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LONG-TERM MONITORING OF DYNAMIC

RESPONSE OF A TALL BUILDING FOR PERFORMANCE

EVALUATION AND LOADING CHARACTERISATION

James Brownjohn University of Sheffield UK

[email protected]

Abstract

Dynamic response of a 280m building in Singapore has been tracked during construction from

1994 to 1995 and since then during normal operation. Initial measurements were of modal

parameters for FE model updating and the system has developed into a monitoring system for

characterising the load and response mechanisms via the validated FE model. The decade of

monitoring has enveloped the era of rapid developments in output-only system identification and

these are explained in the context of application in the building study. The nature of response to

different dynamic loads is presented together with the long term drift in modal properties.

1 Structural health and performance monitoringStructural health monitoring (SHM) for civil infrastructure includes the systems not only for

detection/diagnosis of progressive or sudden damage, but also for performance monitoring to

identify load/response relationships either as a baseline for the structure itself or for calibration of

a loading model or code. The words health and performance are both used in defining SHM

systems and are synonymous, and a major activity for civil infrastructure monitoring is geared

towards a long term evaluation of what is normal structural performance or health.

The monitoring exercise reported in this paper, conducted over the period from late 1993 to 2004,

began as manual readings of strain gauges and has evolved into a system to provide information

about the various forms of environmental loading (wind, tremors and temperature) via measurable

responses (stress, strain, acceleration and displacement). Along the way it has been used as a toolto study a variety of monitoring technologies including operational modal analysis.

As well as manual monitoring of embedded static gauges during construction, natural frequencies

of the building were tracked as construction progressed. A modal survey of the completed but

empty building used the conventional frequency domain identification tools of the time and was

followed by installation of a bi-axial acceleration recorder which developed into a complete

system for recording of wind speed signals together with accelerations from roof and basement

levels. The most recent development has been the installation and extended evaluation of a dual-

rover GPS system integrated with the existing monitoring systems and the ambient response data

have been revisited using more sophisticated analysis tools.

2 Building configurationA full description of this 280m Republic Plaza office tower is provided by the architect [1]. Fig. 1shows a perspective view of the building. The octagonal reinforced concrete (RC) central core wall

maintains a plan area approximately 22m square for almost the full height of the building and the


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perimeter of the building comprises eight large and eight small steel tube columns filled with

concrete up to level 49 and marking out a square of side 45m at ground level. Plan area reduces

with height, tapering sections bring first the large columns then the small columns back towards

the core wall. Double-storey mechanical equipment (M&E) floors are located above the tapering

sections where outriggers are installed to enhance the rigidity of the building frame under lateral

loads. A horizontal steel framing system is pinned at the core and rigidly fixed at the columns and

supports a Bondek-formed office slab. Caisson founds, down to 60m ensure rigid base fixity.

2.1 Construction sequenceFoundation construction began in late 1991 and work on the superstructure began in early 1993

with installation of first static instruments by Shimizu in the core wall at level 18, followed by first

readings on 30th October 1993. The main structural system was completed in March 1995 and

completion of the curtain wall took a further 80 days. Water storage tanks were installed at M&E

floors (rooftop and levels 28, 47 and 65) in mid June 1995 totalling 1.5% of the total structural

dead load and interior finishing works and installations by tenants continued even up to the end of

1996 including the lavish fitting out of the executive club at levels 62 and 63.

3 Tracking natural frequencies during constructionBy mid June 1994 a portable acceleration recorder was available and was used to record horizontalaccelerations in orthogonal symmetry axes (labelled A and B) aligned with the low-rise and high-

rise lift lobbies respectively. Pairs of first mode frequency values were obtained from SDOF curve

fitting to auto-spectra of the signals regularly up to the end of 1995 when a formal modal survey

[2] was undertaken, between 20th November and 1st December 1995.

The variation of period for fundamental modes in each direction i.e. A1 and B1 during

construction is shown in Fig. 2 where it is clear that while B develops into the stiffer direction,

frequencies were originally identical. The difference would be due to the changing arrangement of

the core wall as higher levels feature a large opening previously enclosing low-rise lift shafts.

From the final stages of construction there was no evidence that curtain wall affected either

stiffness or damping characteristics of the structure.

