Structural Health Monitoring & Damage Detection, Volume 7: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017

99 Pages·2017·5.74 MB·English

by  Christopher Niezrecki (eds.)

Conference Proceedings of the Society for Experimental Mechanics Series
Christopher Niezrecki Editor
Structural Health
Monitoring & Damage
Detection, Volume 7
Proceedings of the 35th IMAC, A Conference and Exposition
on Structural Dynamics 2017
Conference Proceedings of the Society for Experimental Mechanics Series
SeriesEditor
KristinB.Zimmerman,Ph.D.
SocietyforExperimentalMechanics, Inc.,
Bethel,CT,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/8922
Christopher Niezrecki
Editor
Structural Health Monitoring & Damage
Detection, Volume 7
Proceedings of the 35th IMAC, A Conference and Exposition on
Structural Dynamics 2017
123
Editor
ChristopherNiezrecki
DepartmentofMechanicalEngineering
UniversityofMassachusetts
Lowell,MA,USA
ISSN2191-5644 ISSN2191-5652 (electronic)
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
ISBN978-3-319-54108-2 ISBN978-3-319-54109-9 (eBook)
DOI10.1007/978-3-319-54109-9
LibraryofCongressControlNumber:2017934884
©TheSocietyforExperimentalMechanics,Inc.2017
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Preface
StructuralHealthMonitoring&DamageDetectionrepresentsoneoftenvolumesoftechnicalpaperspresentedatthe35th
IMAC, A Conferenceand Expositionon StructuralDynamics,organizedby the Society forExperimentalMechanics,and
heldinGardenGrove,California,January30toFebruary2,2017.ThefullproceedingsalsoincludevolumesonNonlinear
Dynamics,DynamicsofCivilStructures,ModelValidationandUncertaintyQuantification,DynamicsofCoupledStructures,
Sensors and Instrumentation, Special Topics in Structural Dynamics, Rotating Machinery, Hybrid Test Methods, Vibro-
Acoustics and Laser Vibrometry, Shock & Vibration, Aircraft/Aerospace and Energy Harvesting, and Topics in Modal
Analysis&Testing.
Eachcollectionpresentsearlyfindingsfromexperimentalandcomputationalinvestigationsonanimportantareawithin
structuraldynamics.Structuralhealthmonitoringanddamageareacoupleoftheseareas.
Theorganizerswouldliketothanktheauthors,presenters,sessionorganizers,andsessionchairsfortheirparticipationin
thistrack.
Lowell,MA,USA ChristopherNiezrecki
v
Contents
1 ExploitingSpatialSparsityinVibration-BasedDamageDetection................................................. 1
ChandlerSmithandEricM.Hernandez
2 Multi-SourceSensingandAnalysisforMachine-ArrayConditionMonitoring................................... 9
ShannonM.Danforth,JadenT.Martz,AlisonH.Root,EricB.Flynn,andDustinY.Harvey
3 WaveletTransform-BasedDamageDetectioninReinforcedConcreteUsing anAir-Coupled
Impact-EchoMethod..................................................................................................... 23
TylerEppandYoung-JinCha
4 DamageDetectionBasedonStrainTransmissibilityforBeamStructurebyUsingDistributed
FiberOptics............................................................................................................... 27
LiangliangCheng,GiorgioBusca,PaoloRoberto,MarcelloVanali,andAlfredoCigada
5 ModalParametersEstimationof anOffshoreWindTurbine Using MeasuredAcceleration
SignalsfromtheDriveTrain............................................................................................ 41
M.El-Kafafy,L.Colanero,N.Gioia,C.Devriendt,P.Guillaume,andJ.Helsen
6 Structural Damage Detectionin Real Time: Implementation of 1D ConvolutionalNeural
NetworksforSHMApplications........................................................................................ 49
OnurAvci,OsamaAbdeljaber,SerkanKiranyaz,andDanielInman
7 MonitoringtheHealthofaCantileverBeamUsingNonlinearModalTracking.................................. 55
TimothyA.Doughty,AlexandraK.Blaser,andJacobR.Johnston
