Adewuyi a., y z. Wu (2009) Vibration-based Structural Health Monitoring

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VOL. 4, NO. 3, MAY 2009 ISSN 1819-6608

ARPN Journal of Engineering and Applied Sciences

2006-2009 Asian Research Publishing Network (ARPN). All rights reserved.

www.arpnjournals.com

VIBRATION-BASED STRUCTURAL HEALTH MONITORING

TECHNIQUE USING STATISTICAL FEATURES FROM

STRAIN MEASUREMENTS

A. P. Adewuyi and Z. S. WuDepartment of Urban and Civil Engineering, Ibaraki University, Hitachi, Japan

E-Mail: [email protected]

ABSTRACTA statistical vibration-based damage identification algorithm to assess the stability of the measurement data,

detect and locate damage in civil structures, where variability in response and modal parameters due to measurement noiseand environmental influence is often inevitable, is presented in this paper. The method exploits the regression analysis ofpeak values of the magnitudes of frequency response function (FRF) of target sensors relative to the reference wherein thestatistical features are employed for data reliability assessment and damage localization. Through experimentalinvestigation of a flexural structure using conventional strain gauges and long gauge fiber Bragg gratings (FBG) sensors,the importance of the technique for civil SHM is established and presented in an easy-to-interpret graphical format foreffective implementation of results. The statistical approach is very effective for damage localization using strain data.

Keywords: damage identification, statistical features, measurement noise, dynamic strain, FBG sensors, structural health monitoring.

INTRODUCTIONProgressive deterioration of civil infrastructure

begins once they are built and subjected to normalcontinuous and occasional excessive loading, and adverseenvironmental conditions. Because the intrinsic changesthat adversely affect the immediate or future performanceof a structural system are usually unknown a priori,prompt and intensive monitoring of structural systems isvery important. The extension of vibration-based damageidentification (VBDI) techniques to civil infrastructure isincreasingly receiving attentions because of rise in socialand economic demands for structural integrity and safety.During the past few decades, a significant amount ofresearch has been conducted in the area of nondestructivedamage detection via changes in modal responses of astructure. A number of model-free damage identificationtechniques have been developed and successfullyinvestigated primarily because of they are computationallysimple without any need for an updated numerical model.Most notable among these techniques are based on naturalfrequency, mode shape curvatures, modal flexibility andits derivatives, modal stiffness, modal strain energy,frequency response function and its curvature, and powerspectral density (PSD). Physical quantities most relevantand sensitive to the structural properties of interest areselected for monitoring purposes. Extensive literaturereviews and advances on VBDI have been reported byDoebling et al. (1996), Sohn et al. (2003) and Carden andFanning (2004). Li and Wu (2008) and Wu and Li (2007)also develop modal macro-strain vector (MMSV) methodof damage identification using the modal parametersextracted from dynamic macro-strain data recorded byarrays of long-gauge FBG sensors distributed throughoutthe full or some partial areas of the flexural structures.

Despite the numerous achievements made so far,the search for more reliable strategies for both damagelocalization and quantification in large-scale civil

structures is still in progress due to inevitable variability inmeasurement data as a result of measurement error andenvironmental factors. So, the ability to correctlydistinguish changes in the modal properties caused bydamage from those arising from variations in themeasurements induced by electrical noise and otherenvironmental conditions is an essential issue requestingserious attention for successful civil SHM. Thus, theprocess of vibration-based SHM can be fundamentallyconsidered as that of statistical pattern recognition. Inquest for statistical damage identification algorithms thatwould take into consideration all the aforementionedfactors, Pape (1993) proposes a technique to identifydamaged parts using statistical methods and measurednatural frequencies. Damages are detected by assessingresonant frequencies that fall outside the mean standarddeviations. The shortcoming of the approach is its inabilityto detect smaller defects. Brincker et al. (1995) use astatistical analysis method independent of the knowledgeof the input signal to detect damage in two concrete beamswith different reinforcement ratios using changes in themeasured vibration frequencies. The method is based onsignificance indicator for any modal frequency or dampingratio determined by scaling the observed changes by theestimated standard deviation of the parameters or a unifiedsignificance indicator expressed as the summation offrequency and damping significance indicators overseveral measured modes. It was noted that measuredmodal parameters with high confidence are weighted moreheavily in the indicator function. Similar to otherfrequency-based damage identification methods, thesignificance indicator proved to be a sensitive structuraldamage indicator, but incapable to localize damage.Doebling and Farrar (1997) develop a statistical procedurethat uses measured coherence functions to estimate theuncertainty bounds on the magnitude and phase of the

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frequency response functions (FRFs), and prorogate theuncertainty to modal parameters.