4 Ambient vibration testing [2]: 1980s technologyAs this conference demonstrates, the last decade has seen a revolution in ambient vibration testing

(AVT) or operational modal analysis (OMA). Until then customary AVT (as it was then known)

used peak-picking, which works on the frequency domain ratio of response signals through

consideration of a common relationship with an unknown input. Specifically, for a specific

(angular) frequency the ratio of acceleration response ( )jX at levelj to force input ( )kP at

level kon a building is defined as the inertance form of the frequency response function (FRF):

( ) ( ) ( )ij j k H X P . 1)

By considering the equations of motion it can be shown [3] that

( )1

Nr r

jk r j k

r

H H =

= 2)

where


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( )2

2 2 2r

r r r

Hi

=

+ +3)

is the dynamic amplification factor and r rj k is the modal constant containing information about

mode shapes r and mass distribution for one ofNpossible modes rhaving natural frequency and

damping ratio ,r r .

For AVT of a building it is assumed that unmeasured forces ( )kP are applied simultaneously at

all m possible levels k, so the response at level j is

( ) ( ) ( )1

Nr r

j k r j k

k r

X P H =

= = ( ) ( )1

Nr r

k r j k

k r

P H =

. 4)

Also it has to be assumed that the input force is not a function of frequency but has a spectrum

with constant (stationary) mean value at each frequency. This is hardly true for wind but,

compared to the fast changing ( )rH , the auto spectral density of wind force per storey is only a

weak function of frequency. The net effect of the distributed load is obtained by summing over the

levels k while taking into account the lack of coherence between loading at different levels,

leading to an approximate distributed effect C and response depending on levelj i.e.

( ) ( )1

nr

j r j

r

X C H =

= . 5)

The spectral approach to predicting dynamic response due to wind is described in detail in other

references [4]. For excitation by ground motion similar analysis can be used except that the

effective forces at each storey are coherent and proportional to ground motion.

From measured time series of acceleration response ( )jx t , the scalar discrete Fourier transforms

(FFTs) are formed into a vector of complex FFTs written here as ( ){ }X to remind that is it avector of functions in the frequency domain. From all combinations of products of these vectors is

created a three-dimensional matrix of cross-spectral density functions. In practice an average is

usually made over a recording divided into Mframes of 2n samples using the Welch method [5],

where windowing and overlapping may be applied. Hence

( ) ( ){ } ( ){ }( )H

XX E X X =S 6)

is the experimentally derived matrix of cross-spectral densities containing at row p and column q

the complex scalar cross-spectral density:

( ) ( )( )*qp p qS E X X = 7)

The area under the single-sided CSD or ASD plots provide mean square values of acceleration and

the square root of ASD is commonly used, having units acceleration/Hz1/2

.

4.1 Peak-picking and operating deflection shapes (ODS)Usually the mode shape is estimated by varying p while keeping a reference q constant and

reading off the values down a column of the CSD matrix at a resonant frequency identified as a


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peak in the spectrum. These values contain phase and amplitude information normalised to a value

of 1 with angle zero by dividing by the ASD of the chosen reference signal. This is called 'peak-

picking' and is evaluated from the ratio of CSD between positionsp and q to ASD at position q:

( )

( )

( ) ( )( )( ) ( )( )

*

*

p qqp

qq q q

E X X S

S E X X

=

=

( )( )

o

o

p r

q r

XE

X

8)

At a specific natural frequencyor

the contribution of mode ro to response dominates over all the

other modes hence:

( )( )

o

o

p r

q r

XE

X

( )

( )

1

1

o

o

Nr

r r p

r

Nr

r r q

r

C H

E

C H

=

=

=

o

o

o

o

r

r p

r

r q

CH

CH

. 9)

Hence as all butor

H are negligible ator

,

( )

( )

o

o

qp r

qq r

S

S

o

o

r

p

r

q

. 10)

This recovers the approximate ratio of modal ordinates between two locations. In fact it provides

the operating deflection shape (ODS), which is an approximation to mode shape. Further, the

ASD ( )qqS around the resonance can be used for estimation of frequency and damping ratio

through curve-fitting. Spectral estimates in ASDs and CSDs are subject to variance errors in

inverse proportion to the number of averages used in the Welch procedure and at least part of these

errors carry over to mode shapes through equation 10). Damping, and to a lesser extent frequency,

are subject to bias and variance errors according to parameters such as type of window used,

number of averages and width of the resonant peak in relation to frequency resolution. For civil

structures with low damping, very long periods of measurement are required and it is (or needs to

be) assumed that the loading spectrum is Gaussian and the modal parameters are stationary

