(119899) is the actual dynamic vibrations of the bridge and119873(119899) is the noise [16] To obtain the vibration frequenciesof the bridge low frequency deflections can be isolatedusing high-pass digital filter that can be designed accordingto the characteristics of the specific vibration signal andChebyshev high-pass digital filter is designed for the vibrationfrequencies extraction of the Forth Road Bridge in this paper

32 Design of Chebyshev High-Pass Digital Filter For Type IChebyshev filter the gain response as a function of angular

frequency 120596 of 119899th-order low-pass filter is equal to theabsolute value of the transfer function119867

119899(119895120596)

119866119899(120596) =1003816100381610038161003816119867119899 (119895120596)

1003816100381610038161003816 =1

radic1 + 12057621198792119899

(1205961205960)

(2)

where 120576 is the ripple factor 1205960is the cut-off frequency and

119879119899is a Chebyshev polynomial of 119899th order The order of

6 Shock and Vibration

Long displacementLong wind speed

Cross correlation 011

242500 243000 243500 244000242000GPS time (s)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

Win

d sp

eed

(km

h)

Figure 8 Longitudinal displacement and wind speed

a Chebyshev filter is equal to the number of reactive compo-nents needed to realize the filter using analogue electronics[21]

The ripple is often given in dB Ripple in dB =20log10

radic1 + 1205762 so that a ripple amplitude of 3 dB results from120576 = 1 The transfer function is then given by

119867119886(119904) =

1

2119899 minus 1

119899

prod

119898=1

1

(119904 minus 119904minus119901119898

) (3)

where 119904minus119901119898

are only those poles with a negative sign in frontof the real term for the poles

The bilinear transform is used to convert a transferfunction 119867

119886(119904) in the continuous-time domain to a transfer

function119867119889(119911) in the discrete-timedomain Itmaps positions

on 119895120596 axis Re[119904] = 0 in 119904-plane to the unit circle |119911| = 1in 119911-plane The bilinear transform essentially uses this first-order approximation and substitutes into the continuous-time transfer function [22]119867

119886(119904)

119904 larr9978882

119879

119911 minus 1

119911 + 1 (4)

That is

119867119889(119911) = 119867

119886(119904)1003816100381610038161003816119904=(2119879)((119911minus1)(119911+1)) = 119867119886 (

2

119879

119911 minus 1

119911 + 1) (5)

The low-pass Type I Chebyshev filter is transferred fromanalogue filter to digital filter by using the above bilineartransformation Subsequently the low-pass digital Type IChebyshev filter is transferred into high pass by the followingequation [23]

Vminus1 = minus119911minus1

+ 120572

1 + 120572119911minus1 (6)

where

120572 =cos ((120596

0+ 1205790) 2)

cos ((1205960minus 1205790) 2) (7)

Equation (5) maps 119911-plane (low pass) to V-plane (highpass) and 120596

0and 120579

0are cut-off frequencies in 119911-plane and

V-plane respectively The loads of the bridge are varyingwith different factors such as wind speeds traffic flow andtemperature variation the optimal filter parameters can bedetermined considering the real deformation By testingdifferent data sets the high-pass digital Type I Chebyshevfilter with a sampling frequency of 20Hz is good enoughfor the data processing of the bridge In a real applicationthe filter is sampled into 10Hz The critical frequency forpass band is 05 pass band attenuation is less than 08 dBthe critical frequency for stopband is 0025Hz stopbandattenuation is greater than 20 dB A high-pass digital TypeI Chebyshev filter is designed with the above parameters(Figure 4)

33 The Scheme for Vibration Frequencies Extraction Theflowchart for vibration frequencies extraction is summarizedin Figure 5 The real-time GPS displacement data sets areinput into the designed high-pass digital filter introduced inSection 32 to eliminate the low frequency interferences As ahigh-pass digital filter cannot be used in a real-time scenarioa GPS data accumulation counter is used to form a time seriesover a sliding window with a predefined length to considerthe different deformation situations such as deformationduring quiet period or busy period a varied window length119879 can be used that is 2000 s or 1000 s used in this paperFinally the vibration frequencies are obtained using the fastFourier transform (FFT) algorithm

4 Vibration Frequencies Extraction

41 Vibration Frequencies Extraction under Ambient Circula-tion Loading Conditions In order to evaluate the safety ofthe large structures such as long span bridges and high-rise buildings it is popular to extract the structural modalparameters such as natural frequencies mode shapes anddamping ratios from GNSS measurements by using theambient loadingsThe Forth Road Bridge was operated undera heavy traffic flow in the daytime especially at rush hour thebridge deck was expected to move under the traffic loads Inthis section we are expected to extract the bridge dynamicsunder ambient circulation loading conditions that is thetraffic flow and wind speed are not high

In the following figure data set of 2000 seconds (242001ndash244000 s) for site F was used to characterize the bridgedynamics and extract the vibration frequencies Figure 6shows the lateral deflection time series and the correspondingwind speed data during the specific period it is evident thatthe peak to peak deflection with the amplitude of about 4 cmis relatively small this is due to existence of low wind speedsthe mean wind speed is 730 kmh during the observationperiod it shows low correlation with the wind speed Wecan also see that very slow movements form a part of thelateral displacement time series while the very slow vibrationcannot indicate the natural frequencies of the bridge In ourpaper the high-pass filter introduced in Section 32 will beapplied to the original displacement time series at 10Hz

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 3

TemperatureHeight displacementMean height displacement

Tem

pera

ture

(∘C)

23456789101112

230

0

170

0

110

0 8

Feb

110

0

170

0

230

0

500

10

Feb

500

9 F

eb

Cross correlation minus055

64

642

644

646

648

65

652

Hei

ght (

m)

Figure 3 Relation between the air temperature and height deflec-tion at site F

calculated using the SPACEGASS structural analysis softwaresuite was used to verify the GPS results [10] The spectraldensity of deflections monitored via a RTK GPS installedon the Dalian Beida Bridge is in coincidence with that of afinite element model (FEM) [11] The study also reveals thepotential of GPS to measure the deflections and the modalfrequencies of rather stiff bridges far exceeding current limitsof the method assumed so far which was verified via anexample by monitoring the oscillations of a 40m long steelfootbridge [12] GPS was also suitable for the identificationof relatively rigid bridges with modal frequencies up to 4Hz[13] The mean amplitude of oscillations was calculated withmillimetre accuracy via a computer based algorithm usingGPS andRoboticTheodolites (RTS) and themethodwas usedto two short span bridges for the structural health monitor-ing [14] Im et al reviewed GPS technology for structuralhealth monitoring [15] GPS is a viable and promising toolfor vibration extraction considering the rapid advancementof GPS devices and algorithms Modal frequencies of theWilford Bridge are accurately identified using GPS mea-surements with a proposed Multimode Adaptive Filtering(MAF) algorithm and validated by accelerometer data Thefundamental frequency 1690Hz of the bridge was detectedwhich is slightly lower than the estimated frequency 1740Hzby the structural analysis [16]

Wind loading and multipath effects mainly contributeto low frequency components of bridge dynamics which aredifficult to separate and affect early alarming The amplitudeof multipath effect can reach a few centimetres in extremeenvironment and an adaptive filtering method can mitigatethe multipath effect for structural deflection monitoring [1718] Dynamic multipath induced by a passing vehicle forbridges was studied for the first time and certain strategies formodelling were proposed [19] Actually monitoring stationshave varying circumstance that produces different multipatheffects that will be considered in this paper

