Application of OMA-EMIF Algorithm to Cable Stayed Bridges

S. Chauhan

Brüel & Kjær Sound & Vibration Measurement A/S,

Skodsborgvej 307, DK-2850 Nærum, Denmark

Email: schauhan@bksv.com

A.J. Helmicki, V.J. Hunt, J.A. Swanson, J.S. Saini, S. Kangas

University of Cincinnati Infrastructure Institute,

University of Cincinnati, Cincinnati, OH USA

Email: Arthur.Helmicki@uc.edu, Victor.Hunt@uc.edu, James.Swanson@uc.edu, jas.saini@gmail.com,

kangassj@email.uc.edu

D.K. Nims

Department of Civil Engineering

University of Toledo, Toledo, OH USA

Email: Douglas.Nims@utoledo.edu

R.J. Allemang

University of Cincinnati, Structural Dynamics Research Laboratory

Department of Mechanical, Industrial, and Nuclear Engineering

Cincinnati, OH USA

Email: Randy.Allemang@uc.edu

Abstract

Enhanced Mode Indicator Function for Operational Modal Analysis or OMA-EMIF algorithm is a

recently proposed spatial domain OMA algorithm that differs from the Frequency Domain Decomposition

(FDD) and Enhanced Frequency Domain Decomposition (EFDD) algorithm by performing the modal

frequency and damping estimation in frequency domain instead of time domain. This paper presents the

results of OMA studies carried out on the US Grant Bridge over the Ohio River in Portsmouth, OH and

MRC Bridge in Toledo, OH using the OMA-EMIF algorithm thus highlighting the utility of this algorithm

in analyzing large and complex structures such as bridges. Further, the results obtained from the algorithm

are compared with those obtained using commercially available FDD/EFDD algorithm.

1 Introduction

The OMA-EMIF algorithm was proposed in 2006 [1]. Like the FDD algorithm [2], it is based on the

popular spatial domain approach, Complex Mode Indicator Function [3-5]. However, unlike EFDD [6],

the OMA-EMIF works in the frequency domain. The technique uses the positive power spectra [7, 13]

instead of the original power spectra and utilizes a first order UMPA (Unified Matrix Polynomial

Approach) [8-10] formulation for mode estimation. Since OMA-EMIF works in frequency domain, it

enables the use of residuals to account for the effect of the out-of-band modes. Also more than one mode

can be estimated at a time. In [1], the OMA-EMIF algorithm was shown to give encouraging results on

analytical and experimental datasets.

In this paper, the OMA-EMIF algorithm is applied to data collected over two cable stayed bridges. The

aim of the paper is to evaluate the performance of the algorithm under practical real life situations.

Additionally, the collected data is also analyzed using commercially available FDD-EFDD algorithm and

the performance of the two algorithms is compared.

Section 2 presents the mathematical details of the OMA-EMIF algorithm. This is followed by the details

of the OMA studies carried out on the US Grant Bridge and the MRC Bridge, which include the

description of the bridges, set up and data acquisition and data analysis. The obtained modal parameters

are compared to those obtained using the FDD-EFDD approach and finally conclusions are provided

based on these results.

2 Theoretical Background

Spatial domain modal parameter estimation algorithms involve singular value decomposition (SVD) of the

frequency response function matrix (in case of EMA) or the power spectrum matrix (in case of OMA).

Popular EMA algorithm, Complex Mode Indicator Function [3-5], belongs to this classification. It

involves a frequency by frequency singular value decomposition of the frequency response function

matrix.

Frequency Domain Decomposition (FDD) algorithm can be looked upon as the equivalent of CMIF

algorithm in OMA. In FDD, singular value decomposition is applied to the power spectrum matrix. To

understand this further, the relationship between the output response power spectra, input force power

spectra and FRFs [11], given by Eq. (1), is considered.

( )[ ] ( )[ ] ( )[ ] ( )[ ]HFFXX HGHG ωωωω = (1)

where [GXX(ω)] is the output response power spectra, [GFF(ω)] is the input force power spectra and [H(ω)]

is the FRF matrix. At this point, it is also important to reiterate the key OMA assumptions that the power

spectra of the input force are assumed to be broadband and smooth. This means that the input

power spectra is constant and has no poles or zeroes in the frequency range of interest. The forcing

is further assumed to be uniformly distributed spatially (Ni (Number of points at which input forces

are being applied) approaching No (Number of points at which response is being measured),

considering that the response is being measured over the entire structure).