In this study, a statistical VBDI algorithm based

on the regression analysis of peak values of themagnitudes of FRF of target sensors relative to thereference is presented for data reliability assessment anddamage localization. The proposed method is suitable forcivil SHM, where variability in response and modalparameters due to measurement noise and environmentalinfluence is often inevitable, to assess data quality prior todamage identification. Also, the ability to effectivelymanage and make sense of enormous amounts of datacollected under continuous monitoring process for aneffective diagnostic and/or prognostic system is an addedadvantage. The effectiveness of the method is establishedthough experimental investigations on a flexural structure

by using strain gauges and long-gauge fiber Bragg grating(FBG) strain sensors.

VIBRATION-BASED STRUTURAL HEALTH

MONITORING USING STATISTICAL FEATURESFarrar et al. (1999) describe the process of SHM

as fundamentally one of statistical pattern recognition. Asuccessful civil SHM program involves selection andplacement of sensors suitable for measurement of keyparameters that influence the performance and health ofthe structural system. This section presents a vibration-based damage identification algorithm using statisticalfeatures extracted from continuous monitoring of dynamic

measurement data for a reliable practical application tocivil infrastructure.

Theoretical backgroundFrom experimental modal analysis (EMA), the strain

frequency response functions (FRFs), between

the applied force and measured strain responses can beexpressed as

)(djkH

+

=r rrrr

krjr

jkiM

H)2(

.)(

22

(1)

where jr represents the

th

r strain mode shaperespectively at response measurement point ; andj kr is

the mode shape component of displacement mode rat

excitation point at DOF. is the modal mass andthk rM

r is the modal damping ratio.

Additionally, the magnitude of strain FRF at resonance forany mode is given by

jr

rrr

kr

r

d

jk MH

== 22)( (2)

It is obvious from equation (2) that for a given mode, the

quantity22 rrr

kr

M

is a constant for all response

measurements at different locations on the structure due to

the same applied excitation at DOF.thk

Most damage identification techniques aredeveloped on the assumption of linear structural behaviorin the pre- and post-damage states. Therefore, dynamicresponses are very suitable for modal parametersuperposition applications. The frequency responsefunctions can be obtained through fast Fourier transforms(FFT). By considering measurement points for thedisplacement transducers and strain sensors at any givenmode, the peak values of FRF magnitude of thedisplacement response data referred to as modal strainvector (MSV) extracted from the peak values of FRFmagnitude of the strain response data is given by

m

{ }Tmrjrrr ......MSV 21= (3)

The strain mode shape at a particularmeasurement point relative to a reference sensor of same

type mounted at an undamaged location is linear and ofconstant slope. Any deviation in this feature is anindication of changes in the dynamic properties of thestructure due to damage. The reference strain sensors

denoted by refr should be carefully selected from any

of the sensors located at points with the leastpossibility of damage. In flexural structures, for example,the reference sensor could be placed at regions of lowbending moment.

m

Because measurement data can be measuredunder different conditions, the ability to normalize the databecomes very central to the damage detection process. Inthis case, the MSV is normalized by the modal response ofthe reference sensor. This approach is meant to minimizeto the extent possible the variability in the data acquisitionprocess. Thus, the normalized MSV with respect to thereference sensors is given by:

{ }

=

refr

mr

refr

mr

refr

r

refr

rmrrmrr

)1(21)1(21 ...... (4)

For long-gauge FBG sensors, the mathematical

expressions for conventional strain measurement are stillvery applicable except that the modal strain now becomesmodal macro-strain (MMS). Further information onpackaging and performance of long-gauge FBG sensor can

be obtained from Li and Wu (2007). The developed

sensors are characterized by the capability of obtaining themeasurements by integrating both local and globalinformation due to the fact that strain is a typical localresponse and distributed sensor placement helps to record

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the data covering the large region of a structure. Moreover,distributed strain sensing technique also reduces thenumber of unknown parameters for effective analysis of

measured data.