This paper proposes an innovative scheme for extractingthe vibration frequencies from high sampling GPS data ofthe Forth Road Bridge In order to extract the deflection aChebyshev high-pass digital filter is designed to eliminatemultipath effects and then an FFT is used to extract thefrequencies information The field experiment for the ForthRoad Bridge is introduced in detail and the data set of amiddle site on the west side of the bridge deck is chosen foranalysing the frequency responses The frequency responsein different situations is analysed and compared to obtain thenatural frequencies of the bridge

2 Field Experiment

21 The Forth Road Bridge in Scotland The Forth RoadBridge opened to traffic in 1964 links the north of Scotlandwith Edinburgh and the south carrying the A90 road ofUnited Kingdom (UK) It has an overall length of 25 km anda main span length of 1006m The road bridge runs at 3∘from north The traffic has increased from 4 million vehiclesin 1964 to over 23 million in 2002 In order to investigatethe dynamic responses of the Forth Road Bridge an overallexperiment was carried out in 2005 by a research groupof the University of Nottingham and the work on the dataprocessing of the deflection and frequency monitoring of theForth Road Bridge has been reported in 2012 [20]

22 Description of the Experiment During a 46 h observationperiod from 8 to 10 February 2005 the data sets werecollected by the staff from the former Institute of EngineeringSurveying and Space Geodesy (IESSG) at the University ofNottingham a part of the field data sets is used in this paper toextract the vibration frequencies in various ambient loadingsFive GPS receivers marked as B C D E and F were fixedto the bridge handrail and two GPS receivers marked as A1and A2 were located on top of the southern support tower asillustrated in Figure 1 [20]

More details of the receiversrsquo locations and their spec-ifications are found in [20] and an overall analysis andcomparisons of the observations of the GPS receivers weredemonstrated in [20] Data collected at station F is applied totest the proposed scheme as the weather station was installedexactly adjacent to F at the midspan on the western footwayA Leica GX1230 dual-frequency GPS receiver equipped witha Leica AT504 choke-ring antenna was used to collect data atthe rate of 10Hz

The raw GPS displacement measurements are first trans-formed into the local bridge coordinate system (BCS) usingthe rotation matrix the vertical component is representedas the height variations above the mean sea level and thehorizontal displacements are obtained by taking a specificposition as the datum

The lateral longitudinal and vertical movements of thebridge in BCS during the 46 h trial are illustrated in Figure 2It can be noted that the lateral direction contains morefrequency information than the other two directions as it ismore vulnerable to ambient loadings

4 Shock and Vibration

10minus10

10minus5

100

Mag

nitu

de

100

101

10minus1

10minus2

Frequency (rads)

minus200

minus100

0

100

200

Phas

e (de

g)

100

101

10minus1

10minus2

Frequency (rads)

minus150

minus100

minus50

0

Mag

nitu

de (d

B)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

minus400

minus300

minus200

minus100

0

Phas

e (de

g)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

Figure 4 The corresponding analogue and digit filter

Yes

No

Low frequencyinterferenceselimination

GPS sensors GPS data accumulation

High-pass digital filter

FFT transform

Vibrationextraction

Counter = 0

counter = counter + 1

Counter ge T

Figure 5 Flowchart for vibration frequencies extraction for the Forth Road Bridge

Lat displacementLat wind speed

Cross correlation minus007

minus003

minus002

minus001

0

001

002

003

Lat

(m)

242500 243000 243500 244000242000GPS time (s)

minus5

0

5

10

15

20

25

Win

d sp

eed

(km

h)

Figure 6 Lateral displacement and wind speed

Obvious systematic variations are shown in three direc-tions that are affected by the temperature and wind accordingto the analysis in literature [20] It is evident that lateralmovements are most significant which reach an order of twometers this is mainly caused by the ambient wind loadings

and the largest deflections occur in the second night due tothe existence of high wind speeds The height component ofthe bridge moves by an order of decimetres and there existsa close relationship between the height response and ambienttemperature variations and traffic loadings in Figure 3 wecan clearly see that a temperature change of about 55∘C canbe observed during the trial and it evidently changes thevertical position of the bridge deck especially the long-termdynamics As expected the longitudinal deflections are quitesmall and the peak to peak movements are at the order ofseveral centimetres Three different deformation situationsare considered to extract the vibration frequencies of thebridge in this paper which will be discussed in detail in latersections

3 Data Processing Scheme

31 Description of the Bridge Vibration Signal The vibrationsignal of a bridge monitored by GPS can be expressed by

119910 (119899) = 119872 (119899) + 119863 (119899) + 119873 (119899) (1)

where119872(119899) represents the low frequency interferences suchas multipath error atmospheric error or clock error at 119899thobservation epoch among which multipath error is the main

Shock and Vibration 5

minus0015

minus001

minus0005

0

0005

001

0015La

t di

spla

cem

ent (

m)

244000 242500 243000 243500242000GPS time (s)

(a)

times10minus3

10minus1

10minus2

100

Frequency (Hz)

0

02

04

06

08

1

12

14

16

18

2

Am

plitu

de(b)

times10minus4

0

1

2

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 7 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

part 119863(119899) is the actual dynamic vibrations of the bridge and119873(119899) is the noise [16] To obtain the vibration frequenciesof the bridge low frequency deflections can be isolatedusing high-pass digital filter that can be designed accordingto the characteristics of the specific vibration signal andChebyshev high-pass digital filter is designed for the vibrationfrequencies extraction of the Forth Road Bridge in this paper

32 Design of Chebyshev High-Pass Digital Filter For Type IChebyshev filter the gain response as a function of angular

frequency 120596 of 119899th-order low-pass filter is equal to theabsolute value of the transfer function119867

119899(119895120596)

119866119899(120596) =1003816100381610038161003816119867119899 (119895120596)

1003816100381610038161003816 =1

radic1 + 12057621198792119899

(1205961205960)

(2)

where 120576 is the ripple factor 1205960is the cut-off frequency and

119879119899is a Chebyshev polynomial of 119899th order The order of

6 Shock and Vibration

Long displacementLong wind speed

Cross correlation 011

242500 243000 243500 244000242000GPS time (s)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

Win

d sp

eed

(km

h)

Figure 8 Longitudinal displacement and wind speed

a Chebyshev filter is equal to the number of reactive compo-nents needed to realize the filter using analogue electronics[21]

The ripple is often given in dB Ripple in dB =20log10

radic1 + 1205762 so that a ripple amplitude of 3 dB results from120576 = 1 The transfer function is then given by

119867119886(119904) =

1

2119899 minus 1

119899

prod

119898=1

1

(119904 minus 119904minus119901119898

) (3)

where 119904minus119901119898

are only those poles with a negative sign in frontof the real term for the poles

The bilinear transform is used to convert a transferfunction 119867

119886(119904) in the continuous-time domain to a transfer

function119867119889(119911) in the discrete-timedomain Itmaps positions

on 119895120596 axis Re[119904] = 0 in 119904-plane to the unit circle |119911| = 1in 119911-plane The bilinear transform essentially uses this first-order approximation and substitutes into the continuous-time transfer function [22]119867

119886(119904)

119904 larr9978882

119879

119911 minus 1

119911 + 1 (4)

That is

119867119889(119911) = 119867

119886(119904)1003816100381610038161003816119904=(2119879)((119911minus1)(119911+1)) = 119867119886 (

2

119879

119911 minus 1

119911 + 1) (5)

The low-pass Type I Chebyshev filter is transferred fromanalogue filter to digital filter by using the above bilineartransformation Subsequently the low-pass digital Type IChebyshev filter is transferred into high pass by the followingequation [23]

