vibration study and application of outlier analysis to the

305

Chapter 15-x

1250

1000

Mah

alan

obis

dis

tanc

e

Number of observations

750

500

250

200 400 600 800 1000 1200

Undamaged

Damage 3

00

Authors:Dionysius M. SiringoringoTomonori NagayamaYozo FujinoDi SuChondro TandianHirotaka Miura

15Vibration Study and Application of Outlier Analysis to the S101 Bridge Full-Scale Destructive Testing

MotivationThe detection of outliers in multi-variant data by online technologies, screening con-

tinuous data streams from monitoring systems, needs to be established in a quick and error free environment. Stable methods in order to avoid false alarms are desired.

Main ResultsAn outlier detection routine capable to be linked to permanent monitoring systems

has been developed. A novel damage detection application based on outlier analysis of the spectral functions, called Mahalanobis distance, has been created.

306

15 Vibration Study and Application of Outlier Analysis to the S101 Bridge Full-Scale Destructive Testing

15-1 IntroductionStructural health monitoring (SHM) of bridges is a subject that has received consider-

able attention in recent years. Recent incidents such as the collapse of the I-35W Bridge in the US, give a clear indication of the importance of SHM. In practice, bridge assessment includes several measures such as inspection, data interpretation, and development of engineering recommendation. Inspection as a starting point requires reliable and use-ful structural information on global and local performance, for which visual inspection, instrumentation, and monitoring have been recognized as indispensable tools.

For global structural assessment in particular, vibration monitoring has been widely used. Vibration characteristics, captured from vibration monitoring, provide global infor-mation on structural behaviours such as stiffness, connectivity, boundary conditions, mass distribution and energy dissipation. The underlying principle of vibration-based structural assessment is that structural changes or defects will create changes in the dynamic re-sponse that can be detected from the changes in vibration characteristics. In other words, changes in frequencies, mode shape, and modal damping can be used as indicators of the changes of physical properties of structures such as mass distribution, stiffness, con-nectivity, boundary conditions, and energy dissipation. Extensive works have been done on developing methods and algorithms for damage detection using vibration character-istics. [Doebling et al., 1996] present a comprehensive list of literature in damage detec-tion and divide the detection algorithms into four levels of increasing complexity. They are: level 1 determination that damage is present in the structure, level 2 determination of the geometric location of the damage, level 3 quantification of severity of damage, and level- 4 prediction of the remaining service life of the structure.

Although many algorithms have been developed, most of them have been of theo-retical or computational nature and verified in finite element simulation or laboratory-scale experiments. There are only few studies that involve verification on a full or near full-scale test of an actual structure subjected to controlled damage. This is understandable since progressive damage tests are costly and sometimes impossible. Therefore, vibration measurement during a progressive damage test of full-scale structure is a very important learning opportunity. From such measurement, one can observe evolution of dynamic characteristics, validate damage detection methods, and formulate the baseline criteria for typical structural deteriorations. Notable studies on the full-scale test damage detec-tion of the bridge are the Z24 Bridge in Switzerland [Peeters and Roeck, 2001] and the Alamosa Canyon Bridge [Farrar et al., 2000]. Both studies have provided a benchmark for damage detection methods and emphasized the importance of environmental effect on the dynamic characteristics of the bridge.

Realizing the importance of a full-scale bridge damage test, observations and lessons learned from such a test are presented in this paper. The paper summarizes the process of vibration measurement and destructive test, analyses the data and presents the results of vibration analysis. Ambient vibration measurements were conducted before, during and after introduction of damage. Sensitive features that can be utilized as indicators of dam-age were extracted from vibration characteristics.

307

Description of S101 Overpass Bridge and Sensing System 15-2

damaged pier

360

602:3

1200 12003200

470

damaged pier

120 120

View of the S101 bridge and bridge dimension F.15-1

15-2 Description of S101 Overpass Bridge and Sensing System

The tested bridge is the S101 bridge overpass located in Reibersdorf, Upper Austria, which is west of Vienna, Austria. The bridge crosses over the motorway A1 Westautobahn Austria. It is a post-tensioned concrete bridge with a main span of 32 m, side spans of 12 m, and a width of 6.6 m (F.15-1). The deck is continuous over the piers and is built into the abutment. The bridge, built in 1960, was a typical overpass in the motorway. Although there were no known structural problems, the bridge had to be demolished to allow a space for an additional lane underneath. Before demolition, a series of vibration tests was carried out by VCE. The authors participated in a two-day measurement from 10 until 11 December 2008. On the first day, preliminary experimental vibration tests were conduct-ed. The purpose of the tests was to obtain an initial estimate of the bridge modal param-eters. An ambient vibration test was conducted with the main source of vibration from the motorway traffic underneath the bridge. The sensing system consists of six triaxial-ac-celerometers CV-373 produced by Tokyo Sokhushin. The sensors measured accelerations at six measurement nodes. Due to limited number of sensors, six sets of sensor arrange-ments were utilized (F.15-2). Two sensors (i. e. node A and B) were kept at the same place throughout the measurement to provide reference for time-synchronization. Four other sensors were the roving sensors that moved from one end to the other end of the bridge. To measure the bridge in undamaged condition, three sensor arrangements were utilized (i. e. sensor arrangement 1–3). On the second day, 11 December 2008, a destructive test was conducted. At this time the sensing system consisted of three sensor arrangements (i. e. sensor arrangement 4–6), where they were mainly placed on the bridge side near the location of damage. Like on the first day, two sensors were placed in the middle of the bridge span and kept at the same place throughout the damage process as a reference for previous measurement. During the two-day measurement, temperature conditions were relatively equal with an average temperature of –3°C.

308


A

Bxz

@5.3 m

@4 mto Vienna

Sensor arrangement #1 Sensor arrangement #2



A

xz

@5.3 m

to Vienna

A

B xz

@5.3 m

@4 m to ViennaA

B xz

xz

xz

@5.3 m

to Vienna

3.25 m 3.25 m4 m

A

B

xz

@5.3 m

@4 m to Vienna to Vienna

B

A

B

xz

3.25 m 4.88 m

@5.3 m

3 24 5

3 24 1 3 24 1

3 24 1

3

3

2

21

4 5

5

Hydraulicjack

Steel columntemporary support

1st layer of column is cut (one layer is about 5 cm)

2nd layer of column is cut

Intact Condition Damage 1 Damage 2 Damage 3

Releasing pressure in hydraulic jack, 1 cm verticalsettlement was observed

1 cm

2 cm 2.7 cmGap between steel column and bridge deck

Steel plate

Hydraulic jack lowered 3 cm,column settlement 2.7 cm.No further settlement. Pier columnwas completely suspended

Hydraulic jack lowered,2 cm vertical settlement was observed

(Data Frame 1–10) (Data Frame 11) (Data Frame 12–15) (Data Frame 16–19)