Data interpretation and features extractionThe study of data features required to distinguish

the damaged structures from undamaged ones has receivedconsiderable attention in the technical literature. AnySHM monitoring system will produce an enormousamount of data from which it will be necessary to selectthe appropriate information. An innovative analysis ofmeasured data and accurate interpretation of extractedfeatures possess essential ability that makes sense of theenormous amounts of data collected during monitoring

exercise for an effective diagnostic and/or prognosticsystem. This supplies useful information that ismeaningful to bridge owners, inspectors and engineers for

practical implementation and effective management ofcivil infrastructure. A 3-step damage identificationalgorithm that evaluates the stability of measurement dataand localizes damage in flexural structures using statisticalfeatures is summarized in Figure-1. Inherent in the featureselection process are the ability to identify theperformance of sensors and effectively condense data. Inaddition, provisions are made for automatic updating ofprevious data if the features remain unchanged, whiledamages are localized at the sensor locations characterizedby feature changes.

Figure-1. Flowchart for structural health monitoring program using statistical features.

The 3-step algorithm for data interpretation andfeature extraction based on dynamic measurement data

from different types of sensing techniques as presented inFigure-1 is described as follows:

Statistical features (slopes of lines

Data condensation and

storage

Step 2Selection and placement of areference andNS target sensors

Featureschange?

Y

N

Implementation andManagement

Step 3

Are datareliable?

Data acquisition

N

Y

Step 1

Select peak values of FRF

magnitude,|H| eak

Extract modalparameters

H eakof SRef

|H|p

eakofS3

H eakof SRef

|H|p

eakofSNS

H eakof SRef

|H|p

eakofS1

H eakof SRef

|H|p

eakofS2

GUI: measurements over a eriod of time

Continuous monitoring

|H| eakof SRef

|H|p

eakofS3

|H| eakof SRef

|H|p

eakofSNS

H eakof SRef

|H|p

eakofS1

H eakof SRef

|H|p

eakofS2

GUI: continuous measurements at two different times

Correlated

?

N

Y

Assess the stability of measurementthrough statistical correlation of data

Results interpretationand recommendations

Step 2

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(1) Selection and placement of adequate

reference sensor and target sensors ( =1, 2

) suitable for measuring key parameters that

influence the performance and health of the structuralsystem are made. Modal parameters are extracted for eachmeasurement after satisfactory preliminary assessment ofthe reliability of the data acquisition systems. The peakvalues of the magnitude of the FRF for each measurementdata are obtained in a way similar to the construction ofeigenvector in modal analysis.

RefS NsS Ns

m

(2) From the records of several measurement dataat a particular state of the structure, a graphical userinterface is created, which consists of m chartscorresponding to the plots ofpeak values of the magnitudeof the FRF of target sensors at y axis against that of thereference sensor at x axis. The consistency of themeasurement data obtained from different sensingtechniques can be assessed through the statisticalcorrelations for each structural condition. For continuousmeasurements at any two different times, comparativeplots ofpeak values of FRF magnitudesare made to assessthe variations in the slopes of lines of fit. Strain as a verysensitive local response can correctly localize damages atsensor points by comparing two consecutive slopes oflines of fit.

(3) If the slope increases, damage is localized atthe region of the sensor. No change in structural conditionis indicated by constant slope, while slope reduction is animplication of damage at the location of the referencesensor. The deviation of slope of the fit lines from the

initial value is clearly a statistical feature for damageidentification. Condensation of huge data is guaranteed bythe technique and the data storage devices are more easily

and effectively managed. Subsequent data collected fromundamaged regions conveniently replace the previous, andthe time-history data and important features immediatelybefore and after damage are also saved. The results areeasy to interpret and appropriate recommendations can be

made for effective management and implementation.

EXPERIMENTAL INVESTIGATION

Experimental set-up and data collectionTo demonstrate the proposed technique

experimentally, three 503960 mm3 simply supportedsteel beam specimens shown in Figure-2 were used. To

contrast FE model, the beam was modeled by 16 elements,17 nodes and 32 degrees of freedom. The Youngsmodulus and the density of the specimens are 2.101011

N/m2and 7862 kg/m3respectively. Damage was simulatedby introducing width reductions from 50mm to 24mm forsingle damage at element 6 and double damages atelements 6 and 10. The intact, single and double damagecases are respectively denoted as C1, C2 and C3.

Figure-2. Experimental specimens and sensor placement.

A succession of single-point impact loads wasapplied at arbitrary locations on the beams to simulateloading with a high bandwidth. Such tests were performed15 times and the measured data were used for modalidentification. The dynamic responses were collectedusing four long-gage FBG sensors (F1~F4) of 240mmgauge length attached to the bottom surface of thespecimens and four conventional strain gauges (S1~S4) of5mm gauge length for comparison. In order to compare

strain measurements between conventional strain gaugesand the long-gauge FBG sensors, the two types ofinstruments were systematically installed such that theircenters coincide.