As a direct consequence of the first assumption, the output response power spectra [GXX(ω)] is assumed to

be proportional to the product [H(ω)][H(ω)]H and order of the output response power spectrum is twice as

that of the frequency response functions. Further, the partial fraction form of GXX, given by Eq. (2) [12,

13], shows that the power spectrum data contains not only the positively damped roots, kλ and ∗kλ but

also the negatively damped roots, kλ− and ∗− kλ . In other words, power spectrum data contains the same

modal information twice (due to the product [H(ω)][H(ω)]H).

( )( ) ( )∑

=∗

∗

∗

∗

−−+

−−+

−+

−=

N

k k

pqk

k

pqk

k

pqk

k

pqk

pqj

S

j

S

j

R

j

RG

1 λωλωλωλωω

(2)

Note that λk is the pole and Rpqk and Spqk are the kth mathematical residues. These residues are different

from the residue obtained using a frequency response function based partial fraction model since they do

not contain modal scaling factor (as no force is measured).

In FDD the singular value decomposition of the GXX matrix at a particular frequency results in the

decomposition,

( )[ ] [ ][ ][ ]HkXX VSUG =ω (3)

where [S] is the singular value diagonal matrix and [U], [V] are singular vector matrices which are

orthogonal. For the case where all the response locations are considered as references to form the square

[GXX] matrix, [U] and [V] are equal. The singular vectors near a resonance are good estimates of the mode

shapes and the modal frequency is obtained by the simple single degree of freedom peak-picking method

[14, 15].

In the EFDD algorithm [6], power spectra of a SDOF system is identified around a peak of resonance (a

peak in the SVD plot). A user defined MAC (Modal Assurance Criterion, a tool for comparing modal

vectors) [16, 17] rejection level is set to compare the singular vectors around the peak. Singular values

corresponding to the singular vectors that match as per the set MAC level are then retained as those

belonging to the SDOF power spectrum. It should be noted that the mode shape corresponding to the

mode is given by the taking the average of these singular vectors. This SDOF power spectrum is

transformed back to the time domain by inverse FFT to obtain the auto/correlation function. The natural

frequency and damping are then estimated for this SDOF system by determining zero crossing time and

logarithmic decrement methods respectively. The entire process is shown in Figure 1.

Figure 1 – EFDD estimation of modal frequency and damping

2.1 ENHANCED MODE INDICATOR FUNCTION (EMIF) FOR OMA

The OMA-EMIF algorithm [1] is based on the reformulation of the Enhanced Mode Indicator Function

(EMIF) [5, 18, 19] algorithm and uses positive power spectrum (PPS) [7, 10] instead of power spectrum.

Positive power spectrum is mathematically given by Eq. (4) and has the same order as FRF. It should be

noted that PPS contain the necessary modal information (Modal frequency, modal damping and mode

shapes) only once unlike the power spectrum, which contains the same information twice. The modal

scaling is however, not estimated as the force is not being measured.

( ) ∑=

∗

∗+

−+

−=

n

k k

pqk

k

pqk

pqj

P

j

PG

1 λωλωω (4)

a)

b)

c)

d)

e)

a) FDD Plot

b) Choosing the peak of resonance

c) Power spectra of the peak

d) Corresponding correlation function

e) Estimated modal parameters

The OMA-EMIF algorithm involves selection of a frequency range containing a discrete number of

frequencies Nf and number of modes Nb to be identified in that range. The number of modes Nb in the

selected frequency zone is identified with the help of the CMIF plot based on the power spectra (similar to

FDD). It should be recalled that the peaks in a CMIF plot indicate the presence of a mode. Further, the

number of modes, Nb in the frequency band cannot be greater than the number of singular values (see Eqn.

(6)). Once the frequency range for analysis and number of modes Nb in the selected frequency range are

determined, a first order model, frequency domain equivalent of the Eigensystem Realization Algorithm

(ERA) [23] method is used to form the augmented matrix [A0] utilizing the positive power spectra matrix.

It should be noted that though the CMIF plot was based on power spectra matrix, the augmented matrix is

formed using positive power spectra matrix in the selected frequency range. p and q are the indices for the

output response and reference response locations.

[ ]( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

=

++

+++

+++

+++

+++

ff

fff

fio

NipqNiqiq

NipipNiiNii

NNxN

GGG

GGGGGG

A

ωωω

ωωωωωω

KKKKKKK

MMMMMMMMMMM

KKKKK

11

1121211111

)(0

(5)

SVD of ][ 0A yields the left and right hand singular vectors as well as the singular values.