(Data Frame 1–10) (Data Frame 30–33) (Data Frame 34–37)

Damage 4 Damage 5 Retrofitted

Steel plated inserted,column rested onsteel plate

Cutting pier‘s section

Removing pier‘s section

Sensor arrangement for vibration measurement (note: A and B are the reference sensors)

Schematic figures of the complete damage process

F.15-2

F.15-3

309

Damage Scenarios and Finite Element Model 15-3

Damage code Frame no. Sensor arrangement Bridge condition

Undamaged 1–4 #1 Structure intact



Damage 1 11 #4 1st layer of column is sliced

Damage 2 12–15 #5 2nd layer of column is sliced

Damage 3 16–19 #6 1 cm vertical settlement

Damage 4 20–29 #6 2 cm vertical settlement

Damage 5 30–33 #6 No further settlement, column is completely suspended

Retrofitted 34–36 #6 Steel plate inserted

Damage stage, sensor position and data framing T.15-1

15-3 Damage Scenarios and Finite Element Model

F.15-3 illustrates the scenarios of damage simulated in this test. Damage was intro-duced to the structure by cutting the pier just above the footing. The cutting was made twice, the first was 2 cm layer of column (named hereafter as damage 1) and the second was another 2 cm (damage 2). During the cutting process, a steel column was placed alongside the pier and tightened to the pier with steel rods to provide temporary support. When the pier had completely severed from the footing cap, the temporary support was gradually released until the pier was completely suspended. During this time vertical set-tlement of the bridge at the pier location was recorded continuously until the total settle-ment reached 2 cm (damage 3 and damage 4). Finally, the pier was completely suspended and no further settlement was observed (damage 5). At the last stage, a steel plate was inserted to close the gap between pier and the footing. In this condition the pier rested on the plate and the stage was named retrofitted stage. Throughout the damage process an ambient response of the bridge was recorded at the sampling rate of 100 Hz. The records were divided into 37 time-windows (frames) of five minutes signal each. Details of the damage stage, sensor position and data framing are listed in T.15-1.

In order to provide a reference for comparison of experimental modal analysis, a Finite Element Model (FEM) was built in [SAP 2000]. The model utilizes 360 frame elements for columns and beams, and 504 shell elements for the deck slab. It is made using as-built drawings by assuming the concrete material of 2400 kg/m3 density and the Young's mod-ulus of 2.48 ⋅ 1010 N/m. Interaction with soil is not taken into consideration in the model and all degrees of freedom of the piers are restrained at the footings. At the abutments, the longitudinal beam and the slab are assumed to be fixed. This assumption was con-sidered after observing the real condition of the bridge. F.15-4 shows the corresponding mode shapes of the undamaged bridge. FEM reveals that the vertical modes are predomi-nant, and the bridge is relatively stiffer in transverse direction than in vertical direction.

310


1 20

10

20

30

40

01 20

10

20

30

40

01 20

10

20

30

40

0

1 20

10

20

30

40

01 20

10

20

30

40

01 20

10

20

30

40

0

Den

sity

Ref A-X

µ = 0.439cv = 2.06 %

Ref A-Y

µ = 0.434cv = 4.66 %

Ref A-Z

µ = 0.363cv = 2.16 %

Den

sity

Ref B-X

µ = 0.380cv = 2.43 %

Ref B-Y

µ = 0.358cv = 1.62 %

RMS [m/s2] RMS [m/s2] RMS [m/s2]

Ref B-Z

µ = 0.533cv = 2.76 %

xyz

xyz xy

z

xyz

Mode 1 : f = 4.07 Hz Mode 2 : f = 6.08 Hz

Mode 3 : f = 10.72 Hz Mode 4 : f = 12.85 Hz

Distribution of RMS of acceleration recorded at reference channels

Mode shapes of the bridge generated by FEM

F.15-5

F.15-4

311

Methodologies for Vibration Analysis 15-4

Sampling time

Mean of RMS of acceleration response at reference sensors (m/s²)

A-longitudinal A-transverse A-vertical B-longitudinal B-transverse B-vertical

1 minute 0.438 (0.021) 0.434 (0.047) 0.3623 (0.022) 0.380 (0.024) 0.357 (0.016) 0.533 (0.028)

5 minutes 0.447 (0.013) 0.446 (0.036) 0.369 (0.017) 0.387 (0.019) 0.364 (0.012) 0.545 (0.015)

all data 0.461 0.484 0.391 0.407 0.379 0.558

Note: value in the bracket denotes the coefficient of variation

RMS of acceleration measured on reference sensor A and B (longitudinal, transversal and vertical direction)

T.15-2

Dominant modes are well separated within the range of 3–18 Hz. The 1st, 3rd and 5th mode correspond to the 1st, 2nd and 3rd bending respectively, while the 2nd and 4th mode are the torsion modes.

15-4 Methodologies for Vibration AnalysisIn this section methodologies employed to analyse vibration data are explained in

detail. At first, we examine the vibration level and test the stationary assumption. The am-bient responses were analysed in both frequency and time domain. In frequency domain the spectrogram analysis is used. In time-domain global system identification using ERA and local (single-node) identification are employed to check the consistency of modal parameter estimates.

15-4-1 Vibration Level Analysis

Preliminary data analysis in time domain is conducted to obtain information about vibration level and to verify stationary assumption. For these purposes the root mean square (RMS) values of the acceleration are calculated. Since only two sensor nodes were placed on the same position throughout the measurement (i. e. reference A and B in F.15-2), only the RMS of these records were relevant for comparison. To observe the stationary of the response, RMS values of accelerations are calculated for three cases: every minute, every five minutes and for the whole data. F.15-5 shows distribution of acceleration RMS for references A and B in three directions calculated from one minute sampling time. The figure shows that the RMS distributions fit the normal distribution. In all three directions, deviations of RMS are very small as denoted by the largest c.o.v of 4.7 %. The same results can be seen for the five minute time sampling (T.15-2), where the largest c.o.v is 3.6 %. The small c.o.v. indicates that the responses are relatively stationary. Also note from T.15-2 that the mean values of RMS of one-minute and five minute sampling-time differ only slightly with the mean value of RMS for the whole record, suggesting ergodicity of the response. These observations indicate that the responses recorded throughout measure-ment are stationary and ergodic.

312


15-4-2 Spectrogram Analysis

A spectrogram of the vibration response provides a close-up look on the frequency components of vibration as function of time. In this study a spectrogram plot shows pow-er-spectra-density (PSD) of acceleration computed at each time-window and normalized to the maximum value. The ordinate of spectrogram denotes the time-window (in this case frame number) that corresponds to the time when responses were sampled and the subsequent damage stage. The abscissa represents the frequency component of the ac-celeration. By observing a spectrogram plot, one can follow evolution of frequency com-ponents throughout the measurement.