Vminus1 = minus119911minus1

+ 120572

1 + 120572119911minus1 (6)

where

120572 =cos ((120596

0+ 1205790) 2)

cos ((1205960minus 1205790) 2) (7)

Equation (5) maps 119911-plane (low pass) to V-plane (highpass) and 120596

0and 120579

0are cut-off frequencies in 119911-plane and

V-plane respectively The loads of the bridge are varyingwith different factors such as wind speeds traffic flow andtemperature variation the optimal filter parameters can bedetermined considering the real deformation By testingdifferent data sets the high-pass digital Type I Chebyshevfilter with a sampling frequency of 20Hz is good enoughfor the data processing of the bridge In a real applicationthe filter is sampled into 10Hz The critical frequency forpass band is 05 pass band attenuation is less than 08 dBthe critical frequency for stopband is 0025Hz stopbandattenuation is greater than 20 dB A high-pass digital TypeI Chebyshev filter is designed with the above parameters(Figure 4)

33 The Scheme for Vibration Frequencies Extraction Theflowchart for vibration frequencies extraction is summarizedin Figure 5 The real-time GPS displacement data sets areinput into the designed high-pass digital filter introduced inSection 32 to eliminate the low frequency interferences As ahigh-pass digital filter cannot be used in a real-time scenarioa GPS data accumulation counter is used to form a time seriesover a sliding window with a predefined length to considerthe different deformation situations such as deformationduring quiet period or busy period a varied window length119879 can be used that is 2000 s or 1000 s used in this paperFinally the vibration frequencies are obtained using the fastFourier transform (FFT) algorithm

4 Vibration Frequencies Extraction

41 Vibration Frequencies Extraction under Ambient Circula-tion Loading Conditions In order to evaluate the safety ofthe large structures such as long span bridges and high-rise buildings it is popular to extract the structural modalparameters such as natural frequencies mode shapes anddamping ratios from GNSS measurements by using theambient loadingsThe Forth Road Bridge was operated undera heavy traffic flow in the daytime especially at rush hour thebridge deck was expected to move under the traffic loads Inthis section we are expected to extract the bridge dynamicsunder ambient circulation loading conditions that is thetraffic flow and wind speed are not high

In the following figure data set of 2000 seconds (242001ndash244000 s) for site F was used to characterize the bridgedynamics and extract the vibration frequencies Figure 6shows the lateral deflection time series and the correspondingwind speed data during the specific period it is evident thatthe peak to peak deflection with the amplitude of about 4 cmis relatively small this is due to existence of low wind speedsthe mean wind speed is 730 kmh during the observationperiod it shows low correlation with the wind speed Wecan also see that very slow movements form a part of thelateral displacement time series while the very slow vibrationcannot indicate the natural frequencies of the bridge In ourpaper the high-pass filter introduced in Section 32 will beapplied to the original displacement time series at 10Hz

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Shock and Vibration

10minus10

10minus5

100

Mag

nitu

de

100

101

10minus1

10minus2

Frequency (rads)

minus200

minus100

0

100

200

Phas

e (de

g)

100

101

10minus1

10minus2

Frequency (rads)

minus150

minus100

minus50

0

Mag

nitu

de (d

B)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

minus400

minus300

minus200

minus100

0

Phas

e (de

g)

0 1 15 2 25 3 35 4 45 505Frequency (Hz)

Figure 4 The corresponding analogue and digit filter

Yes

No

Low frequencyinterferenceselimination

GPS sensors GPS data accumulation

High-pass digital filter

FFT transform

Vibrationextraction

Counter = 0

counter = counter + 1

Counter ge T

Figure 5 Flowchart for vibration frequencies extraction for the Forth Road Bridge

Lat displacementLat wind speed

Cross correlation minus007

minus003

minus002

minus001

0

001

002

003

Lat

(m)

242500 243000 243500 244000242000GPS time (s)

minus5

0

5

10

15

20

25

Win

d sp

eed

(km

h)

Figure 6 Lateral displacement and wind speed

Obvious systematic variations are shown in three direc-tions that are affected by the temperature and wind accordingto the analysis in literature [20] It is evident that lateralmovements are most significant which reach an order of twometers this is mainly caused by the ambient wind loadings

and the largest deflections occur in the second night due tothe existence of high wind speeds The height component ofthe bridge moves by an order of decimetres and there existsa close relationship between the height response and ambienttemperature variations and traffic loadings in Figure 3 wecan clearly see that a temperature change of about 55∘C canbe observed during the trial and it evidently changes thevertical position of the bridge deck especially the long-termdynamics As expected the longitudinal deflections are quitesmall and the peak to peak movements are at the order ofseveral centimetres Three different deformation situationsare considered to extract the vibration frequencies of thebridge in this paper which will be discussed in detail in latersections

3 Data Processing Scheme

31 Description of the Bridge Vibration Signal The vibrationsignal of a bridge monitored by GPS can be expressed by

119910 (119899) = 119872 (119899) + 119863 (119899) + 119873 (119899) (1)

where119872(119899) represents the low frequency interferences suchas multipath error atmospheric error or clock error at 119899thobservation epoch among which multipath error is the main

Shock and Vibration 5

minus0015

minus001

minus0005

0

0005

001

0015La

t di

spla

cem

ent (

m)

244000 242500 243000 243500242000GPS time (s)

(a)

times10minus3

10minus1

10minus2

100

Frequency (Hz)

0

02

04

06

08

1

12

14

16

18

2

Am

plitu

de(b)

times10minus4

0

1

2

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 7 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

part 119863(119899) is the actual dynamic vibrations of the bridge and119873(119899) is the noise [16] To obtain the vibration frequenciesof the bridge low frequency deflections can be isolatedusing high-pass digital filter that can be designed accordingto the characteristics of the specific vibration signal andChebyshev high-pass digital filter is designed for the vibrationfrequencies extraction of the Forth Road Bridge in this paper

32 Design of Chebyshev High-Pass Digital Filter For Type IChebyshev filter the gain response as a function of angular

frequency 120596 of 119899th-order low-pass filter is equal to theabsolute value of the transfer function119867

119899(119895120596)

119866119899(120596) =1003816100381610038161003816119867119899 (119895120596)

1003816100381610038161003816 =1

radic1 + 12057621198792119899

(1205961205960)

(2)

where 120576 is the ripple factor 1205960is the cut-off frequency and

119879119899is a Chebyshev polynomial of 119899th order The order of

6 Shock and Vibration

Long displacementLong wind speed

Cross correlation 011

242500 243000 243500 244000242000GPS time (s)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

Win

d sp

eed

(km

h)

Figure 8 Longitudinal displacement and wind speed

a Chebyshev filter is equal to the number of reactive compo-nents needed to realize the filter using analogue electronics[21]

The ripple is often given in dB Ripple in dB =20log10

radic1 + 1205762 so that a ripple amplitude of 3 dB results from120576 = 1 The transfer function is then given by

119867119886(119904) =

1

2119899 minus 1

119899

prod

119898=1

1

(119904 minus 119904minus119901119898

) (3)

where 119904minus119901119898

are only those poles with a negative sign in frontof the real term for the poles

The bilinear transform is used to convert a transferfunction 119867

119886(119904) in the continuous-time domain to a transfer

function119867119889(119911) in the discrete-timedomain Itmaps positions

on 119895120596 axis Re[119904] = 0 in 119904-plane to the unit circle |119911| = 1in 119911-plane The bilinear transform essentially uses this first-order approximation and substitutes into the continuous-time transfer function [22]119867