(constant) for the duration

4.2 1995 Ambient vibration test procedureThe procedure for the AVS data collection used in the 1995 test used a reference accelerometer q

at the same location (one corner of the highest -65th-level close to the core wall) and while moving

three rover accelerometers p to different locations throughout the height of the building and

applying equation (10) at recurrent spectral peaks. Signals were sampled, at 15Hz, for as long as

possible while keeping accelerometers aligned in one direction, before rotating them all by 90,measuring again, then shifting the three accelerometers to new floors. The sequence was repeated

over several days to map modal ordinates throughout the whole building in A and B directions

with respect to a vertical line through the height of the building at the corner of the core wall.

As the measurements progressed it became clear that modes did not divide exactly into expected A

and B directions, rather that the principal axes of movement were rotated unknown angles with

respect to these obvious symmetry axes. Also, there was evidence of significant torsional responseeven in the translational modes, so a set of four measurements was made, one at each of floors 18,


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32, 46 and 65 referenced to one of the locations in the vertical roving of accelerometers, to identify

the unknown angles and mode shapes in horizontal planes using the set of four accelerometers

arrayed at four corners.

The resulting pieces of mode shapes have been glued together to generate a complete set of

twelve modes numbered A1 through A4 for modes closest to the A direction, B1 through B4 for

modes aligned closest to B direction and T1 through T4 for modes of almost pure torsion. Modes

A1, A2, A3 and T1 are illustrated in Fig. 3 together with a typical non-dimensional auto-spectrumof acceleration.

5 Finite element model updatingUsing the experimental modal parameters identified in the 1995 AVT, a complete set of drawings

and information from the contactor concerning mass loadings, a thorough study of the building

structure was been undertaken via a model updating exercise [6]. The procedure used a

combination of the SAP2000 code and an expert system shell to search a progression of model

variants for a reasonable match between experimental and analytical natural frequencies and mode

shapes. Further validation has since been provided by comparing simulated and measured response

to measured ground motions [7].

6 Acceleration recording systemFrom October 1996 to the present, acceleration signals have been recorded and analysed with a

few breaks due to data download, hardware faults or maintenance. In the initial installation, two

accelerometers were placed in a telecoms riser cabinet with the acquisition system used for the

modal survey and left recording continuously for two weeks as part of the learning experience to

track the levels of normal response. During that period the response caused by a strong (Ms6.3)

and relatively close (epicentral distance 700km) earthquake that occurred in Indonesia in October

1996 was recorded, being the first time series recording of building structural response in

Singapore.

From early 1997, the acceleration recording system component of the monitoring system

comprised two pairs of accelerometers, attached to the corner of the core wall at basement level

(B1) and top M&E floor (65) and connected by signal cable to the four channel signal conditioner

comprising power supply, low pass filter, accelerometer offset adjust and amplification used in theAVT. The accelerometers are Quartz-flex QA-700 servo accelerometers that have noise threshold

of around 1 micro-g, can be run noise-free on very long cables and generate current proportional to

total (static+dynamic) acceleration that is dropped across a user supplied load resistor to provide

adjustable gain. Acceleration signals have been sampled in frames of 4096 samples acquired either

at 7.5Hz (before 11/2001) or 8Hz (after 11/2001). A triggering system has been evolved to capture

the few % of records that have strong or interesting response, for example a one-off strong signal

occurring during a quiet period (at night) indicating an earthquake.

The 1995 AVT was too short and signal to noise rations too low to identify reliably building

response at the very low floors, but from an ensemble of large amplitude response time histories

since collected during strong winds it has been possible to identify to good accuracy the mode

shape ordinates at basement, normalised to unity at the roof. For the first three modes these values

are 0.006, -0.010 and 0.016. As this shows the foundation to be very rigid, it has been argued that

the basement performance is a good representation of local ground movement hence, with thesensitive mode 2 trigger the building works as a sensitive seismometer.


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7 Operational modal analysis [8]: 1990s technologyWith ten years of acceleration response data it was useful to apply some of the newly developed

operational modal analysis technology to study the mode frequencies and damping, together with

orientation in detail based on the four channels of roof and basement signal. For this purpose the

natural excitation technique (NExT) was used together with the eigensystem realization algorithm

(ERA) and supplemented by the existing vibration test procedures.