The dynamic responses from FBG sensors andstrain gauges were recorded at a sampling rate of 250Hzand 500Hz, respectively; and impulsive excitations byimpact hammer recorded at 500Hz. The FRF was obtainedfrom the spectral densities of the force input and response

50

50

50

C3: Beam with two damages at elements 6 and 10

3

C1: Intact beam

C2: Beam with one damage at element 6

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outputs at each measurement point. The FRF can becalculated via the classical fast Fourier transforms (FFT)algorithms expressed as

)(

)(

)()(

)()()(

ff

fz

S

S

FF

FZH ==

(5)

Where )(Z and )(F are the FFTs of the response

and force time domain signals, and , and the

asterisk denotes the complex conjugate.

)(tz )(tf

)(zfS is the

cross spectrum between the output and input signals; and

)(ffS is the auto-spectrum of the input signals. The

symbols and denote the response signals and

excitation signals, respectively. The approach wasemployed to reduce the effect of noise due to uncorrelatedexcitation.

z f

Mode shapes were extracted using global curve-fitting techniques. Figure-3 shows that the mode shapescomputed using ANSYS program and measured usingFBG sensors have good agreements.

0

0.2

0.4

0.6

0.8

1

1.2

F1 F2 F3 F4

Sensor designation

(a)

Strain

mod

e

shape

Theory

Test

C1

0

0.2

0.4

0.6

0.8

1

1.2

F1 F2 F3 F4

Sensor designation

(b)

Strainmo

deshape Theory

Test

C2

0

0.2

0.4

0.6

0.8

1

1.2

F1 F2 F3 F4

Sensor designation

(c)

Strainmo

deshape

Theory

Test C3

Figure-3. Theoretical versus experimental distributed strain mode shape for first mode.

DISCUSSION OF EXPERIMENTAL RESULTSTable-1 gives the first modal frequency extracted

from the response data of the three sensors for thedifferent structural states. All the data perfectly agree with

high precision.

Table-1. Identified resonant frequencies using different

sensors.

Resonant frequencies (Hz)Scenarios

FBG sensors Strain gauges

C1 6.021 6.021

C2 5.822 5.825

C3 5.638 5.637

The frequency spectra for the different measurement dataunder a typical excitation for the three structural cases C1,C2 and C3 measurement data are shown in Figures 4 and5.

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Figure-4. Typical frequency response spectra from strain gauges.

0 25 50 75 100 1250

0.5

1

1.5

2

2.5

3

3.5

FRFMagnitude(/N)

Frequency (Hz)

FBG Sensor - C1

F1

F3F2

F4

(a)

5 5.5 6 6.5 70

0.5

1

1.5

2

2.5

3

3.5

FRFMagnitude(/N)

Frequency (Hz)

F1

F3F2

F4(b)

C1

5 5.5 6 6.5 70

1

2

3

4

5

6

FRFMagnitude(/N)

Frequency (Hz)

F1

F3

F2F4

C2

(c)

5 5.5 6 6.5 70

2

4

6

8

10

FRFMagnitude(/N)

Frequency (Hz)

F1

F3

F2F4

C3

(d)

0 25 50 75 100 1250

1

2

3

4

5

FRFMagnitude(/N)

Frequency (Hz)

Strain Gauge - C1

S1

S2

S3

S4

(a)

5 5.5 6 6.5 70

0.5

1

1.5

2

2.5

FRFMagnitude(/N)

Frequency (Hz)

S1

S2

S3

S4

(b)

C1

5 5.5 6 6.5 70

2

4

6

8

FRFMagnitude(

/N)

Frequency (Hz)

S1

S2

S3

S4

C2

(c)

5 5.5 6 6.5 70

2

4

6

8

10

12

FRFMagnitude(/N)

Frequency (Hz)

S1

S2

S3

S4

C3

(d)

Figure-5. Typical frequency response spectra measured with long-gage FBG sensors.

By taking the first modal parameters intoconsideration, it is evident from the figures that the naturalfrequencies and the damping ratios reduce with increase inthe damage extent. The stability of the measurements can

be evaluated through the statistical correlation of the peakvalues of FRF magnitudes of the target sensors relative tothat of the reference sensor. The reference sensors for thisinvestigation are strain gauge S4 and FBG sensor F4.