119886(119904)

119904 larr9978882

119879

119911 minus 1

119911 + 1 (4)

That is

119867119889(119911) = 119867

119886(119904)1003816100381610038161003816119904=(2119879)((119911minus1)(119911+1)) = 119867119886 (

2

119879

119911 minus 1

119911 + 1) (5)

The low-pass Type I Chebyshev filter is transferred fromanalogue filter to digital filter by using the above bilineartransformation Subsequently the low-pass digital Type IChebyshev filter is transferred into high pass by the followingequation [23]

Vminus1 = minus119911minus1

+ 120572

1 + 120572119911minus1 (6)

where

120572 =cos ((120596

0+ 1205790) 2)

cos ((1205960minus 1205790) 2) (7)

Equation (5) maps 119911-plane (low pass) to V-plane (highpass) and 120596

0and 120579

0are cut-off frequencies in 119911-plane and

V-plane respectively The loads of the bridge are varyingwith different factors such as wind speeds traffic flow andtemperature variation the optimal filter parameters can bedetermined considering the real deformation By testingdifferent data sets the high-pass digital Type I Chebyshevfilter with a sampling frequency of 20Hz is good enoughfor the data processing of the bridge In a real applicationthe filter is sampled into 10Hz The critical frequency forpass band is 05 pass band attenuation is less than 08 dBthe critical frequency for stopband is 0025Hz stopbandattenuation is greater than 20 dB A high-pass digital TypeI Chebyshev filter is designed with the above parameters(Figure 4)

33 The Scheme for Vibration Frequencies Extraction Theflowchart for vibration frequencies extraction is summarizedin Figure 5 The real-time GPS displacement data sets areinput into the designed high-pass digital filter introduced inSection 32 to eliminate the low frequency interferences As ahigh-pass digital filter cannot be used in a real-time scenarioa GPS data accumulation counter is used to form a time seriesover a sliding window with a predefined length to considerthe different deformation situations such as deformationduring quiet period or busy period a varied window length119879 can be used that is 2000 s or 1000 s used in this paperFinally the vibration frequencies are obtained using the fastFourier transform (FFT) algorithm

4 Vibration Frequencies Extraction

41 Vibration Frequencies Extraction under Ambient Circula-tion Loading Conditions In order to evaluate the safety ofthe large structures such as long span bridges and high-rise buildings it is popular to extract the structural modalparameters such as natural frequencies mode shapes anddamping ratios from GNSS measurements by using theambient loadingsThe Forth Road Bridge was operated undera heavy traffic flow in the daytime especially at rush hour thebridge deck was expected to move under the traffic loads Inthis section we are expected to extract the bridge dynamicsunder ambient circulation loading conditions that is thetraffic flow and wind speed are not high

In the following figure data set of 2000 seconds (242001ndash244000 s) for site F was used to characterize the bridgedynamics and extract the vibration frequencies Figure 6shows the lateral deflection time series and the correspondingwind speed data during the specific period it is evident thatthe peak to peak deflection with the amplitude of about 4 cmis relatively small this is due to existence of low wind speedsthe mean wind speed is 730 kmh during the observationperiod it shows low correlation with the wind speed Wecan also see that very slow movements form a part of thelateral displacement time series while the very slow vibrationcannot indicate the natural frequencies of the bridge In ourpaper the high-pass filter introduced in Section 32 will beapplied to the original displacement time series at 10Hz

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 5

minus0015

minus001

minus0005

0

0005

001

0015La

t di

spla

cem

ent (

m)

244000 242500 243000 243500242000GPS time (s)

(a)

times10minus3

10minus1

10minus2

100

Frequency (Hz)

0

02

04

06

08

1

12

14

16

18

2

Am

plitu

de(b)

times10minus4

0

1

2

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 7 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

part 119863(119899) is the actual dynamic vibrations of the bridge and119873(119899) is the noise [16] To obtain the vibration frequenciesof the bridge low frequency deflections can be isolatedusing high-pass digital filter that can be designed accordingto the characteristics of the specific vibration signal andChebyshev high-pass digital filter is designed for the vibrationfrequencies extraction of the Forth Road Bridge in this paper

32 Design of Chebyshev High-Pass Digital Filter For Type IChebyshev filter the gain response as a function of angular

frequency 120596 of 119899th-order low-pass filter is equal to theabsolute value of the transfer function119867

119899(119895120596)

119866119899(120596) =1003816100381610038161003816119867119899 (119895120596)

1003816100381610038161003816 =1

radic1 + 12057621198792119899

(1205961205960)

(2)

where 120576 is the ripple factor 1205960is the cut-off frequency and

119879119899is a Chebyshev polynomial of 119899th order The order of

6 Shock and Vibration

Long displacementLong wind speed

Cross correlation 011

242500 243000 243500 244000242000GPS time (s)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

Win

d sp

eed

(km

h)

Figure 8 Longitudinal displacement and wind speed

a Chebyshev filter is equal to the number of reactive compo-nents needed to realize the filter using analogue electronics[21]

The ripple is often given in dB Ripple in dB =20log10

radic1 + 1205762 so that a ripple amplitude of 3 dB results from120576 = 1 The transfer function is then given by

119867119886(119904) =

1

2119899 minus 1

119899

prod

119898=1

1

(119904 minus 119904minus119901119898

) (3)

where 119904minus119901119898

are only those poles with a negative sign in frontof the real term for the poles

The bilinear transform is used to convert a transferfunction 119867

119886(119904) in the continuous-time domain to a transfer

function119867119889(119911) in the discrete-timedomain Itmaps positions

on 119895120596 axis Re[119904] = 0 in 119904-plane to the unit circle |119911| = 1in 119911-plane The bilinear transform essentially uses this first-order approximation and substitutes into the continuous-time transfer function [22]119867

119886(119904)

119904 larr9978882

119879

119911 minus 1

119911 + 1 (4)

That is

119867119889(119911) = 119867

119886(119904)1003816100381610038161003816119904=(2119879)((119911minus1)(119911+1)) = 119867119886 (

2

119879

119911 minus 1

119911 + 1) (5)

The low-pass Type I Chebyshev filter is transferred fromanalogue filter to digital filter by using the above bilineartransformation Subsequently the low-pass digital Type IChebyshev filter is transferred into high pass by the followingequation [23]

Vminus1 = minus119911minus1

+ 120572

1 + 120572119911minus1 (6)

where

120572 =cos ((120596

0+ 1205790) 2)

cos ((1205960minus 1205790) 2) (7)

Equation (5) maps 119911-plane (low pass) to V-plane (highpass) and 120596

0and 120579

0are cut-off frequencies in 119911-plane and

V-plane respectively The loads of the bridge are varyingwith different factors such as wind speeds traffic flow andtemperature variation the optimal filter parameters can bedetermined considering the real deformation By testingdifferent data sets the high-pass digital Type I Chebyshevfilter with a sampling frequency of 20Hz is good enoughfor the data processing of the bridge In a real applicationthe filter is sampled into 10Hz The critical frequency forpass band is 05 pass band attenuation is less than 08 dBthe critical frequency for stopband is 0025Hz stopbandattenuation is greater than 20 dB A high-pass digital TypeI Chebyshev filter is designed with the above parameters(Figure 4)