15-4-3 NExT – ERA Global System Identification

Global modal parameters are derived from ambient acceleration response under the assumption of stationary random excitation. To extract modal parameters, the Natural Excitation Technique (NExT) [James et al., 1993] and Eigensystem Realization Algorithm [Juang and Pappa, 1985] are employed in this study. In the NExT the cross-correlation function (CCF) between reference and roving nodes is computed and treated as the free-vibration responses. Considering sensor arrangement, the global system identification is performed in two parts, one is for undamaged stage where fourteen measurement nodes are used, and the other is for damaged stage, where only six measurement nodes are used. For the damage stage, responses of six nodes are sampled simultaneously. For the undamaged stages, however, the responses were not sampled simultaneously, so that a time-normalization technique is required before starting the system identification pro-cedure. Assuming that the responses are stationary as indicated by the result of inves-tigation in the previous section, the relation between reference and roving nodes can be established. As is shown in [Siringoringo and Fujino, 2009], the relation between the response of reference node Rj and roving node (Xy ), both sampled at time tj , and the re-sponse of reference node Rk and roving node (Xik ), both sampled at time tk , can be defined as:

( )

( ) ( )( )

k k

ik k ij i

i i

R RX R X R

R R

PG G

P

ωω ω

ω= E.15-1

where ( ) * [ ( )] [ ( )]uyG m F u t F y t= and ( ) * [ ( )] [ ( )]uuP m F u t F u t= , respectively as defined in [Bendat and Pierson, 1980], and F denotes the Fourier transform and (*) is the complex conjugate. E.15-1 indicates that the cross-spectrum of roving nodes and the reference nodes measured at starting time tj are different from the cross-spectrum at starting time tk by factor of ( ) ( ) ( )RR RRy m P m JP m= . Therefore we can compute the cross-spectra of all sen-sors by multiplying each cross-spectrum response with its corresponding ( )y m factor. After computing cross-spectra, the cross-correlation function of each node is generated using inverse Fourier transform. By employing E.15-1 and selecting a sensor at location B as reference, responses from 14 nodes that were sampled in three different time bases (i. e. sensor arrangement #1, #2 and #3) can be normalized into one equal time base. Since

313

Methodologies for Vibration Analysis 15-4

there are four data frames in sensor arrangement #1, two data frames in sensor arrange-ment #2, and four data frames in sensor arrangement #3, a total of 32 time-normalized CCF data sets are obtained. Once the CCFs are calculated, the Hankel matrix is constructed to implement the ERA method.

( ) ( 1) ( 1)( 1) ( 2) ( )

[ ( 1)]

( 1) ( ) ( 2)

CCF k CCF k CCF k qCCF k CCF k CCF k q

H k

CCF k p CCF k p CCF k p q

+ + − + + + − =

+ − + + + −

E.15-2

where p and q are the user-defined quantities that represent the number of columns and rows in the Hankel matrix, respectively. To select the system order, the singular value decomposition (SVD) of the Hankel matrix is performed (i. e. \[ (0)] [ ][ ][ ]TH P D V= ), in which

\\[ ]D is a diagonal matrix of singular values that corresponds to the modal parameters.

Large singular values indicate the strong participation of the modes in the response. To realize the system matrices, only several large singular values (N ) are retained. The first N sub-vectors form the matrices DN , PN and VN that are used to generate the state matrix [A] according to the following equation:

1/2 1/2[ ] [ ] [ ] [ (1)][ ][ ]TN N N NA D P H V D− −= E.15-3

The quantity [ H(1)] in E.15-3 denotes the time-shifted Hankel matrix. [A] is the system state matrix, whose eigenvalues characterize the dynamic parameters of the system, and generate the natural frequencies and modal damping ratios. The eigenvectors of the state space matrix produce the mode shapes matrix of the structure.

15-4-4 Statistical Analysis of Global Modal Parameters

Variability is an inevitable nature of ambient vibration measurement. Different envi-ronment conditions, source of vibration excitation, and also noise in instrumentation may affect the response and the extracted modal parameters. To investigate the effect of vari-ability and to estimate the confidence bounds of identified modal parameters, a statistical analysis is essential. By quantifying statistical properties we can interpret the results with confidence. For this purpose, the Bootstrap method [Efron and Tibshirani, 1993] is em-ployed in this study. The Bootstrap method randomly selects and replicates the response from a limited number of records to create an ensemble average of a larger population of response. Statistical properties of the ensemble average are computed to determine the bounds of uncertainty. To implement Bootstrap analysis, a large number of CCF data sets was randomly selected from the available time-normalized CCF data, and the CCF ensembles are formed. On each ensemble, the CCF ensemble average is computed, and then treated as Markov parameter in the Hankel matrix of ERA. This procedure is repeated for a large number of times to form a histogram of the identified modal parameters. The confidence bounds of modal parameters are calculated by the percentile interval method [Bendat and Pierson, 1980] that computes the 95 % confidence limit by sorting the mod-

314


CCF1, CCF2, CCF3,…CCFNω1, ξ1, φ1

Ensemble 1(m component)

CCF1, CCF5, CCF3,…CCFMCompute CCF average

ERARandomly selected

ω2, ξ2, φ2

Ensemble 2(m component)



CCF: Cross-Correlation FunctionERA: Eigensystem Realization Algorithm

ωp, ξp, φp

Ensemble p(m component)


Estimate mean value and 95%

confidence bound


Flowchart of Bootstrap Analysis F.15-6

al parameters in an ordered list and defining the value of upper and lower 2.5 % percen-tile. The complete Bootstrap procedure is illustrated in F.15-6.

15-4-5 Local System Identification

Local system identification allows us to identify damping from single sensor accel-eration thus providing a way to observe spatial distribution of damping. It also provides comparison of natural frequencies in addition to global system identification (ERA) and spectrogram analysis. The identification procedure is as follows. At first the auto-spectra of single node acceleration are computed. By applying a bandpass filter for the frequency range of interest and the least-square smoothing technique [Savitzky and Golay, 1964], we obtain the single mode auto-spectra. The result is transferred to time-domain using inverse Fourier transform to obtain the single mode free-vibration response. Using the free-vibration response, the local modal damping ratio is extracted by the logarithmic decrement method as follows.

1

1

1 ln( )n

xn n xδ

+= , 1

1

m

nmn

δ δ=

= ∑ E.15-4

2 2 2(2 )

δ δξππ δ

= ≅+

E.15-5

In the equation above xn is the j-th peak of single-mode free-vibration response, nδ is the logarithmic decrement between xn and xn+1 , δ is the averaged logarithmic decre-ment, and Z is the averaged damping ratio.