7.1 NExT: Natural Excitation TechniqueProcedures are now available to improve the accuracy and ease of AVT data analysis and the

ability to discriminate close modes. One valuable contribution is NExT [9] that can obtain a set of

frequencies, damping ratios and true mode shapes..

NExT may use ERA [10] applied to a set of impulse response functions (IRFs) which can be

obtained either through cross-covariance functions of the original time series or the inverse Fourier

transforms of their frequency domain equivalent, the cross-spectral densities (CSDs). In the

applications described here the combined procedure is termed NExT/ERA.

A discretised structural system is represented as having mass, damping and stiffness M, C and K.

For a stick model of a building having one lumped mass at each floor and one spring element

(column) between floors, the storey or level displacements form a time-varying vectorx. Theequations of motion are then written as

+ + =Mx Cx Kx p . 11)

These are transformed to the state space form of first order equations

= +z Az Bp 12)

where, for example,

=

1 1M C M KA

I 0

=

xz

x

and

-1MB =

0.

The frequencies and damping ratios of the MCK system of equation (11) appear as conjugate pairs

of eigenvalues ofA:

21i = A 13)

and the eigenvectors ofA are also the eigenvectors of equation (11) for free vibration. Hence once

a form ofA representing a discretised modal model of the true structure can be found from test

data, the modal parameters can be 'realised'. ERA recovers a candidate A from IRFs that represent

the multi-mode behaviour described by equations (11) and (12). The IRFs can be shown to be

equivalent (except for a common scale factor) and contain the same information when recovered

from:

a) Directly measurement of free decay in time domainb) Inverse FFTs of frequency response functions such as given in equation 1)c) Cross-covariance functions of random responses to a common (Gaussian) excitationd) Inverse FFTs of cross-spectral densities such as given in equation 7) for common

(Gaussian) excitation channels

Fig. 4 shows the time series of basement (channel 1) and level 65 (channel 3) response resultingfrom weak ground motions due to a tremor some 600km distant. The spectrograms show the


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broadband character of the ground motion and resonant amplification at the upper floors. These are

used to generate cross-covariance functions R11,R13,R31 andR33 that forma square matrix or 2x2

matrix or blockiX . Hence A is a covariance block Hankel matrix and the method is termd

CBHM. These are obtained directly from the short sequence of the data of Fig. 4 and represent

case c) above. Wind-induced response is similarly broad band but there is no basement response.

R13,R31 are mirrorimages of each other if negative (time) lags are included.

Equivalent plots could be obtained as in case d) by inverse FFT of CSDs either from a singlemeasurement or from averaging over many records (e.g. obtained during strong winds).

The examples are for scalar or square forms of iX . A third and more usual case is where IRFs,

FRFs, cross-covariance functions or CSDs are formed between a group ofn signals and a common

reference; in this case iX is a nx1 column vector.

7.2 ERA: Eigensystem Realisation AlgorithmWith

iX representing as a scalar, vector or matrix the cross-covariance or impulse response

function (IRF) at the ith time sample, a matrix is constructed by stacking thei

X :

( )

0 1

1 2 1

1

0

a

a

b b a b

+

+ +

=

X X X

X X XH

X X X

14)

This form is called the Hankel matrix 'at time 0' and the sequence ofiX at discrete times i are

known as the Markov parameters. As H(0) contains IRFs which represent the vibration

characteristics, it also contains information about the mode shapes, frequencies and decay rates. As

more rows and columns are added the rank grows until, in theory, it reaches a limit according to

number of vibration modes contributing. A minimum rank form ofH is reconstructed and a state

matrix A is recovered from it. The procedure of ERA is described very thoroughly elsewhere [10].

7.3 Variations of modal parametersThe efficient NExT/ERA procedure is useful for examining variations of natural frequencies, since

some researchers have considered them to be directly or indirectly useful as damage/degradation

sensitive parameters for SHM. Data from 15 days of continuous recording of wind-induced

response were analysed frame by frame (case c) above), with a degree of overlap, to extract modal

parameters. Fig. 5 shows the results for mode A1; the bars indicate by height (z-axis, labeled

msv) and lightness of shading the strength of a mode identified at a time and frequency located

in the horizontal plane of the figure. In order to judge the repeatability of the estimates using ERA,

different sizes of H were used, equivalent to different numbers of lags in the cross-covariance

functions constructed from overlapping pieces of the 1Hz sampled time series (decimated from the

original 8Hz). The two solid lines plot (with arbitrary scaling) variations of mode A1 RMS

amplitude (lower line) and ambient temperature value (upper line). The ambient temperature

variations would certainly differ from the structure core temperatures but there is a clear diurnal

effect, with no convincing effect of mode amplitude.