33 The Scheme for Vibration Frequencies Extraction Theflowchart for vibration frequencies extraction is summarizedin Figure 5 The real-time GPS displacement data sets areinput into the designed high-pass digital filter introduced inSection 32 to eliminate the low frequency interferences As ahigh-pass digital filter cannot be used in a real-time scenarioa GPS data accumulation counter is used to form a time seriesover a sliding window with a predefined length to considerthe different deformation situations such as deformationduring quiet period or busy period a varied window length119879 can be used that is 2000 s or 1000 s used in this paperFinally the vibration frequencies are obtained using the fastFourier transform (FFT) algorithm

4 Vibration Frequencies Extraction

41 Vibration Frequencies Extraction under Ambient Circula-tion Loading Conditions In order to evaluate the safety ofthe large structures such as long span bridges and high-rise buildings it is popular to extract the structural modalparameters such as natural frequencies mode shapes anddamping ratios from GNSS measurements by using theambient loadingsThe Forth Road Bridge was operated undera heavy traffic flow in the daytime especially at rush hour thebridge deck was expected to move under the traffic loads Inthis section we are expected to extract the bridge dynamicsunder ambient circulation loading conditions that is thetraffic flow and wind speed are not high

In the following figure data set of 2000 seconds (242001ndash244000 s) for site F was used to characterize the bridgedynamics and extract the vibration frequencies Figure 6shows the lateral deflection time series and the correspondingwind speed data during the specific period it is evident thatthe peak to peak deflection with the amplitude of about 4 cmis relatively small this is due to existence of low wind speedsthe mean wind speed is 730 kmh during the observationperiod it shows low correlation with the wind speed Wecan also see that very slow movements form a part of thelateral displacement time series while the very slow vibrationcannot indicate the natural frequencies of the bridge In ourpaper the high-pass filter introduced in Section 32 will beapplied to the original displacement time series at 10Hz

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

Long displacementLong wind speed

Cross correlation 011

242500 243000 243500 244000242000GPS time (s)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

Win

d sp

eed

(km

h)

Figure 8 Longitudinal displacement and wind speed

a Chebyshev filter is equal to the number of reactive compo-nents needed to realize the filter using analogue electronics[21]

The ripple is often given in dB Ripple in dB =20log10

radic1 + 1205762 so that a ripple amplitude of 3 dB results from120576 = 1 The transfer function is then given by

119867119886(119904) =

1

2119899 minus 1

119899

prod

119898=1

1

(119904 minus 119904minus119901119898

) (3)

where 119904minus119901119898

are only those poles with a negative sign in frontof the real term for the poles

The bilinear transform is used to convert a transferfunction 119867

119886(119904) in the continuous-time domain to a transfer

function119867119889(119911) in the discrete-timedomain Itmaps positions

on 119895120596 axis Re[119904] = 0 in 119904-plane to the unit circle |119911| = 1in 119911-plane The bilinear transform essentially uses this first-order approximation and substitutes into the continuous-time transfer function [22]119867

119886(119904)

119904 larr9978882

119879

119911 minus 1

119911 + 1 (4)

That is

119867119889(119911) = 119867

119886(119904)1003816100381610038161003816119904=(2119879)((119911minus1)(119911+1)) = 119867119886 (

2

119879

119911 minus 1

119911 + 1) (5)

The low-pass Type I Chebyshev filter is transferred fromanalogue filter to digital filter by using the above bilineartransformation Subsequently the low-pass digital Type IChebyshev filter is transferred into high pass by the followingequation [23]

Vminus1 = minus119911minus1

+ 120572

1 + 120572119911minus1 (6)

where

120572 =cos ((120596

0+ 1205790) 2)

cos ((1205960minus 1205790) 2) (7)

Equation (5) maps 119911-plane (low pass) to V-plane (highpass) and 120596

0and 120579

0are cut-off frequencies in 119911-plane and

V-plane respectively The loads of the bridge are varyingwith different factors such as wind speeds traffic flow andtemperature variation the optimal filter parameters can bedetermined considering the real deformation By testingdifferent data sets the high-pass digital Type I Chebyshevfilter with a sampling frequency of 20Hz is good enoughfor the data processing of the bridge In a real applicationthe filter is sampled into 10Hz The critical frequency forpass band is 05 pass band attenuation is less than 08 dBthe critical frequency for stopband is 0025Hz stopbandattenuation is greater than 20 dB A high-pass digital TypeI Chebyshev filter is designed with the above parameters(Figure 4)

33 The Scheme for Vibration Frequencies Extraction Theflowchart for vibration frequencies extraction is summarizedin Figure 5 The real-time GPS displacement data sets areinput into the designed high-pass digital filter introduced inSection 32 to eliminate the low frequency interferences As ahigh-pass digital filter cannot be used in a real-time scenarioa GPS data accumulation counter is used to form a time seriesover a sliding window with a predefined length to considerthe different deformation situations such as deformationduring quiet period or busy period a varied window length119879 can be used that is 2000 s or 1000 s used in this paperFinally the vibration frequencies are obtained using the fastFourier transform (FFT) algorithm

4 Vibration Frequencies Extraction

41 Vibration Frequencies Extraction under Ambient Circula-tion Loading Conditions In order to evaluate the safety ofthe large structures such as long span bridges and high-rise buildings it is popular to extract the structural modalparameters such as natural frequencies mode shapes anddamping ratios from GNSS measurements by using theambient loadingsThe Forth Road Bridge was operated undera heavy traffic flow in the daytime especially at rush hour thebridge deck was expected to move under the traffic loads Inthis section we are expected to extract the bridge dynamicsunder ambient circulation loading conditions that is thetraffic flow and wind speed are not high

In the following figure data set of 2000 seconds (242001ndash244000 s) for site F was used to characterize the bridgedynamics and extract the vibration frequencies Figure 6shows the lateral deflection time series and the correspondingwind speed data during the specific period it is evident thatthe peak to peak deflection with the amplitude of about 4 cmis relatively small this is due to existence of low wind speedsthe mean wind speed is 730 kmh during the observationperiod it shows low correlation with the wind speed Wecan also see that very slow movements form a part of thelateral displacement time series while the very slow vibrationcannot indicate the natural frequencies of the bridge In ourpaper the high-pass filter introduced in Section 32 will beapplied to the original displacement time series at 10Hz

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001Lo

ng d

ispla

cem

ent (

m)

242500 243000 243500 244000 242000GPS time (s)

(a)

times10minus4

0

1

2

3

4

Am

plitu

de

100

10minus2

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 9Thefiltered longitudinal displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c)

firstly then the output of the high-pass filtered data is usedto obtain the vibration frequencies of the bridge The filteredlateral movements and the corresponding frequencies aredemonstrated in Figure 7 it can be seen that the amplitude ofthe dynamic displacements is small a low frequency responsepeaked at 0067Hz is significant in the frequency spectrawhich is mainly induced by the ambient wind loadings fivehigher dominant frequencies with smaller amplitude can alsobe extracted from the spectra the extracted frequencies are

listed in Table 1 and this correlates well with our experiencefor such long span bridge

The corresponding results for longitudinal deflections aredemonstrated in Figure 8 as can be seen from the figurethe lateral response is constrained due to the stiffness ofthe bridge deck and the bridge is not highly vulnerableto longitudinal motions as can be validated from the lowcorrelation between the longitudinal response and the windspeed Figure 9 gives the corresponding natural frequencies

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

minus008

minus006

minus004

minus002

0

002

004

006

008

01H

eigh

t disp

lace

men

t (m

)

242500 243000 243500 244000242000GPS time (s)

0

0002

0004

0006

0008

001

Am

plitu

de

10minus1

Frequency (Hz)