315

Results of Vibration Analysis for Undamaged and Damaged Stages 15-5

35

30

25

20

Fram

e nu

mbe

r

Frequency [Hz]

15

10

5

5 10 150

35

30

25

20

Frequency [Hz]

15

10

5

0.9

1

0.8

0.7

0.5

0.6

0.4

0.3

0.2

0.1

5 10 150

Spectrogram of undamaged and damage stages. Vertical acceleration measured at reference A (left) and reference B (right)

F.15-7

15-5 Results of Vibration Analysis for Undamaged and Damaged Stages

Vibration analysis is conducted for the undamaged and damage stage. For damage stages, the analysis consists of three main parts:

1) during pier cutting (i. e. damage 1–4), 2) when the pier is completely suspended (damage 5), and 3) when a steel-plate was inserted to close the gap between pier and footing (retrofit-

ted).

During all stages the accelerations were recorded, with the main source of vibration com-ing from traffic. During the first stage of damage, some vibration noise from a cutting machine was noted. However, the effect of machine vibration to the total response can be considered negligible since in both undamaged and damaged stages the level of accel-erations remains constant, with the RMS measured at reference channel A and B ranged between 0.3 to 0.9 cm/s2. In the following section, the results of vibration analysis are pre-sented through spectrogram analysis, global and local system identification.

15-5-1 Spectrogram Analysis

The frequency content of response was observed in the frequency range 1 to 50 Hz. The dominant frequencies at the girder in vertical direction appear in the range of 1 to 15 Hz. F.15-7 shows the spectrogram of reference sensors A and B throughout the meas-urement. The ordinate consists of two parts: the undamaged part (frame numbers 1 to 10), and damaged part (frame number 11 onward). In the undamaged part, one can see four distinct vertical lines representing four natural frequencies within the range of 3 to

316


0 2 40

10

20

30

40

50

6 8Frequency [Hz]

CSD

of

acce

lera

tion

[cm

2/s]

10 12 14 16 18

0 0.5 1−0.1

−0.05

0

0.05

0.1

0.15

1.5 2Time [sec]

Cros

s-co

rrel

[cm

2/s2

]

2.5 3 3.5 4 4.5 5

Typical cross-spectra density and cross-correlation function of acceleration of the undamaged stage

F.15-8

14 Hz. The first line is around 4 Hz, the second line is around 6 Hz, the third and the fourth lines are around 9 Hz and 13 Hz respectively. Despite the fact that the amplitude of am-bient vibration was small, the frequency spectra show very clear peaks indicating well-separated modes and suggesting that the records have a high signal-to-noise ratio. The four vertical straight lines suggest constant peaks in frequencies plot and small variation of natural frequency estimates.

Unlike the undamaged part, the damaged part shows distinct variation of frequen-cies. Starting from frame number 11 one can observe the leftward shift of natural frequen-cies especially the fourth mode (13 Hz). The other modes show an apparent shift starting from frame 20 onward, which corresponds to the time when the bridge experienced 2 cm of vertical settlement. Leftward frequency shifts of the first, second and third modes con-tinue until frame number 34. The largest shifts were observed at the time when the pier was completely suspended indicating the significant reduction of stiffness. Starting from frame number 35 onward, we can observe a rightward shift of the natural frequencies. For the 1st mode, the frequency shifted back almost to its original position, while some residual frequency shifts were observed for the 2nd, 3rd and 4th modes. Note that frame 35 corresponds to the time when the steel-plate was inserted and the structure was in the “retrofitted” state. This result indicates that the steel-plate insertion reduces the vertical flexibility of the structure as evident by the rightward shift of the 1st and 3rd mode (all are bending), but not in the same degree as it reduces the torsional flexibility, as evident by residual frequency shift in 2nd and 4th mode (torsional modes). Results of the spectrogram analysis reveal the evolution of natural frequencies during damage stages.

317


Mode 1 : f = 4.01 Hz Mode 2 : f = 6.38 Hz

Mode 3 : f = 9.67 Hz Mode 4 : f = 13.14 Hz

4

00 10 20 30 40 50

0

1

–1

4

00 10 20 30 40 50

0

1

–1

4

00 10 20 30 40 50

0

1

–1

4

00 10 20 30 40 50

0

1

–1

Mode Mean frequency [Hz]

95 % confidenceinterval [Hz]

Damping[%]

95 % confidenceinterval [%]

1st bending mode 4.02 0.01 1.37 0.24

1st torsion mode 6.31 0.09 1.19 1.93

2nd bending mode 9.65 0.11 1.30 0.39

2nd torsion mode 13.37 0.22 1.45 1.21

Modal parameters of undamaged bridge identified by ERA

The first four modes of S101 bridge for undamaged condition identified by ERA

T.15-3

F.15-9

15-5-2 ERA Global System Identification and Statistical Significance of Modal Parameters

For each measurement node the first five seconds of CCF data are utilized as Markov parameter in Hankel matrix. Typical CCF and CSD of vertical acceleration of the undam-aged stage are shown in F.15-8. It can be seen that dominant modes clearly present and are well separated within the range of 3 to 18 Hz. T.15-3 lists the identified vertical modes of the undamaged stage along with their statistical properties. The corresponding mode shapes are shown in F.15-9. T.15-3 shows that variations of natural frequencies of the first four modes for undamaged stage are very small, suggesting no significant difference in natural frequencies during a two-day measurement of undamaged stage. For damping, the averaged damping ratios are from 1 to 1.5 %. Larger variances of damping ratios were observed especially for the fourth mode. Therefore it can be concluded that the uncer-tainty of damping estimates was greater than the natural frequency estimates.

318


1.81.61.41.21.0

Freq

uenc

y [H

z]

1st bendingmode

1st torsionmode

2nd bendingmode

Frequency change95% confidence

2nd torsionmode

0.80.60.40.21.8

3.5

3.0

2.5

Freq

uenc

y [H

z]

1st bendingmode

1st torsionmode

2nd bendingmode


2nd torsionmode

2.0

1.5

1.0

0.5

0

2.5

2.0

1.5

Freq

uenc

y [H

z]

1st bendingmode

1st torsionmode

2nd bendingmode


2nd torsionmode

1.0

0.5

0

60

50

40

Mod

al d

ispl

acem

ent

chan

ge [%

]

Damage3–4

Damage5

Damage3–4

Damage5

Identified change95% confidence

Retro-fitted

Retro-fitted

0.15 0.26 0.23 0.23 0.040.09

30

20

10

0

a) Damage 3 & 4 b) Damage 5

c) Retrofitted d) Modal displacement of pier-girder connection node

Mode Frequency [Hz] Damping ratio [%]

Damage 3 & 4 Damage 5 Retrofitted Damage 3 & 4 Damage 5 Retrofitted

1st bending mode 3.90 (0.13) 3.65 (0.05) 3.94 (0.07) 1.98 (3.19) 2.10 (1.31) 2.76 (2.62)

1st torsion mode 5.84 (0.08) 5.22 (0.20) 5.76 (0.05) 2.14 (1.23) 2.72 (2.54) 1.93 (1.05)

2nd bending mode 9.21 (0.13) 8.16 (0.39) 9.04 (0.06) 2.12 (1.25) 1.93 (3.91) 2.13 (0.63)

2nd torsion mode 11.76 (0.307) 10.28 (0.16) 11.06 (0.44) 1.49 (3.07) 1.23 (2.29) 1.48 (3.65)

Modal parameters of damaged bridge identified by ERA T.15-4

Identified changes of frequencies due to damage F.15-10

For damage stages, three sensor arrangements are available. However, for the com-parison of mode shapes we analyse only data from frame numbers 16 to 37, since the responses from those data frames have equal sensor arrangements (i. e. sensor arrange-ment no.6). In this arrangement there are six measurement nodes, five nodes aligned on one side of the span near to the damaged pier, while one node (sensor number 4) was located on the other side of the span. For computation of CCF in NExT, sensor number 4 is utilized as the reference. It should be mentioned that since all data were sampled simulta-neously, a time synchronization procedure is not required at this time.

