Adewuyi a., y z. Wu (2009) Vibrationbased Structural Health Monitoring

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8/13/2019 Adewuyi a., y z. Wu (2009) Vibrationbased Structural Health Monitoring
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VOL. 4, NO. 3, MAY 2009 ISSN 18196608
ARPN Journal of Engineering and Applied Sciences
20062009 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
VIBRATIONBASED 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
EMail: [email protected]
ABSTRACTA statistical vibrationbased 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 easytointerpret 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 vibrationbased 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 modelfree 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 macrostrain vector (MMSV) methodof damage identification using the modal parametersextracted from dynamic macrostrain data recorded byarrays of longgauge 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 largescale 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 vibrationbased 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 otherfrequencybased 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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VOL. 4, NO. 3, MAY 2009 ISSN 18196608
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20062009 Asian Research Publishing Network (ARPN). All rights reserved.
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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 longgauge fiber Bragg grating(FBG) strain sensors.
VIBRATIONBASED 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 vibrationbased 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 postdamage 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 longgauge FBG sensors, the mathematical
expressions for conventional strain measurement are stillvery applicable except that the modal strain now becomesmodal macrostrain (MMS). Further information onpackaging and performance of longgauge 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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20062009 Asian Research Publishing Network (ARPN). All rights reserved.
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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 3step damage identificationalgorithm that evaluates the stability of measurement dataand localizes damage in flexural structures using statisticalfeatures is summarized in Figure1. 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.
Figure1. Flowchart for structural health monitoring program using statistical features.
The 3step algorithm for data interpretation andfeature extraction based on dynamic measurement data
from different types of sensing techniques as presented inFigure1 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
Hp
eakofS3
H eakof SRef
Hp
eakofSNS
H eakof SRef
Hp
eakofS1
H eakof SRef
Hp
eakofS2
GUI: measurements over a eriod of time
Continuous monitoring
H eakof SRef
Hp
eakofS3
H eakof SRef
Hp
eakofSNS
H eakof SRef
Hp
eakofS1
H eakof SRef
Hp
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 timehistory 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 setup and data collectionTo demonstrate the proposed technique
experimentally, three 503960 mm3 simply supportedsteel beam specimens shown in Figure2 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.
Figure2. Experimental specimens and sensor placement.
A succession of singlepoint 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 longgage 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 longgauge 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 autospectrum 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 curvefitting techniques. Figure3 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
Figure3. Theoretical versus experimental distributed strain mode shape for first mode.
DISCUSSION OF EXPERIMENTAL RESULTSTable1 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.
Table1. 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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Figure4. 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)
Figure5. Typical frequency response spectra measured with longgage 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.
Figure6. 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 of reference sensor F4
MMS
ofFBGs
ensors
C3F1C3F2C3F3C3F4
Figure7. Modal macrostrain 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 Table2.
Table2.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. Table3 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.
Table3. 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 Figure8. 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 longterm reliability render straingauges unfit for largescale civil SHM.
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Figure8.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 Figure9.
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 magnitude of reference sensor S4
FRF
m
agnitu
de
ofS2
C1S2 C2S2 C3S2
0
20
40
60
80
0 5 10 15 20
FRF magnitude of reference sensor S4
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
MMS of reference sensor F4
M
M
So
fFBGs
ensorF3
C1F3 C2F3 C3F3
Figure9. Variation of slopes of fit lines for FBG sensors.
There is no appreciable change in slope of sensorF1 in Figure9a 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 easytointerpret 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 longgage FBG sensors aremore efficient choice for effective identification andlocalization of damage.
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