[ ] [ ] [ ] [ ]HNNNi VSUA

fio=× )(0 )(ω (6)

The dominant right singular vectors {U} corresponding to the number of modes Nb in the frequency band

are then used as a modal filter to obtain the enhanced positive power spectrum (ePPS) in the frequency

band of interest that is similar to the eFRF in case of EMIF algorithm [5, 18, 19]. Thus,

( )[ ] ( )[ ]ioobib NN

T

NNNN GUGePPS ×+

×× == ωωω ][)( (7)

A first order UMPA equation can be formed utilizing these ePPS’s and Nr residual terms [βm] can be

included to account for out of band modes.

[ ] ( ) [ ][ ] [ ] ( )[ ]

=+ ∑

=

r

ixNbNibbbbb

N

m

m

m

xNNxNNxNNjGjj

0

0

0

1 )()()( ωβωωαωαω (8)

Eq. (8) can be solved by either normalizing the [α0] or the [α1] coefficient matrix. Eq. (9) represents the

[α0] normalization obtained by setting [α0] equal to [I]. Similar equation can be obtained for [α1]

normalization by setting [α1] equal to [I].

[ ] [ ] [ ][ ] ( )[ ]( )[ ][ ]

( )[ ]

+

−

−−=

][

01

Ij

I

Gj

G

m

m

ω

ωω

ωββαM

K (9)

The + sign in the above equations represents Moore-Penrose pseudo inverse of a matrix. The eigenvalues

of the system can then be computed as the eigenvalues of the matrix [α0], which are also the measure of

the natural frequency and damping of the system. The eigenvectors are the eigenvectors of the enhanced

system and therefore they have to be converted back to the original physical coordinates. This is

performed by multiplying the eigenvectors from the enhanced system by the eigenvectors from the

original physical system.

{ } [ ] { }11 ×××

=bboo

NEnhancedNN

H

Nphysical U ψψ (10)

3 Application to Civil Structures

3.1 US GRANT BRIDGE, PORTSMOUTH, OH

The US Grant cable stayed bridge is shown in Figure 2. The bridge is a three span bridge built over the

Ohio River at Portsmouth, Ohio. It connects the states of Ohio and Kentucky and was opened to public in

October, 2006. The plan and elevation of the bridge is shown in Figure 3.

Figure 2 – US Grant Cable Stayed Bridge

Figure 3 – US Grant Cable Stayed Bridge: Plan and Elevation

A finite element model of the bridge was developed and frequency analysis was performed to compute the

modal frequencies and the mode shapes [20]. One of the simplifications made while preparing the finite

element model of the bridge involved modeling the beam and shell elements of the various girders and the

deck in the same horizontal plane. A stiffness correction is applied to account for this which minimizes the

differences in the bridge bending modes; however, the torsional behavior is not corrected. Due to this

factor, it is expected that torsional modes (as well as higher frequency modes) obtained from OMA might

differ from those estimated by the FE model.

The modal frequencies and the mode shapes are listed in Table 1 along with the corresponding modal

participation factors. The modes with high participation factors are highlighted in the table. It should be

noted that most of these modes are vertical bending modes. Thus, the sensor layout for the final

superstructure test was chosen in a manner that ensured the observation of these critical modes.