Figure 10 The filtered height displacements and corresponding frequencies

Table 1 Vibration frequencies extracted from lateral GPS measurements (119883 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0067 0073 0105 0118 0269 0345 0160 730

Strong wind (abrupt wind speed change) 0069 0077 0106 0110 0267 0345 mdash 52490068 0071 0105 0110 0270 0344 0097 0101 5583

Two 40 t lorries passing 0064 0073 0103 mdash 0268 mdash 0132 0147 4475

0

50

100

150

Win

d sp

eed

(km

h)

250000 300000 350000200000 400000 GPS time (s)

0

100

200

300

400

Win

d di

rect

ion

(deg

)

250000200000 350000 400000 300000GPS time (s)

Figure 11 The wind speed and direction during the observationperiod

extract from the filtered longitudinal movements it can beseen that the longitudinal displacements are noisier thanlateral displacements the amplitude of the local frequencypeak is not significantly large thus the frequencies extractedfrom longitudinal movements are less accurate comparedto the results extracted from lateral movements and higher

frequencies above 02Hz cannot be detected from the filteredlongitudinal displacement time series

The filtered height deflections and the correspondingfrequencies are shown in Figure 10 and it can be seen thatthe frequency response is significant at 0103Hz which isbelieved to be the natural frequency of the bridge theamplitude of the frequency response at higher frequencyband is obviously smaller than the first natural frequencyresponse It can be concluded that the vibration frequenciesare successfully detected from the high-pass filtered displace-ment time series that is the frequencies extracted from thedisplacement time series in different direction are varied andthis can be explained by the fact that deflections in differentdirection are actually induced by different loading effects

42 Vibration Frequencies Extraction during Wind EffectDuring the observation period the anemometer was used torecord the wind speed and direction at 30 s sampling interval(Figure 11) As can be seen in Figure 11 the Forth RoadBridge was subject to high wind loadings during the wholeobservation session the maximum wind speed exceeded100 kmh this will cause a large movement for the bridgedeck and bridge tower On the first day the wind directionwas almost perpendicular to the main axis of the bridge(Figure 12) while the wind direction was changed on thesecond day and the corresponding wind speed was alsoincreased

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

0

30

60

90 (E)

120

150180

210

240

300

330

(W) 270

Bridge deck

(S)

(N)

Figure 12 The wind direction variation during the observation period

Win

d sp

eed

Win

d sp

eed

minus100

minus50

050

100

(long

km

h)

250000 300000 350000 400000 200000GPS time (s)

250000 300000 350000 400000 200000

250000 300000 350000 400000 200000

minus50

0

50

100

(lat

kmh

)

005

115

Lat

defle

ctio

n (m

)

Figure 13 The wind speed resolved to BCS and the correspondingdeflection

Due to the stiffness of bridge the longitudinalmovementsof the bridge deck are small while the lateral movements aresubject to wind actionThe original wind speed data was firstresolved to BCS for further analysis Figure 13 shows windspeed in BCS and the corresponding lateral deflections it canbe seen that the lateralmovements have good correlationwithhigh wind speed the sudden change of wind direction causesthe peak vibration of the lateral deflection once the windspeed keeps stable at a higher speed the deflection becomessmall as the heavy body of the bridge will be dragged downby the force of gravity and the action of wind speed in lateraland longitudinal direction is cross-conditioning

Wind speed decreasing Wind speed increasing

Cross correlation 081

minus05

0

05

1

Lat

(m)

minus50

0

50

100

Win

d sp

eed

(km

h)

330000325000 335000 340000320000315000GPS time (s)

Lat wind speedMean lat wind speed

Lat displacementMean lat displacement

Figure 14 Lateral displacement and wind speed during the abruptwind speed changing period

In our paper in order to characterize the interactionbetween the wind speed and deflection we provide two windspeed changing situations for frequencies extraction usingGPS namely

(a) wind speed decreasing period 317001ndash327000 s(b) wind speed increasing period 327001ndash337000 s

Figure 14 illustrates lateral deflections and the corre-sponding wind speed during the selected wind speed abruptchanging period It can be seen that there is high correlationbetween the deflection and wind speed (081 as shown in thefigure) where the mean wind speed exceeds 50 kmh and

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

325000 326000 326500325500 327000 GPS time (s)

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 15 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed decreasing period

the strongwind causes largemovement along lateral directionfor the bridge deck

The lateral deflections contain very slow movementswhich are beyond the natural frequency band the bilinearChebyshev high-pass filter was applied to the original dis-placement time series The filtered lateral displacements andcorresponding vibration frequencies under ambient windloadings are shown in Figures 15 and 16 the extracted localvibration frequencies less than 5Hz using GPS displacement

under two different wind loading conditions show similarcharacteristics above 01 Hz frequency band this indicatesthat no significant changes occur in the structural charac-teristics while the frequency response extracted from case(b) contains a local peak at 0097Hz which is mainly causedby wind conditions The low frequency colour noise is stillevident in the filtered displacement time series thus theidentification of the dominant frequencies becomes difficultThe amplitude of the high frequency response at 044Hz

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

minus003

minus002

minus001

0

001

002

003La

t di

spla

cem

ent (

m)

329000 328000 328500327500327000GPS time (s)

(a)

times10minus3

0

05

1

15

2

25

3

Am

plitu

de

100

10minus1

Frequency (Hz)

(b)

times10minus3

0

01

02

03

04

05

06

07

08

09

1

Am

plitu

de

10minus1

Frequency (Hz)

(c)

Figure 16 The filtered lateral displacements (a) corresponding vibration frequency ((b) full-scale band) and zoom-in of high frequencycomponent (c) during the wind speed increasing period

during the wind speed increasing period is larger than thatof the response occurring during the wind speed decreasingperiod

The longitudinal displacement measurements during thespecific observation period are demonstrated in Figure 17it can be noted that the wind speed data is noisy andthe correlation between the longitudinal response and thewind data is low The excitation of longitudinal response isactually a combination of wind loadings traffic loadings and

thermal effects The filtered results are shown in Figures 18and 19 the peak amplitude of the vibration is quite smallof the order of plusmn5mm the frequency characteristics arequite different from that of lateral response the detectedvibration frequency is lower than 03Hz and the dom-inant frequency response is significant at 0129 (0126Hzfor wind increasing period) 0134 and 0151Hz the lowfrequency noise is still evident in the filtered displacementtime series

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

Long displacementLong wind speed

Cross correlation 014

minus01

minus005

0

005

01

Long

(m

)320000 325000 330000 335000 340000315000

GPS time (s)

minus20

0

20

40

60

Win

d sp

eed

(km

h)

Figure 17 Longitudinal displacement and wind speed

325500325000 326500326000 327000GPS time (s)

minus001

minus0008

minus0006

minus0004

minus0002

0

0002

0004

0006

0008

001

Long

disp

lace

men

t (m

)

times10minus4

0

1

2

3

4

5A

mpl

itude

100

10minus1

Frequency (Hz)

Figure 18 The filtered longitudinal displacements and corresponding frequencies during the wind speed decreasing period

The corresponding filtered height response is shown inFigures 20 and 21 compared to the horizontal response theamplitude of the height dynamic displacement is obviouslylarger which is due to existence of traffic loadings As can beseen from the frequency spectrum a significant amplitudepeak at 0102Hz is detected using the height displacementtime series while a slightly different frequency at 0104Hz isobserved for the wind speed increasing period two higherfrequency peaks can be detected for both wind loadingconditions The vibration frequencies extracted from heightdisplacement time series seem to be clearer than the frequen-cies extracted using horizontal displacement time series thisdemonstrates the superiority of using height deflections formonitoring the frequency response