Results of identification for damage stages are listed in T.15-4. In this table the results are divided into three groups: damage 3 & 4 (frame numbers 16 to 29), damage 5 (frames

319


Mode Frequency change [%]

Damage 3 & 4 Damage 5 Retrofitted

1st bending mode −3.01 −9.23 −2.01

1st torsion mode −7.49 −17.31 −8.86

2nd bending mode −4.51 −15.40 −6.27

2nd torsion mode −12.02 −23.09 −17.26

ERA-identified changes in frequencies due to damage T.15-5

30 to 33) and retrofitted stage (frames 34 to 36). F.15-10 shows the comparisons of the 95 % confidence bound estimated by the Bootstrap method and T.15-5 lists the identified change of frequencies as a result of damage. It can be seen in the figure and the table that for damage 3 & 4, natural frequencies of the second, third and fourth modes experience significant changes as denoted by frequency changes that are larger than the 95 % con-fidence bound. These changes,although small, can be considered statistically significant and be used with confidence as damage indicators. On the contrary, a frequency change of the first mode is statistically insignificant because its value is smaller than the 95 % confidence bound and thus cannot be used as damage indicator. In the damage 5 stage, the changes in natural frequencies of all modes become more significant. All frequency changes are now larger than the 95 % confidence bounds. For damping ratio (T.15-4), there is a slight increase in the mean value as a result of damage. The averaged values of damping for all four modes were between 1.2 to 1.5 % for undamaged structures with small bounds of 95 % confidence. These values increase slightly up to 2 % for damage 3, 4, and 5; and up to 2.7 % for retrofitted condition. Note, however, that in damage condi-tion the 95 % confidence bounds were significantly larger than during the undamaged stage. These large bounds indicate large variation in damping estimates. Therefore, even though damage caused changes in damping, they are statistically insignificant and can-not be used with confidence as damage indicators.

Another important aspect is the effect of damage on the mode shape. Simulation us-ing FEM suggested that when damage altered the support condition, significant changes in mode shapes resulted as shown in F.15-11. Two stationary points that were initially lo-cated at the pier-girder connections become only one or shifted next to the undamaged pier. This change is obvious because the pier that restrains vertical movement on the pier-girder-connection node does not function anymore in damage condition. Observation on identified mode shapes reveals a similar outcome. Unfortunately, due to the limited number of sensors, only half-span of mode shapes can be analysed. To compare these half-span mode shapes of a damaged bridge with the complete span mode shape of an undamaged bridge, the first and second modes (i. e. bending and torsion) are normalized to the maximum value that occurred in the midpoint of the span. Mode shape compari-sons are shown in F.15-11. In both modes, we can observe large modal displacements at the pier-girder connection during damage stages. The largest modal displacement was observed in damage 5, when the pier was completely suspended. In addition, during damage 5, the highest modal displacement points of the torsion mode shifts toward dam-aged pier as suggested by FEM.

320


−0.5

−1

0

0 10 20 30Bridge longitudinal direction [m]

Damaged pier

40 50

Und (mode 1)Dam (mode 1)Und (mode 2)Dam (mode 2)

60

0.5

Nor

mal

ized

mod

al d

isp 1

1.5

−0.5

−1

0


Damaged pier

40 50

Unda (01)Dam4 (20)Dam5 (30)Retr (36)

60

0.5

Nor

mal

ized

mod

al d

isp 1

1.5

−0.5

−1

0


Damaged pier

40 50

Unda (01)Dam4 (20)Dam5 (30)Retr (36)

60

0.5

Nor

mal

ized

mod

al d

isp 1

1.5

FEM generated mode 1 and mode 2

Experimentally identified mode 1

Experimentally identified mode 2

Mode shapes of undamaged and damaged stages F.15-11

To quantify the significance of the change in modal displacement, the 95 % confidence bounds of identified mode shapes are computed for all damage stages. For comparison, we compute the modal displacement at the pier-girder connection using FEM for the first and second modes in undamaged and damaged stages. For the undamaged stage, their values are 0.017 and 0.03 for the first and second modes, respectively. And for the dam-age 5 case, the values become 0.47 and 0.93, respectively. T.15-6 lists the identified values of modal displacement at the pier-girder node for undamaged, damaged and retrofitted cases. One can see that for undamaged stage, modal displacement is very small, 0.02 for modes 1 and 2. For damage 5 the values increase up to 0.28 and 0.57 for the first and the second modes, respectively. Note that the latest values are still below the upper-bounds of 0.47 and 0.93 as predicted by FEM. The values decrease at the retrofitted stage to 0.1 and 0.31 suggesting additional stiffness from the steel plate. Note that the effect of retro-fitting is more apparent in vertical bending mode than in torsional mode.

A comparison of the changes of modal displacements due to damage and the 95% confidence bounds is presented in F.15-10d. For mode 1, the changes in mean values are 0.03, 0.26 and 0.07 for damage 3 & 4, damage 5, and retrofitted stage respectively.

321


Mode Undamaged [Hz] Damage 5 [Hz] Retrofitted

FEM [Hz]

ERA[Hz]

Disc[%]

FEM [Hz]

ERA[Hz]

Disc[%]

FEM [Hz]

ERA[Hz]

Disc[%]

1st bending mode 4.07 4.02 −1.23 3.23 3.65 13.00 3.99 3.94 −1.25

1st torsion mode 6.08 6.31 3.78 5.07 5.22 2.96 6.04 5.76 −4.64

2nd bending mode 10.72 9.65 −9.98 7.60 8.16 7.37 10.58 9.04 −14.56

2nd torsion mode 12.85 13.37 4.05 10.64 10.28 −3.38 12.20 11.06 −13.05

Undamaged Damage 3 &4 Damage 5 Retrofitted

Mode 1 (mean) 2.37 5.37 28.56 10.07

95 % confidence 0.05 0.15 0.26 0.09

Mode 2 (mean) 2.26 22.34 57.29 31.75

95 % confidence 0.11 0.23 0.23 0.04

Comparisons of FEM and ERA frequencies

Comparison of modal displacement value at the pier-girder connection with respect to damage stages (values are in %)

T.15-7

T.15-6

These changes are significantly larger than the 95 % confidence bounds. For mode 2, the changes in mean values are even larger: 0.2, 0.5 and 0.29 for damage 3 & 4, damage 5 and retrofitted stage respectively. These changes are also significantly larger than the 95 % confidence bounds indicating that for both modes, the changes of modal displace-ment on the pier-girder connection are statistically significant and can be used as damage indicator.