Table 1: Frequency Response from Finite Element Analysis

Modal Participation Factors (%) Frequency (Hz.) Mode Description

UX UY UZ RX RY RZ

0.2936 Bending-1 0.297 0.000 1.427 0.000 0.025 0.000

0.3443 Tower Sway 0.000 13.22 0.000 63.59 0.000 14.33

0.3842 Tower AntiSway 0.000 4.040 0.000 15.89 0.000 0.066

0.4827 Bending-2 0.318 0.000 5.586 0.000 10.14 0.000

0.6786 Torsion-1 0.000 0.025 0.000 1.678 0.000 0.017

0.7052 Bending-3 0.076 0.000 21.67 0.000 31.35 0.000

0.7971 Torsion-2 0.000 0.806 0.000 0.054 0.000 0.822

0.8150 Bending-4 0.182 0.000 4.624 0.000 0.448 0.000

0.8391 Torsion-3 0.000 0.703 0.000 0.001 0.000 2.593

0.9230 Bending-5 0.160 0.000 12.97 0.000 6.900 0.000

0.9511 Torsion-4 0.000 0.131 0.000 0.002 0.000 0.059

1.0201 Torsion-5 0.000 1.385 0.000 0.031 0.000 0.811

1.0855 Bending-6 0.369 0.000 1.771 0.000 1.141 0.000

1.1678 Torsion-6 0.000 0.321 0.000 0.043 0.000 0.410

1.1749 Bending-7 0.194 0.000 0.015 0.000 1.196 0.000

1.2571 Torsion-7 0.000 0.049 0.000 0.008 0.000 0.397

1.4233 Bending-8 1.247 0.000 0.902 0.000 0.583 0.000

1.5113 Torsion-8 0.011 0.023 0.000 0.031 0.000 0.021

1.5122 Bending-9 44.36 0.000 0.000 0.000 0.042 0.000

3.1.1 Test Set-up, Data Acquisition and Data Processing

In order to observe both bending and torsional modes, accelerometers were placed along the inner and

outer girders on the upstream side and on the outer girders on the downstream side to measure the

acceleration in the vertical direction. As shown in Figure 4, the central span is more heavily instrumented

in comparison to the side spans. 31 accelerometers were used in total, with 27 (3 lines of 9 sensors each,

extending from the Kentucky tower to middle of the central span) on the central span and two each on the

outer girder, both upstream and downstream side of the side spans. The objective of instrumenting the side

spans was to distinguish the mode shapes that appear to be similar in the central span but differ in side

spans. Further details of the test set up and acquisition can be found in [13].

Figure 4 – Sensor Layout

Kentucky Side

Ohio Side

Upstream

Downstream

The data acquisition parameters are as follows:

Sampling Rate 40 Hz

Frequency Range 0 – 15 Hz

Test Duration 10 Min

Only ambient excitation sources (wind, river flow) were present while acquiring the data. Additionally, a

van was driven over the bridge during the test duration.

For the purpose of parameter estimation, the output power spectra were calculated using the Welch

Periodogram method [21, 22]. A block size of 4096 was used with Hanning window and 66.67% overlap.

Similar data processing parameters were chosen for both the algorithms (OMA-EMIF and FDD/EFDD) to

have a fair comparison. Figure 5 and 6 show typical auto/cross power spectrum and the CMIF plot based

on the calculated power spectra. The zoomed portion of the CMIF plot indicates the presence of modes in

the frequency range of interest. It is interesting to note that the CMIF plot indicates the presence of two

closely spaced modes around 0.9 Hz.

Figure 5 – Auto/Cross Power Spectrum

Figure 6 – CMIF Plot based on Output Power Spectra

3.1.2 Modal Parameter Estimation

Table 2 shows the modal parameters obtained using the OMA-EMIF and the EFDD algorithms. The

modal frequencies estimated using the OMA-EMIF algorithm are very close to those obtained using the

standard FDD/EFDD algorithm. The discrepancy in the damping estimates (EFDD estimates being lower

in comparison to OMA-EMIF) is due to the dependence of damping estimation process on a number of

factors which are algorithm specific. This can be explained by understanding the manner in which the

modal parameters are identified using these two algorithms.

In case of EFDD, a SDOF spectral bell function is estimated in the vicinity of a singular value peak and

then estimation of modal frequency and damping is carried out by using SDOF curve fitting techniques in

time domain. This involves the use of linear regression to fit a straight line to logarithm of the

exponentially decaying correlation function (see Figure 7). The estimation of the SDOF spectral bell

function depends on the chosen MAC acceptance level [6, 14] and it has been observed that though this

might not have much effect on the frequency, it affects damping a lot. Further, the damping estimation

also depends heavily on the length of the correlation function chosen for linear regression (Figure 7).

Similarly, in OMA-EMIF, the damping estimates are affected by the frequency range and number of

residuals chosen. Due to sensitivity of damping to so many factors, it was decided to use the default values

(for EFDD, these values were chosen as those provided in the PULSE Operational Modal Analysis Type

7760).