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Fig. 6 plots the variation of mode A2, B2, A3 and B3 frequencies over a period of 6 years,.

identified using the simple auto-power SDOF curve fitting technique. The frequencies drop on

average 0.65% per annum but there is considerable scatter, in part due to the variability of the

identification method and in part due to the type of systematic variation evident in Fig. 5.

Other methods of system identification based only on output measurements have been used. The

transmissibility (frequency response) function measured between roof and basement shows clearly

the characteristic of a lightly damped multi-degree of freedom system and is amenable tofrequency domain curve fitting techniques usually applied to frequency response functions from

forced vibration.

Fig. 7 shows the real and imaginary parts of the transmissibility function using cross-powers

averaged over a set of earthquakes, and the resulting circle fit for mode A2. Using single events

works only for certain tremor signals, while averaging broadens the peaks (as the characteristics

are not stationary), but this does demonstrate the possibilities of appropriate signal processing.

8 Global positioning systemWith a proven track record in recording dynamic structural deflections in suspension bridges [11],

the global positioning system (GPS) offers possibilities of absolute position measurement for

resonant, dynamic non-resonant and static responses. Hence, in 1999 the acceleration and wind

recording system was upgrade to integrate a dual rover GPS system.

The system at Republic Plaza was designed to operate in both RTK and off-line post-processing

modes. RTK solutions output at 1Hz for each sample as text data are immediately converted to

analog signals that are supplied to and recorded by additional channels on the existing data

acquisition system. Hence GPS would provide displacement data from DC to 0.5Hz while

acceleration data would also provide, by integration, absolute displacements down to

approximately 0.2Hz.

The initial GPS data appeared very noisy and not to correlate with other signals, hence it was

difficult to believe what the data represented. In fact validating the GPS data was a major issue, as

the signals are subject to various forms of error such as multi-path, cycle-slip, random noise and

systematic noise. Also, the total movement of the building, expected to be of the order of +/-0.1m,

is expected to comprise components of dynamic and static response to wind as well as static

response to temperature changes in and around the building. As well as using Direct evidence ofsystem operation by physically moving the antenna, oscillatory displacements at least 5mm

amplitude induced by strong winds were compared with acceleration data.

Response during strong winds shows a clear modal response, but the best evidence so far is from

low frequency ground movements generated by the Aceh earthquake of 26/12/2004; oscillations of

around 2cm amplitude were observed, relative to the base station receiver. Unlike accelerometers,

which provide absolute displacements, RTK GPS provides relative displacement information.

Displacement relative to building foundation is available by integrating acceleration data at

basement as well as roof, but is likely to be different motion relative to a building some distance

away due variations in ground motion. Figure 8 (left) compares GPS eastings from both rovers

(first two rows) with double-integrated accelerations. There are differences, in part due to the

uncertain base station movement but there is clear correspondence. More evidence is provided in

the right hand plot that shows modes identified using the CBHM approach on the time series,

taking different number of blocks (d). The modes and damping ratios are perfectly in line withthose from accelerometer data.


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So far, due to the high stiffness and small movements, GPS has been unable to identify clearly and

convincingly the slowly varying movement of the building during wind, but this is largely due to

relatively benign conditions. As always, an extreme event (wind storm) would provide valuable

data for evaluating not only the building but the GPS itself.

9 ConclusionsA range of output-only identification procedures have been applied to data from bothaccelerometers and GPS to show not only the power of the techniques but also to learn in detail

about the modal properties of the building, which have allowed for the building to be used as a

giant load cell and seismometer for ambient loads.

10 References[1] Teh HS, Lai HP, Structural aspects of Republic Plaza. Proc Seminar on Tall Buildings

Design and Construction, Singapore, The Institution of Engineers Singapore., 1997

[2] Brownjohn JMW, Pan TC and Cheong HK, 'Dynamic response of Republic Plaza , Singapore.'The Structural Engineer, London, 76(11), 221-226, 1998.