15-5-3 Comparison of FEM and ERA-Generated Mode Shapes

Three FEM models were built to simulate condition of undamaged, damage 5 and retrofitted stages. To simulate damage 5, one pier in the model is suspended by releasing all of the restraints at the footing level and reducing the pier height by 4 cm. In the ret-rofitted stage, the model is similar to the undamaged one, but the restraint of one pier is modified from the fixed to partial-hinge condition. In the latter condition, only the vertical and rotational displacement from the x- and y-axis are restrained. This restraint model is selected to represent the condition of plate insertion between the pier and the footing.

Comparisons of the first four modes of the models computed numerically from modal analysis using SAP-2000 software and the ERA identified frequencies are listed in T.15-7. From this table, it can be seen that the results of ERA are within reasonable agreement with the FEM results in all three cases. In the undamaged case the largest frequency dis-crepancy is 9.9 %, which occurs at the third mode. Note that for undamaged stage the ERA frequencies of modes 1 and 2 are very close to that of FEM. In this study no model updating was performed. The differences between FEM and ERA frequencies are thought to be attributed to the difference between the Young's modulus of concrete used in the model and that of the actual structure considering the age of the bridge. Nevertheless,

322


43.5

4.5

0.2 4.2 8.2 12.2 17.5 22.8 33.428.1Sensor location [m]

44 56524838.7

5.55

Freq

uenc

y [H

z]

66.5

7.57

8

0

−10.2 4.2 8.2 12.2 17.5 22.8 33.428.1

Sensor location [m]44 56524838.7

2

1Dam

ping

[%]

3

5

4

6

mode 1 mode 2

Spatial distribution of frequency and damping for undamaged stage F.15-12

one can see from the results that the decreases of frequencies during damage 5 as sug-gested by FEM are well verified by ERA results. Likewise, the increase of frequencies during retrofitted stage identified by ERA can be represented in FEM by the change of boundary condition of the damaged pier.

15-5-4 Local System Identification

F.15-13 shows the spatial distribution of natural frequency and damping ratio of the undamaged stage identified from single node acceleration response. The figure shows the distribution of frequency and damping ratio of the first and second modes in three spans: side-span 1 (0.2 to 14 m), middle span (14 to 44 m) and side-span 2 (44 to 56 m). For the first mode, the average value of frequency is around 4.0 Hz, in all three spans. Note that the damping ratio does not show large variation spatially, with the average of damp-ing ratio around 1 %. Both estimates are in agreement with the results of the ERA global system identification. It should be mentioned, however, that variation of the damping ratio for the nodes that are close to the pier is larger than that of other nodes.

For the second mode, frequency is identified rather constantly around 6.3 Hz in three spans. Damping estimates, on the other hand, show a distinct pattern. In the middle span, the average damping is 1.3 %, the results that closely match the ERA results. Side-spans’ damping are generally higher than that of the middle span. These, however, are followed by larger variation in damping estimates of each node as compared to that of the mid-dle-span nodes. The large variation makes it difficult to consider the result as statistically

323


0 8

3.5

3

4.5

4

5.5

5

6.5

6

7

11

Freq

uenc

y [H

z]

17 22 27 0 8

3.5

3

4.5

4

5.5

5

6.5

6

7

11 17 22 27 0 8

3.5

3

4.5

4

5.5

5

6.5

6

7

11 17 22 270 8

3.5

3

4.5

4

5.5

5

6.5

6

7

11

mode 1 mode 2

17 22 27

0 8

1

0

3

2

4

5

6

11Sensor location [m]

Dam

ping

[%]

17 22 27 0 8

1

0

3

2

4

5

6


17 22 27 0 8

1

0

3

2

4

5

6


17 22 27 0 8

1

0

3

2

4

5

6


17 22 27

Damage 3 Damage 4 RetrofittedDamage 5

Spatial distribution of frequency and damping for damaged stages F.15-13

significant. This may be explained as follows. The second mode at the side spans is not well excited by ambient vibration as evident by significantly smaller peaks in frequency compared to that of the first mode. Considering that both ends of the side span firmly rest on the abutments, and that the side-spans are relatively short (i. e. 12 m), the torsional motions may not contribute largely to the total motion of the side span. The frequency peaks of torsional modes identified from single nodes on the side-span are not so sharp and small in amplitude. This generates a wide-band of frequencies under the peak, which yields large local damping estimates.

F.15-14 shows the spatial distribution of frequency and damping of the first and second modes identified from single node acceleration during damage stages. The fig-ure clearly shows that the changes in frequencies due to damage are observable from all sensor nodes. There is no significant variation in spatial distribution of frequency dur-ing damage stages. For the first mode, frequency of 4 Hz is estimated from most of the sensor nodes in damage 3, damage 4 and retrofitted condition. The largest change for this mode, 3.6 Hz, occurs during damage 5 and is estimated by all sensor nodes. For the second mode, the change is observable from damage 4 where the frequency shifts to 5.8 Hz. A further decrease is evident in damage 5 (i. e. 5.5 Hz), before increasing to 5.8 Hz in retrofitted condition. Note that spatial variation of the second mode is very small in each damage stage. For damping estimates, relatively large variations were observed in

324


0.9

0.8

0.7

0.6

0.5

Nor

mal

ized

aut

o-sp

ectr

a va

lue

Dimension number [m]

0.4

0.3

0.2

0.1

10 20 30 40 50 60 70 80 90 10000

1.0

Example of 100 data-points acceleration auto-spectra between 3 and 7 Hz used in calculation of Mahalanobis distance

F.15-14

each damage stage. For damage 3, the average values of the damping ratio are 1 to 3 % for the first mode, and 1.5 to 4 % for the second mode. Note that for the second mode of damage 3 slightly large damping estimates were observed on sensors 3 and 5, which are located on the side span. The reason behind this is as explained in the damping estimate of the side-span of the undamaged stage. Damping estimates slightly increase for dam-age 4 & 5 with the average values of 2.5 to 3 %. Although some spatial variations of damp-ing are present during the two damage stages, no significant local damping changes are observed. During retrofitted stage, damping decreases slightly with the average value of 2 %. It should be mentioned that despite some small spatial variations, the values of local damping estimates are within the same range of global damping estimated by the ERA global system identification.