Figure 7 – Damping Estimation using EFDD Algorithm

Table 2: Modal Parameter Estimates

OMA-EMIF EFDD

Modal Freq (Hz) Damping (%) Modal Freq (Hz) Damping (%)

0.4805 1.2717 0.4826 0.6697

0.6939 0.6669 0.6937 0.5613

0.7414 1.1607 0.7430 1.0510

0.8387 0.5438 0.8389 0.5320

0.9200 0.6559 0.9203 0.3698

0.9314 0.6443 0.9308 0.4809

1.1006 0.8624 1.1066 0.2483

1.1389 0.6267 1.1389 0.2975

1.2030 0.6571 1.2052 0.3476

1.4111 0.6326 1.4118 0.5537

1.4533 0.6732 1.4442 0.2772

1.5084 0.8470 1.5055 0.5024

Figure 8 shows the Auto MAC for the OMA-EMIF mode shape estimates. It indicates that some of the

modes appear similar to each other (like 0.74 and 0.93 Hz modes). One of the reasons for this might be the

limited spatial resolution, as only a certain portion of the bridge was instrumented. Also, since the

vibrations were measured only in the vertical direction, it is possible that some of these modes might not

be clearly observed.

Figure 8 – Auto MAC plot for OMA-EMIF Estimates (US Grant Bridge)

The comparison of the OMA-EMIF and FDD/EFDD mode shapes is shown in the Cross MAC plot

(Figure 9). Most of the modes match comparatively very well with each other. However two of the modes,

at 1.10 Hz and 1.44 Hz are not matching, which means that either they have not been estimated correctly

(on account of issues pertaining to that of observability, only vertical modes being measured or presence

of local cable modes, etc.) or that there is essentially no mode at these frequencies. Overall, the results of

the two algorithms match quite satisfactorily.

Figure 9 – Cross MAC plot between OMA-EMIF and FDD/EFDD Estimates (US Grant Bridge)

Finally the MAC comparison between bending modes obtained from OMA-EMIF algorithm and the FE

model is shown in Table 3. As mentioned earlier, only those modes which had high modal participation

factor based on the FE model are used for this comparison, and most of them are bending modes. The

OMA-EMIF modes compare well within limits with the FE model prediction.

Table 3: Cross MAC between OMA and FEM Bending Modes (US Grant Bridge)

FEM (Hz) OMA-EMIF

(Hz) MAC

0.483 0.480 0.88

0.704 0.694 0.91

0.815 0.839 0.60

0.924 0.920 0.84

1.087 1.139 0.69

1.178 1.203 0.89

3.2 MAUMEE RIVER CROSSING CABLE STAYED BRIDGE, TOLEDO, OH

The MRC Bridge or the Veterans’ Glass City Skyway Bridge (Figure 10), as it is now called, is a single

pylon cable-stayed bridge in Toledo, Ohio over the Maumee River on Interstate 280 on the eastern edge of

Toledo downtown. The bridge replaces the Craig Memorial Bridge which was one of the last remaining

drawbridges on the US interstate highways. The bridge opened to public in June, 2007. More details of the

bridge can be found in [13].

Figure 10 - Maumee River Crossing Bridge, Toledo, OH

3.2.1 Test Set-up, Data Acquisition and Data Processing

Figure 11 shows the test set-up layout. The sensor grid used for the test is much coarser in comparison to

the one used for the US Grant Bridge and thus it is expected that some of the modes might appear to be

similar (poor observability). A total of 10 sensors are used, 5 on each side of the parapet. The sensor lines

extend from the back span side to the front span side with 8 sensors on one side of the pylon and 2 on the

other as indicated in Figure 11. The sensor line extends 500m from Cable 14B on the back span to 6A on

the front span. Note that notations A and B are for front and back spans respectively. Figure 12 shows one

of the accelerometers glued on the bridge superstructure.

The data acquisition parameters for the test were set as following

Sampling Rate 40 Hz

Frequency Range 0 – 15 Hz

Test Duration 20 Min

The bridge was partially opened to public and one lane of traffic was open during the test.

Figure 11 - OMA Test Set-Up Layout for the MRC Bridge

Figure 12 - Typical accelerometer set up for the MRC Bridge OMA test

A block size of 2048, along with the application of Hanning window and 66.67 % overlap was used for

processing the output time histories to obtain the power spectra. The autopower plot of individual channels

is shown in Figure 13. The plot indicates the presence of at least 6 modes below 1.4 Hz frequency range.

Further, the CMIF plot (Figure 14) indicates the presence of two close modes around 1 Hz in addition to

the modes indicated by the Autopower plot.