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Figures 6 and 7 show the behavior of the modalparameters extracted from measurement data collectedfrom the two sensor types under the random excitations of

different magnitudes for the three structural conditions ofthe beam specimens. From the plots of the modalparameters of each sensor against the reference sensor, the

linearity of the relationships for all excitation cases withsingle point impulsive load arbitrarily applied on thebeams can be established for all the sensing techniques.

By fitting the discrete points, good lines of fit implyingstability of the measurements can be obtained.

Figure-6. Modal strain parameter extracted from strain gauges.

0

20

40

60

80

0 4 8 12 16 20

Microstrain of reference sensor S4

M

M

So

fStrain

Gauges

C3S1

C3S2

C3S3

C3S4

0

3

6

9

12

0 1 2 3 4 5

Microstrain of reference sensor S4

M

M

So

fStrain

G

auges

C1S1

C1S2

C1S3

C1S4

0

10

20

30

40

50

0 2 4 6 8 10 12

Microstrain of reference senso r S4

MMS

ofStrainGauges

C2S1

C2S2

C2S3

C2S4

0

2

4

6

8

0 1 2 3 4

MMS of reference s ensor F4

MMS

ofFBGs

ensors

C1F1C1F2C1F3C1F4

0

5

10

15

20

25

0 2 4 6 8

MMS of reference sensor F4

MMSofFBGs

ensors

C2F1

C2F2

C2F3

C2F4

0

15

30

45

60

0 5 10 15 20


MMS

ofFBGs

ensors

C3F1C3F2C3F3C3F4

Figure-7. Modal macro-strain measurements from FBG sensors.

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The stability of the measurement data is evaluated via thecorrelation of the modal data of each sensor type relative

to its reference as shown in Table-2.

Table-2.Statistical correlation of modal parameters using different sensors.Correlation coefficients

CasesStrain gauges FBG sensors

S1 S2 S3 F1 F2 F3

C1 0.9992 0.9996 0.9996 0.9964 0.9996 0.999

C2 0.9993 0.9993 0.999 0.9987 0.9964 0.9979

C3 0.9994 0.9998 0.9998 0.9997 0.9995 0.9995

It is clear that the measurement data from all thesensors have perfect statistical correlations with respect to

the reference. These excellent correlation coefficientssignify the stability and reliability of the response datameasured by all the three sensors. It can be inferred thatthe effects of noise on the measurements is minimal.

Statistical feature for damage localizationThe lines of fit have dual features: the correlation

coefficient and the slope or equation of fit line. While theformer assesses the consistency or stability of the data, the

slope is employed to localize damage. A close monitoringof the variation of slopes of fit lines for each sensorcorresponding to the structural scenarios under different

excitations at any different times gives clear indication oflocation of damage. The plots of variation of slopes of fitlines for the two sensor types are shown in Figures 8 and9. Table-3 gives the variation of slopes of lines of fit forstrain gauges and FBG sensors in which the underlinedfigures in bold indicate the significant change indicatingdamages.

Table-3. Statistical features indicated by variation of slopes of fit lines.

Cases Slope of fit lines

Strain gauges FBG sensorsS1 S2 S3 F1 F2 F3

C1 1.145 6.3502 6.0371 0.916 4.738 4.911

C2 0.9781 14.178 5.8734 1.0209 8.827 5.1164

C3 0.9917 13.613 14.31 0.8934 9.099 8.781

The variation of slope of fit lines correspondingto the strain gauges S2 and S3 clearly localized thedamage as shown in Figure-8. The plots are made onsimilar scale for easy comparison of the structuralcondition at the location of sensors. It is evident from

Figure 8a that there is no significant change in the slope ofstrain gauge S1, which implies that no damage has takenplace within the coverage of the sensor. However,damages are clearly localized at the locations sensors S2and S3 as indicated by increase in slopes of fit lines in

Figures 8b and 8c. Damages for scenario C2 is locatedclose to sensor S2, while damage scenario C3 is located inthe region of sensor S2 and S3. The statistical damageidentification method has reaffirmed that strain is verysensitive response to local damage. However, strain

gauges cannot reflect influence of damage effectivelyunless they are located at the damaged region. Moreover,the challenges of huge data acquisition and processingcosts, durability and long-term reliability render straingauges unfit for large-scale civil SHM.

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Figure-8.Variation of slopes of fit lines for strain gauges.

Similar to strain gauge measurements, damages are evidently localized by FBG sensors F1 and F3 as shown in Figure-9.