43 Vibration Frequencies Extraction of the Lorry LoadingThe Forth Road Bridge has experienced increased traffic

loadings since the opening of the bridge and the heavy trafficloadings play an important role in the bridge deformationespecially for the height deflections During the second nighta specific trail with two 40 t lorries running on the bridge wascarried out to evaluate the pattern of deflection the bridgewas closed off to other traffic during the trial in addition thelorries travelled at a low speed manner the running speedwas about 32 kmh The travelling period used for analysis inthis paper was described as follows

(a) One lorry ran from north to south(b) One lorry ran from south tomidspan on the west side

and stopped and then the other lorry moved north tosouth

The data set duration is 1000 s (349705ndash350704 s) theexperienced wind speed had subsided slightly during theobservation periodThe absolute deflections for site F during

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

minus0015

minus001

minus0005

0

0005

001

0015

Long

disp

lace

men

t (m

)

327000 328000327500 329000328500GPS time (s)

0

1

2

3

4

5

Am

plitu

de

100

10minus1

Frequency (Hz)

times10minus4

Figure 19 The filtered longitudinal displacements and corresponding frequencies during the wind speed increasing period

325500 326000 326500 327000325000GPS time (s)

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

0

0005

001

0015

002

0025

003

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 20 The filtered height displacements and corresponding frequencies during the wind speed decreasing period

the lorries passing were illustrated in Figure 22 it can be seenthat the movements in different direction are deflected bydifferent magnitudes among which the height componentexperienced the largest deflections of the order of plusmn03mThe bridge experienced downward deflections as the lorrytravelled approaching the midspan of bridge and upwardmovements were observed when the lorry moved awaythis is due to existence of the elastic suspension cablewhich pulled up the bridge main span The GPS measureddeflectionsmatchwell with that of FEMpredicted results andoccurrence of such bridge deflection can be well explainedby the lorriesrsquo mass It should be noted that the patterns of

the lateralmovements do not completely coincidewith heightmovements actually the lateral movements are partiallyinduced by the ambient wind loadings

To extract the vibration frequencies during the lorrypassing period the original displacement time series wasfirst filtered using the bilinear Chebyshev high-pass filterthe resulting dynamic lateral deflections and extracted fre-quencies are illustrated in Figure 23 the amplitude of thedynamic displacements exceeds 2 cm it can be seen thatthe high frequency response at 0345Hz is not significantfrom frequency spectrum while the frequency response at0064 and 0073Hz is still the most significant Compared to

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Shock and Vibration

minus01

minus005

0

005

01

015

Hei

ght d

ispla

cem

ent (

m)

327000 328000327500 328500 329000GPS time (s)

0

0005

001

0015

002

0025

Am

plitu

de

100

10minus1

Frequency (Hz)

Figure 21 The filtered height displacements and corresponding frequencies during the wind speed increasing period

the deformation induced by the low wind loadings thefrequency extraction under high wind loadings becomesclearer

The filtered longitudinal displacements and extractedfrequencies are demonstrated in Figure 24 it can be seen thatthe amplitude of the dynamic displacements is below 1 cmand the dynamic response is actually not highly affected bythe lorry loading the frequency characteristic of the responseis similar to the response under ambient circulation loadingexpect one suspected high frequency at 0332Hz detectedfrom the displacement time series indeed the high frequencyresponse is vanished due to the existence of high frequencynoise

The corresponding height dynamic displacements andthe extracted frequencies are shown in Figure 25 the ampli-tude of the dynamic deflections exceeds 01m the mostsignificant frequency response is still at 0103Hz it seems thatno significant frequency deviation occurs from the frequencyspectrum

44 Extracted Frequencies Comparisons As previously anal-ysed we have successfully extracted the vibration frequenciesof the bridge under different loading conditions that isthe ambient circulation loading strong wind speed suddenchanging period and the specific trial with two 40 t lorriespassing the bridge The results of the extracted frequenciesare listed in Tables 1ndash3 By comparing the results we cansee that the vibration frequencies extracted from the GPSmeasurements in different direction are varied greatly fromeach other Due to the bridge deck stiffness of the bridge deckthe movement along the bridge main axis is small and lowfrequency noise can be obviously observed in the longitudi-nal displacement time series which makes the frequenciesextraction more difficult using the peak-picking approachand the extracted frequencies show different characteristic

By making a detailed comparison of Tables 1 and 3 wecan find that two common frequencies can be extracted fromboth lateral displacement time series and height displacementtime series though the dynamics are induced by differentloading effects that is 0105 and 0269Hz (slightly differentunder different ambient loading conditions) so it may bededuced that the two frequencies are the natural frequenciesof the bridge While the other computed frequencies maynot indicate the modal characteristics they mainly indicateexcitation frequencies these frequencies are significant onlyif they approachmodal frequencies withmuch energyOn theother hand it should be noted that the extracted frequenciesactually varied under different loadings this will greatlybenefit the online damage identification process because thefrequency response is an indicator of structural behaviourWe can also find that height frequency responses are relativelystable for they are mainly affected by the traffic loadings andthermal effects

5 Conclusions

This paper investigated a GPS deformation trial carried outon the Forth Road Bridge in Scotland It shows that GPS cancapture the absolute 3D deflections of the bridge accuratelyat a 10Hz sampling rate The results have shown that lateralmovements highly correlate with the ambient wind loadingas the wind speed is high while the height deflections aremainly caused by the traffic loading and thermal effect themovement along the bridge main axis is small due to thestiffness of the bridge deck

To demonstrate the frequency response under differentloadings three different ambient loading conditions areconsidered namely the ambient circulation loading strongwind abrupt speed changing period and the specific trialwith two 40 t lorries passing the bridge A bilinear Chebyshev

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 15

349800 350200 350400 350600350000GPS time (s)

minus008

minus006

minus004

minus002

0

002

004

006

008

01

Lat

(m)

(a)

minus003

minus002

minus001

0

001

002

003

Long

(m

)

349800 350200 350400 350600350000GPS time (s)

(b)

minus03

minus02

minus01

0

01

02

Hei

ght (

m)

349800 350200 350400 350600350000GPS time (s)

Two 40 t lorries passing

(c)

Figure 22 Absolute deflections of bridge site F during the two 40 t lorries passing

Table 2 Vibration frequencies extracted from longitudinal GPS measurements (119884 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed(kmh)Common frequencies Distinct frequencies

Ambient circulation loading 0095 0105 mdash 0136 0149 0108 0117 0161 3196

Strong wind (abrupt wind speed change) 0091 mdash 0129 0134 0151 0184 0262 1221mdash mdash 0126 0134 0151 0216 1646

Two 40 t lorries passing 0106 0129 0131 0150 0172 0332 1334

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

16 Shock and Vibration

350600350400350200350000349800GPS time (s)

minus003

minus002

minus001

0

001

002

003

Lat

disp

lace

men

t (m

)

0

05

1

15

2

25

3

35

4

Am

plitu

de

times10minus3

100

10minus1

Frequency (Hz)

Figure 23 The filtered lateral displacements and corresponding frequencies

350000 350200 350400 350600349800GPS time (s)

times10minus4

0

1

2

3

4

5

6

7

8

Am

plitu

de

100

10minus1

Frequency (Hz)

minus001

minus0005

0

0005

001

Long

disp

lace

men

t (m

)

Figure 24 The filtered longitudinal displacements and corresponding frequencies

Table 3 Vibration frequencies extracted from height GPS measurements (119880 direction of BCS)