Figure 13 - Autopower spectrum of individual channels (MRC Bridge)

Figure 14 - Complex Mode Indicator Function Plot (MRC Bridge)

3.2.2 Modal Parameter Estimation

Table 4 shows the modal parameters obtained using the OMA-EMIF and the EFDD algorithms. In this

case as well the modal parameters obtained from the two algorithms are comparable. The modal

frequencies obtained using two algorithms match well. However, the damping estimates differ on account

of reasons given before. Damping for the mode at 1.66 Hz (highlighted in green) is not estimated using the

EFDD algorithm as the SDOF spectral bell curve could not be identified properly at this frequency. The

frequency and mode shape in this case is result of SDOF peak picking approach as used in FDD.

Table 4: Modal Parameter Estimates

OMA-EMIF EFDD

Modal Freq (Hz) Damping (%) Modal Freq (Hz) Damping (%)

0.4340 2.6277 0.4342 1.6064

0.6444 3.5642 0.6490 3.2492

0.7083 1.8282 0.7095 1.4179

0.9851 1.2470 0.9895 1.1213

0.9921 1.1892 0.9914 1.2432

1.1876 1.6644 1.1910 1.1651

1.3116 1.3653 1.3107 1.4484

1.5177 2.4909 1.5048 1.3426

1.6168 0.8962 1.6012 0.5292

1.6671 2.1747 1.6894 -

1.9462 1.8112 1.9307 0.8183

2.0528 1.2576 2.0534 0.9176

2.0994 1.2064 2.0699 0.5118

2.2993 1.7047 2.2869 0.8706

2.4204 1.6692 2.4206 0.3266

The Auto MAC between the various OMA-EMIF mode shapes (Figure 15) shows that lot of modes look

similar to each other in spite of differing significantly in frequency (Such modes are indicated by orange

in the table). This is essentially a problem of observability (Lack of sufficient spatial resolution due to a

coarse sensor grid) because even in the CMIF plot there are distinct peaks at these frequencies. Local

modes due to cable and tower moment might also affect these estimates and none of these were monitored

when the measurements were being taken. The sensor layout also does not account for the lateral modes

and it is possible that some of these appear in the measurements but not in a well defined manner.

These observations concerning some of the modes provide little confidence in these modes. The problem

can be attributed to several factors including instrumenting only a section of the bridge resulting in

insufficient spatial resolution, a limited sensor grid, mounting the sensors in only the vertical direction

thus not accounting for lateral motion of the bridge, tower sway and cable vibrations, etc. However these

limitations are not on part of the algorithm but due to the chosen test set up and resulting data acquisition.

Thus just like EMA, the need for proper test design is very important for getting good estimates of the

modal parameters.

Figure 15 – Auto MAC plot for OMA-EMIF Estimates (MRC Bridge)

The Cross MAC plot (Figure 16) shows good correspondence of the modes estimated using two

algorithms, except for a few modes, such as 1.68 Hz, which in case of FDD/EFDD appears similar to

previous three modes, although it appeared different in case of OMA-EMIF algorithm (Figure 15).

Figure 16 – Cross MAC plot between OMA-EMIF and FDD/EFDD Estimates (MRC Bridge)

4 Conclusions In past, the OMA-EMIF algorithm has been shown to give good results on analytical and lab based

experimental data [1]. In this study, the performance of this algorithm is further analyzed by means of

studies conducted on two cable stayed bridges. It is observed, based on this study, that this algorithm

works satisfactorily on data collected under practical real life situations and this makes it suitable for such

purposes. The estimates obtained are shown to have comparative results with respect to the well known

OMA algorithm; Frequency Domain Decomposition and Enhanced Frequency Domain Decomposition,

which is yet another indicator of the good performance of this algorithm.

The discrepancy in damping estimates of the two algorithms can be explained by means of numerous

parameters such as chosen frequency range, number of residuals used, length of correlation function

chosen, chosen MAC acceptance level etc. among others, on which damping depends heavily.

In certain cases, the mode shapes appear to be similar. One of the reasons for this is the limited spatial

resolution, which gives rise to observability related issues. However, with the help of the available

knowledge in terms of FE model, all the important modes have been estimated properly. Thus the study

underlines the two key points of modal analysis in general that 1) its always good to have some a priori

information available, and 2) the importance of good test planning, set up and good data acquisition

because the parameter estimation algorithm is only as good as the data collected.

Acknowledgements

Author S. Chauhan is thankful to the Ohio Department of Transportation (ODOT), University of

Cincinnati Infrastructure Institute (UCII) and Structural Dynamics Research Laboratory (SDRL) at

University of Cincinnati for providing him the opportunity to carry out this work as a part of his doctoral

studies at Department of Mechanical Engineering, University of Cincinnati.

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