[3] Maia NMM, Silva JMM, He J, Lieven NAJ, Lin RM, Skingle GW, To W, Urgueira APVTheoretical and Experimental Modal Analysis, Research Studies Press Ltd, 1997.

[4] Simiu E, Scanlan RH, Wind Effects on Structures. Wiley, Third Edition, New York, 1996.[5] Welch PD, 'The use of fast Fourier transform for the estimation of power spectra: A method

based on time averaging over short, modified periodograms', IEEE Transactions, AU-15, 70-

73, 1967.

[6] Brownjohn JMW, Pan TC and Deng XY, Correlating dynamic characteristics from fieldmeasurements and numerical analysis of a high-rise building. , Earthquake Engineering and

Structural Dynamics 29(4), 523-543, 2000.

[7] Pan TC, Brownjohn JMW, You X,. Correlating measured and simulated dynamic response ofa tall building to long-distance earthquakes. Earthquake Engineering and Structural

Dynamics, 33(5), 543-668, 2004.

[8] Brownjohn, JTC[9] James GH, Carne TG, Lauffer JP, The natural excitation technique (NExT) for modal

parameter extraction from operating structures, Journal of Analytical and Experimental

Modal Analysis, 10 (2), 260-277, 1995.

[10]Juang J-N, Pappa RS, An eigensystem realisation algorithm for modal parameteridentification and model reduction, AIAA Journal of Guidance, 8(5), 620-627, 1985

[11]Ashkenazi V, and Roberts GW, Experimental monitoring of the Humber Bridge using GPS.Civil Engineering, Proceedings, Institution of Civil Engineers, London, 120 177-182, 1007.


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0

10

20

30

40

50

60

70

0 200 400 600days

storeys,

mass/106kg

0

1

2

3

4

5

6

7

mode

period/sec

core w all core Slab office Slab

CFT Column curtain Wall massmode A1 mode B1

N

Figure 1 View of top of Republic Plaza building

Figure 3 (below), clockwise from top

left: mode A1, mode A2, mode A3,

mode T1.

Bottom right, auto spectral density of

acceleration response in A-direction

Figure 2 (below) variation of principal axis fundamental

vibration mode (A1, B1) frequencies

with building construction

N

N N


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Figure 4 Time series and spectrogram for basement (ch1) and roof (ch3) acceleration signals

recorded resulting from regional (Indonesian) earthquake

Figure 5 Block-by-block application of NExT/ERA to free-vibration (wind-induced) building

response over 17 days, showing scatter of mode A1 and B1 frequencies and limited pattern.

400 500 600 700 800-0.5

0

0.5

1

ch1(mm/sec

2)

t/sec

qk11

t/sec

ch3f/Hz

qk11

400 500 600 700 8000

0.5

1

1.5

2

2.5

3

3.5

400 500 600 700 800-5

0

5

ch3(mm/sec

2)

t/sec

qk11

t/sec

ch1f/Hz

qk11

400 500 600 700 8000

0.5

1

1.5

2

2.5

3

3.5


12/12

-20

0

20

ch1(mm)

xv_aceh_disps_rotated

-20

0

20

ch3(mm)

8 10 12 14 16 18

-20

0

20

minutes

ch5

(mm)

0.17

0.180.19

0.2

0

50100

150

2000

0.5

Frequency /Hz

increase d, keep Poles same

d

/

%

-60

-50

-40

-30

-20

-10

0

Imaginary

Real

cpsfensemble ch3/ch1 1/mod=0.6059 =167.9 f=0.1822Hz = 1.19%

Mod(RE)=i.j/T[m] Mod(TF)=i.[m]./

T[m] = iL / M

Figure 6 (left) variation of mode A3

and B3 frequencies over 6 years

Figure 7 (below):left: real and imaginary parts of

ensemble average of (non-

dimensional transfer functions for a

collection of tremor signals

right: circle fit of same data

showing clear SDOF system

identification

Figure 8 Displacement time series from GPS during Aceh earthquake and ERA results

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-40

-30

-20

-10

0

10

20

30

40R: ch3 vs ch1

f /Hz

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-60

-40

-20

0

20

40

60I: ch3 vs ch1

f /Hz

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54Brownjohn AVT