15-6 Damage Detection Using Multivariate Outlier Analysis

Damage detection using statistical pattern recognition has gained increased atten-tion recently. The main idea is to combine the use of damage-sensitive features and sta-tistical novelty detection method to detect the presence of damage. One such method is outlier detection. Outlier is an element of a data set that appears inconsistent with the rest of data and is thus perceived to be governed by other mechanisms. The advantage of this approach over modal-based damage detection is that it only requires data from un-damaged structures. Based on these data, the statistical pattern of undamaged structures is formulated and utilized as a baseline for evaluation of future data. When the statistical

325

Damage Detection Using Multivariate Outlier Analysis 15-6

property of future data is inconsistent with that of the baseline, they will be considered as possible outliers.

In the case of univariate data, one can detect the outliers by simply employing statisti-cal deviation such as mean and standard deviation. For multivariate data that consist of m variables and n observations, outlier detection is more complicated. A common approach that is based on univariate detection approach is the discordancy test using Mahalanobis squared distance [Worden et al., 2000]:

1( ) ( ) [ ] ( )TMD u u uµ µ−= − −S E.15-6

where ( )MD u denotes the squared Mahalanobis distance of multivariate data u = [u1u2 …uN ]T, with mean values 1 2[ ]T

NU M M M= and covariance matrix S.

15-6-1 Feature Selection

To implement outlier detection for structural health monitoring, the first and arguably the most important step is to select the damage sensitive feature. The feature should be sensitive to damage and can be preferably extracted directly from measurement with-out too much preprocessing. The use of outlier detection and several damage sensitive features have been reported in literature. The study by [Worden et al., 2000] utilized the transmissibility function of acceleration response, whereas [Mustapha et al., 2007] used the waveform. Static-strain data in conjunction with auto-regressive integrated mov-ing average (ARIMA) is used by [Omenzetter et al., 2004] to observe different structure changes during construction. [Gul and Catbas, 2009] used the feature vectors of auto-regressive models (AR) of free-vibration response, which was derived from ambient re-sponse by Random Decrement technique. In this study we investigate the feasibility of auto-spectra of acceleration as damage sensitive feature. The auto-spectra contain at least two basic pieces of information of structures that are sensitive to damage: natural fre-quency – indicated by spectra peaks, and damping – indicated by the sharpness of the peaks. It is a simple feature that can be derived directly from ambient measurement and it captures changes in natural frequency and damping simultaneously.

To implement the method, a number of data points (m ) within the frequency range of interest are selected from spectra plot and treated as a multivariate feature vector. The procedure is repeated for several data sets under the same undamaged condition. In order to provide a clear distinction between inlier and outlier there needs to be some threshold value. In this study we closely follow the method by [Savitzky and Golay, 1964], in which the threshold value is set by Monte Carlo simulation using the following steps:

1) Creating a data bank for undamaged condition. For this purpose, 100 equally-sampled data points (m = 100) are selected as feature vector from auto-spectra of references A and B during undamaged stage. Data in the feature vector are within the frequency range of 3 to 7 Hz. Since there are only 10 data frames for undamaged condition, only 20 numbers of observation (n) are available. This is considered insuf-ficient. To provide an appropriate mean and covariance matrix for undamaged condi-tion a larger number of observation is required. For this purpose, the feature vectors

326


290

280

270

260

250

Max

imum

squ

ared

Mah

alan

obis

dis

tanc

e

Number of trials

240

230

220

1000 2000 3000 4000 5000 6000 7000

Max value of each trial99.99 % percentile: 295

8000 9000 100000210

300

Results of Monte Carlo simulation for outlier threshold setting F.15-15

were randomly copied 500 times, and for each copy Gaussian random vectors with rms of 0.01 of the maximum value were added to simulate noise.

2) Computing the largest Mahalanobis squared distances. The largest values of Ma-halanobis distance were calculated exclusively for each observation. This procedure was repeated for a large number of trials (in this study 10 000 trials) and all the larg-est values are ordered. The threshold is then defined as 99.99 percentile value of the largest Mahalanobis squared distance in all trials.

After defining the threshold, Mahalanobis distances for all feature vectors in each damage stage are computed and their status as outliers or inliers are conformed.

15-6-2 Results of Outlier Detection for Damage Stages

The first step in implementing the outlier detection is to select the feature vector of undamaged stage. F.15-14 shows an example of 100-dimensional feature vector data se-lected from the auto-spectrum of reference sensor B of undamaged stage sampled over the frequency range of 3 to 7 Hz. Within this range, the spectrum is characterized by two peaks that correspond to modes 1 and 2. The next step is to set the threshold value. For this purpose Monte Carlo simulation was performed. In each simulation, 500 feature vec-tors were generated using the procedure explained in section 15-6-1, and the mean vec-tor µ as well as the covariance matrix [S] were calculated. F.15-15 shows the maximum values of Mahalanobis distance after 10 000 trials, from which the 99.99 percentile is se-lected as the threshold value. In this case the Mahalanobis distance set for the threshold value is 295.

After obtaining the threshold value, computation of Mahalanobis distance for dam-age stages is performed. F.15-16 shows the values of Mahalanobis distance for four dam-age cases. The figure consists of two parts, one is a training set, which represents undam-aged stage, and the other is the testing sets, obtained from auto-spectra of reference

327

Damage Detection Using Multivariate Outlier Analysis 15-6

1500

1250

1000

Mah

alan

obis

dis

tanc

e

750

500

250

200 400 600 800 1000 1200

UndamagedDamage 1 & 2

00

1500

1250

1000

750

500

250

200 400 600 800 1000 1200

UndamagedDamage 4

00

1500

1250

1000

Mah

alan

obis

dis

tanc

e


750

500

250

200 400 600 800 1000 1200

UndamagedDamage 3

00

1500

1250

1000


750

500

250

200 400 600 800 1000 1200

UndamagedDamage 5

00

Mahalanobis distance plots for all damage stages F.15-16

sensors in damage stages. In the training set, the mean vector and covariance matrix are estimated by following the procedure in section 15-4-6 for 1000 trials. To simulate a real-istic condition of the feature vector for undamaged structure, Gaussian random noise is added in the auto-spectra. Simulation yields the horizontal threshold value of 295, which represents 99.99 % confidence level of detection. One can see from F.15-16 that all points in the undamaged stage fall well below the threshold line. There are no false negatives observed, indicating that the threshold line clearly separates the condition of damage and undamaged.

For damage 1 & 2, and damage 3 most of the points are detected as outliers. False positives, however, are obtained from two points in each damage stage. These two points are from data sets with the frequencies of 3.8 and 3.9 for mode 1, and frequencies of 6.1 and 5.9 for mode 2, respectively. The two false positive data sets are from frames 11 and 12 that correspond to the time when damage is still in progress. Therefore, it is under-standable that the damage has not changed the structure significantly. When damage has significantly changed the characteristics of the structure such as the case of damage 4 and damage 5, all points are unambiguously detected as outliers. Note that the distance between undamaged points and that of damage points of damage 4 and damage 5 are increasing as damage becomes larger. This is a rather expected result since the larger the damage is the more the auto-spectra deviate from the undamaged pattern. In these two cases, the distance between outliers and threshold line can be used as indicator of dam-age severity.