Situations Extracted frequencies (Hz) Mean wind speed (kmh)Ambient circulation loading 0092 0103 0207 0270 mdash

Strong wind (abrupt wind speed change) 0095 0102 0205 0268 mdash0098 0104 0204 0270 mdash

Two 40 t lorries passing 0096 0103 0202 0268 mdash

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 17

minus01

minus005

0

005

01

015H

eigh

t disp

lace

men

t (m

)

350000 350200 350400 350600349800GPS time (s)

0

0005

001

0015

002

0025

003

Am

plitu

de

10minus1

100

Frequency (Hz)

Figure 25 The filtered height displacements and corresponding frequencies

high-pass filter was presented and applied to the originaldisplacement time series to remove the very slowmovementswhich do not locate in the structural natural frequency bandThe FFT algorithm was applied to the filtered displacementtime series and the vibration frequencies are extractedusing the peak-picking approach The results show that thefrequency responses in different directions vary greatly witheach other and the frequency responses at 0105 and 0269Hzextracted from lateral displacement time series correlate wellwith the data using height displacement time series thenatural frequencies change slightly under different ambientloadings The approach introduced in this paper can be wellapplied for the future online bridgemonitoring the structuraldeterioration and failure will bemonitored using the real GPSdata in real time and the frequency response becomes thebasis to evaluate the behaviour of the bridge

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thedata acquisitionwas sponsored by the Forth Road BridgeThe other colleagues of the University of Nottingham areacknowledged This work was partially supported by theFundamental Research Funds for the Central Universities(no 2014ZDPY15) the Program for New Century ExcellentTalents in University (no NCET-13-1019) a project fundedby the Priority Academic Program Development of JiangsuHigher Education Institutions and the Cooperative Innova-tion Centre of Jiangsu Province

References

[1] M LeachMHyzak and SHoroschak ldquoValidation and analysisof results from a bridge motion monitoring experimentrdquo inProceedings of the 49th Annual Meeting of the Institute ofNavigation Future Global Navigation and Guidance pp 519ndash527 Cambridge Mass USA June 1993

[2] J W Lovse W F Teskey G Lachapelle and M E CannonldquoDynamic deformation monitoring of tall structure using GPStechnologyrdquo Journal of Surveying Engineering vol 121 no 1 pp35ndash40 1995

[3] A Wieser and F Brunner ldquoAnalysis of bridge deformationsusing continuous GPSmeasurementsrdquo in Proceedings of the 2ndConference of Engineering Surveying (INGEO rsquo02) pp 45ndash52Bratislava Slovakia November 2002

[4] G W Roberts E Cosser X Meng and A Dodson ldquoHighfrequency deflection monitoring of bridges by GPSrdquo Journal ofGlobal Positioning Systems vol 3 no 1-2 pp 226ndash231 2004

[5] X Meng G W Roberts A H Dodson E Cosser J Barnesand C Rizos ldquoImpact of GPS satellite and pseudolite geometryon structural deformation monitoring analytical and empiricalstudiesrdquo Journal of Geodesy vol 77 no 12 pp 809ndash822 2004

[6] A P C Larocca R E Schaal M C Santos and R B LangleyldquoMonitoring the deflection of the pierre-laporte suspensionbridge with the phase residual methodrdquo in Proceedings of the18th International Technical Meeting of the Satellite Division ofthe Institute of Navigation (IONGNSS rsquo05) pp 2023ndash2028 LongBeach Calif USA September 2005

[7] W-S Chan Y-L Xu X-L Ding Y-L Xiong and W-J DaildquoAssessment of dynamicmeasurement accuracy of GPS in threedirectionsrdquo Journal of Surveying Engineering vol 132 no 3 pp108ndash117 2006

[8] A Nickitopoulou K Protopsalti and S Stiros ldquoMonitor-ing dynamic and quasi-static deformations of large flexibleengineering structures with GPS accuracy limitations andpromisesrdquo Engineering Structures vol 28 no 10 pp 1471ndash14822006

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

18 Shock and Vibration

[9] X Meng A H Dodson and G W Roberts ldquoDetecting bridgedynamics with GPS and triaxial accelerometersrdquo EngineeringStructures vol 29 no 11 pp 3178ndash3184 2007

[10] C Watson T Watson and R Coleman ldquoStructural monitoringof cable-stayed bridge analysis of GPS versus modeled deflec-tionsrdquo Journal of Surveying Engineering vol 133 no 1 pp 23ndash282007

[11] T H Yi H N Li and M Gu ldquoFull-scale measurementsof dynamic response of suspension bridge subjected toenvironmental loads using GPS technologyrdquo Science China-Technological Sciences vol 53 no 2 pp 469ndash479 2010

[12] F Moschas and S Stiros ldquoMeasurement of the dynamicdisplacements and of the modal frequencies of a short-spanpedestrian bridge usingGPS and an accelerometerrdquo EngineeringStructures vol 33 no 1 pp 10ndash17 2011

[13] P Psimoulis S Pytharouli D Karambalis and S Stiros ldquoPoten-tial of Global Positioning System (GPS) to measure frequenciesof oscillations of engineering structuresrdquo Journal of Sound andVibration vol 318 no 3 pp 606ndash623 2008

[14] P A Psimoulis and S C Stiros ldquoA supervised learningcomputer-based algorithm to derive the amplitude of oscilla-tions of structures using noisy GPS and Robotic Theodolites(RTS) recordsrdquoComputers amp Structures vol 92-93 pp 337ndash3482012

[15] S B Im S Hurlebaus and Y J Kang ldquoSummary review ofGPS technology for structural health monitoringrdquo Journal ofStructural Engineering vol 139 no 10 pp 1653ndash1664 2013

[16] J Y Yu X L Meng X D Shao B F Yan and L Yang ldquoIden-tification of dynamic displacements and modal frequenciesof a medium-span suspension bridge using multimode GNSSprocessingrdquo Engineering Structures vol 81 pp 432ndash443 2014

[17] A Dodson X Meng and G Roberts ldquoAdaptive method formultipath mitigation and its applications for structural deflec-tionmonitoringrdquo in Proceedings of the International Symposiumon Kinematic Systems in Geodesy Geomatics and Navigation(KIS rsquo01) pp 5ndash8 Banff Canada June 2001

[18] GW Roberts X Meng and A H Dodson ldquoUsing adaptive fil-tering to detect multipath and cycle slips in GPSaccelerometerbridge deflection monitoring datardquo in Proceedings of the 22ndInternational Congress of the FIG pp 19ndash26 Washington DCUSA April 2002

[19] F Moschas and S Stiros ldquoDynamic multipath in structuralbridge monitoring an experimental approachrdquo GPS Solutionsvol 18 no 2 pp 209ndash218 2014

[20] G W Roberts C J Brown X Meng O Ogundipe C Atkinsand B Colford ldquoDeflection and frequency monitoring of theForth Road Bridge Scotland by GPSrdquo Bridge Engineering vol165 no 2 pp 105ndash123 2012

[21] B A Shenoi Introduction to Digital Signal Processing and FilterDesign John Wiley amp Sons 2005

[22] J H Lodge and M M Fahmy ldquoThe bilinear transformationof two-dimensional state-space systemsrdquo IEEE Transactions onAcoustics Speech and Signal Processing vol 30 no 3 pp 500ndash502 1982

[23] T W Parks and J H McClellan ldquoChebyshev approximation fornonrecursive digital filters with linear phaserdquo IEEETransactionson Circuit Theory vol 19 no 2 pp 189ndash194 1972

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of