0

20

40

60

80

0 5 10 15 20

FRF magnitude of reference sensor S4

FRF

m

agnitude

ofS1

C1S1 C2S1 C3S1

0

20

40

60

80

0 5 10 15 20


FRF

m

agnitu

de

ofS2

C1S2 C2S2 C3S2

0

20

40

60

80

0 5 10 15 20


FRF

ma

gnitude

ofS3

C1S3 C2S3 C3S3

0

20

40

60

80

0 5 10 15 20 25MMS of Reference sensor F4

M

M

So

fFBGs

ensorF1

C1F1 C2F1 C3F1

0

20

40

60

80

0 5 10 15 20 25

MMS of Reference sensor F4

M

M

So

fFBG

sensorF2 C1F2 C2F2 C3F2

0

20

40

60

80

0 5 10 15 20 25


M

M

So

fFBGs

ensorF3

C1F3 C2F3 C3F3

Figure-9. Variation of slopes of fit lines for FBG sensors.

There is no appreciable change in slope of sensorF1 in Figure-9a while Figures 9b and 9c show indicationsof damage in the regions covered by sensors F2 and F3.Damages for scenarios C2 and C3 are located within the

gauge length of sensor F2 and damage scenario C3 islocated within sensor F3. One of the benefits of distributedstrain sensing technique over the conventional strain gaugeis that every critical section of the structure is covered

without any loss of vital information for damageidentification.

CONCLUSIONS

A damage identification strategy adaptable tocivil structures using statistical features of dynamic strainmeasurements has been presented and verified throughexperimental study. The method has the capability to

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reliably assess the consistency of the measurement data,promptly identify faulty sensors and accurately locatedamages in structure by using statistical features. The

importance of the technique for civil SHM was establishedby using both point and distributed strain data andpresented in an easy-to-interpret graphical format foreffective implementation. The stability of all measurementdata was perfectly determined via the correlation of modalparameters of target sensor with the reference. The abilityof strain gauges to correctly locate damage is limited to itsshort gage length, while the long-gage FBG sensors aremore efficient choice for effective identification andlocalization of damage.

REFERENCES

Brincker R., P. Anderson, P.H. Kirkegaard and J.P.Ulfkjaer. 1995. Damage Detection in Laboratory ConcreteBeams. Proceedings of the 13th International ModalAnalysis Conference. pp. 668-674.

Carden P.E. and P. Fanning. 2004. Vibration BasedCondition Monitoring: A Review. Structural HealthMonitoring. 3(4): 355-377.

Doebling S.W. and C.R. Farrar. 1997. Using StatisticalAnalysis to Enhance Modal-Based Damage Identification.Structural Damage Assessment Using Advanced SignalProcessing Procedures. Proceedings of DAMAS 97

University of Sheffield, UK. pp. 199-210.

Doebling S.W., C.R. Farrar, M. B. Prime and D. W.Shevita. 1996. Damage identification and healthmonitoring of structural and mechanical systems fromchanges in their vibration characteristics: A literaturereview. Los Alamos National Laboratory Report.

Farrar C.R., T.A. Duffey, S.W. Doebling and D.A. Nix.1999. A Statistical Pattern Recognition Paradigm forVibration-Based Structural Health Monitoring.Proceedings of the 2nd International Workshop onStructural Health Monitoring, Stanford, CA. Sept 8-10.

Li S.Z. and Z.S. Wu. 2007. Development of DistributedLong-gage Fiber Optic Sensing System for StructuralHealth Monitoring. Structural Health Monitoring. 6(6):133-143.

Li S.Z. and Z.S. Wu. 2008. Modal Analysis on Macro-strain Measurements from Distributed Long-gage FiberOptic Sensors. Journal of Intelligent Material Systems andStructures. 19(8): 937-946.

Pape D.A. 1993. A Modal Analysis Approach to FlawDetection in Ceramic Insulators. Proceedings of the 11th

International Modal Analysis Conference. pp. 35-40.

Sohn H., C.R. Farrar, F.M. Hemez, D.D. Shunk, D.W.Stinemates and B. R. Nadler. 2003. A Review of

Structural Health Monitoring Literature: 1996-2001. LosAlamos National Laboratory Report. LA-13976-MS.

Wu Z. S. and S. Li. 2007. Two-level Damage DetectionStrategy Based on Modal Parameters from DistributedDynamic Macro-strain Measurements. Journal ofIntelligent Material Systems and Structures. 18(7): 667-676.

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Documents

Adewuyi a., y z. Wu (2009) Vibration-based Structural Health Monitoring