328


15-7 Summary and ConclusionsObservations and lessons learned from the progressive damage test of an overpass

bridge were presented in this paper. The study described the process of vibration meas-urement and presented the results of vibration analysis. Through systematic data analysis that includes spectrogram analysis, global and local system identification, dynamic char-acteristics of the bridge before, during and after damage are identified and evaluated. In evaluation of global modal parameters, in particular, statistical analysis by means of Bootstrap method was employed to quantify the confidence level and hence facilitate the statistical interpretation of the results. In addition to data analysis, feasibility of multivari-ate outlier-detection using auto-spectrum in identifying damage presence and severity were investigated. Important results of the study are summarized as follows:

1) A non-uniform pier settlement simulated as damage in this study, affects global stiff-ness of structure significantly. This is evident by the significant change in frequency of low-order modes. The effects are more obvious in torsional modes than in bend-ing modes as indicated by larger changes in frequencies of torsional modes than that of bending modes. Accordingly, this finding can be used as an indicator of the presence of a non-uniform pier settlement.

2) Damage in the form of pier settlement also alters the mode shapes locally. Modal dis-placements at the pier-girder node for damage cases significantly increase suggest-ing immediate effect of constraint-losing at the boundary condition. The changes are evident from the bending and torsional low-order modes and are well predicted by FEM. It should be mentioned that the effects of damage on mode shapes are more obvious in torsional modes than in bending modes as indicated by larger changes in modal displacements of pier-girder nodes of torsional modes than that of bending modes.

3) In general damping increases as the damage level increases. Estimations from ERA indicate that damping in damage stages increases up to 2.5 to 3 % from previously 1.5 % for undamaged stage. Spatial distribution of damping ratios was also evaluated by extracting individual damping ratios using autocorrelation and logarithmic decre-ment technique. Spatial distribution of damping reveals that damping of side-spans is generally higher than that of the middle span. During damage stages, some spatial variations of damping were observed. These spatial variations, however, do not reveal any distinct patterns that can be used conclusively as indication of damage location.

4) Feasibility of multivariate outlier detection using auto-spectra as damage features was investigated in this study. The results show that the use of Mahalanobis distance can detect the presence of damage at the earliest stage (i. e. damage 1). When dam-age has significantly changed the characteristics of the structure such as the case of damage 4 and damage 5, all points are unambiguously detected as outliers indicat-ing the clear presence of damage. The distance between threshold line and damage points in outlier detection is increasing as damage becomes larger. This distance can be used further as indicator of damage severity.

329

References 15

Members of the Bridge and Structure Laboratory measurement team posing with Dr. Helmut Wenzel and colleagues from VCE during the destructive testing.From left to right: Tomonori Nagayama, Helmut Wenzel, Dionysius Siringoringo, Chondro Tandian, Hirotaka Miura, Di Su, Paul Jaornik, Martin Stöger, Monika Widmann

F.15-17

Acknowledgement

The authors wish to express their sincere gratitude to Dr. Helmut Wenzel, Robert Veit-Egerer and Monika Widmann from VCE Vienna Consulting Engineers ZT GmbH for this precious test opportunity, and acknowledge their fruitful discussions and assistance dur-ing the authors’ technical visits. This study was also supported by Japan Society for the Promotion of Science. Full version of this report has been published in the Journal of En-gineering Mechanics ASCE [Siringoringo et al., 2013]. The University of Tokyo, Bridge and Structure Laboratory involved in the measurement include F.15-17.

ReferencesBendat, J. S. and Pierson, A. G., 1980. Engineering Applications of Correlation and Spectral

Analysis. New York: John Wiley.Doebling, S. W., Farrar, C. R. and Prime, M. B., 1996. Damage Identification and Health

Monitoring of Structural and Mechanical Systems from Changes in their Vibration Charac-teristics: a Literature Review. Los Alamos National Laboratory Report No. LA-13070-MS.

Efron, B. and Tibshirani, R. J., 1993. An Introduction to the Bootstrap. New York: Chapmann & Hall, Monographs on Statistics and Applied Probability 57.

Farrar, C. R., Cornwell, P. J., Doebling, S. W. and Prime, M. B., 2000. Structural Health Moni-toring Studies of the Alamosa Canyon and I-40 Bridges. Los Alamos Laboratory Report No. LA-13635-MS.

330


Gul, M. and Catbas, N., 2009. Statistical Pattern Recognition for Structural Health Monitor-ing Using Time Series Modeling: Theory and Experimental Verifications. Mechanical Sys-tems and Signal Processing 23(7):2192–2204.

James, G. III, Carne, T. G. and Lauffer, J. P., 1993. The Natural Excitation Technique (NExT) for Modal Parameter Extraction from Operation Wind Turbines. Sandia Report SAND92-1666, UC-261.

Juang, J. N. and Pappa, R. S., 1985. An Eigensystem Realization Algorithm for Modal Param-eter Identification and Model Reduction. Journal of Guidance, Control and Dynamics 8(5):620–627.

Mustapha, F., Worden, K., Manson, G. and Pierce, S. G., 2007. Damage Detection Using Stress Waves and Multivariate Statistics: an Experimental Case Study of an Aircraft Com-ponent. Strain 43(1):47–53.

Omenzetter, P., Brownjohn, J. M. W. and Moyo, P., 2004. Identification of Unusual Events in Multi-Channel Bridge Monitoring Data. Mechanical Systems and Signal Processing 18(2):409–430.

Peeters, B. and DeRoeck, G., 2001. One-Year Monitoring of the Z24-Bridge: Environmental Effects versus Damage Event. Earthquake Engineering and Structural Dynamics 30(2): 149–171.

SAP 2000. Manual Analysis Reference Manual. Computer and Structures Inc, 1995 Berkeley, California, USA.

Savitzky, A. and Golay, M. J. E., 1964. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry 36(8):1627–1639.

Siringoringo, D. M. and Fujino, Y., 2009. Noncontact Operational Modal Analysis of Struc-tural Members by Laser Doppler Vibrometer. Computer-Aided Civil and Infrastructure Engineering 24:249–265.

Siringoringo, D. M., Fujino, Y. and Nagayama, T., 2013. Dynamic Characteristics of an Over pass Bridge in a Full-Scale Destructive Test. Journal of Engineering Mechanics ASCE 139(6):691–701.

Worden, K., Manson, G. and Fieller, N. R. J., 2000. Damage Detection Using Outlier Analysis. Journal Sound and Vibration 229(3):647–667.

vibration study and application of outlier analysis to the

Documents