8 UsingModalParametersforStructuralHealthMonitoring ........................................................ 67
ShawnRichardson,JasonTyler,BrianSchwarz,PatrickMcHargue,andMarkRichardson
9 CurrentChallengeswithBIGDATAAnalyticsinStructuralHealthMonitoring................................. 79
NurSilaGulgec,GolnazS.Shahidi,ThomasJ.Matarazzo,andShamimN.Pakzad
10 DetectionofCracksinBeamsUsingTreedGaussianProcesses..................................................... 85
M.Civera,C.Surace,andK.Worden
vii
Chapter 1
Exploiting Spatial Sparsity in Vibration-Based Damage Detection
ChandlerSmithandEricM.Hernandez
Abstract One of the main limitations traditionally encounteredin vibration-basedstructural health monitoring(SHM) is
detecting,localizingandquantifyinglocalizeddamageusingglobalresponsemeasurements.Thispaperpresentsanimpulse
responsesensitivityapproachenhancedwithaLASSOregularizationinordertodetectspatiallysparse(localized)damage.
TheanalyticalexpressionforimpulseresponsesensitivitywasderivedusingVettercalculus.Theproposedalgorithmexploits
thefactthatwhendamageissparse,anl -normregularizationismoresuitablethanthemorecommonleastsquares(l -norm)
1 2
minimization.Theproposedmethodologyissuccessfullyappliedinthecontextofasimulatednon-uniformshearcantilever
beamwithnoise-contaminatedinput–outputmeasurements.
Keywords Sparsity • Impulseresponse • Lasso • Damage • Sensitivity
1.1 Introduction
Detectingdamageintheformofstiffnessreductionisanimportantprobleminstructuralhealthmonitoring(SHM).Avariety
ofmethodshavebeenproposedinthelastthreedecades[1,2].Theconceptofspatialsparsityandhowtobestexploitinthe
contextofvibration-baseddamagedetectionhasbeenrecentlyproposed.KaoukandZimmerman[3]derivedalgorithmsto
detectdamageusingaminimumrankperturbationcriteria.Althoughlowrankperturbationofthestiffnessmatrixdoesnot
necessarilyimplyspatialsparsity,theirworkrepresentsoneofthefirstcontributionsintheusesparsityasaconstraint.
Morerecently,LinkandZimmerman[4]usedgreedypursuitmethodstodetectspatiallysparsedamageusingfrequency
response functions. However, more effective and efficient sparse recovery algorithms such as the Basis Pursuit are more
commonlyused.OneexampleofexploitingspatialsparsityinSHMwithbasispursuitalgorithmscanbefoundinworkby
Hernandez[5,6]whichutilizeseigenvaluesensitivityandl minimizationtolocatesparsedamages.Thealgorithmhasbeen
1
validatedexperimentally.
This paper extends the idea presented in [5, 6] into the time domain and uses impulse response sensitivity to locate
andquantifyspatiallysparsedamage.Themainhypothesisisthatbyusingimpulseresponsesensitivitywecaneffectively
andcompactlycombinetheeffectofdamageinmodeshapes,frequencyanddampinginasinglemetric.Usingchangesin
theimpulseresponseasadamagesensitivefeaturehasbeenusedbyotherresearchers[7,8],howeverwithoutimposingthe
spatialsparsityconstraintexplicitly.UsingVettercalculus,ananalyticalexpressionforthesensitivityoftheimpulseresponse
isobtainedandusedtosetuptheinverseproblemofdetectingreductionsinmodelparametersbasedonidentifiedchangesin
impulseresponse.TheinverseproblemiseffectivelysolvedusingLASSOregularization,anefficientl -basedoptimization
1
scheme.
Thepaperbeginsbypresentingthe systemsofinterestandthemethodof approach.Thisisfollowedbya briefsection
on LASSO regularizationandthena sectiononimplementationandverification.Thenumericalimplementationis carried
out using a shear-beam structure with 21 degrees of freedom. In all cases, limited spectral data and noise-contaminated
singleinput-singleoutput(SISO)areconsidered.Thepaperendswithasectioninvestigatingtheeffectsofmodelerrorand
conclusions.
C.Smith•E.M.Hernandez((cid:2))
CollegeofEngineeringandMathematicalSciences,UniversityofVermont,Burlington,VT05405,USA
e-mail:[email protected];[email protected]
©TheSocietyforExperimentalMechanics,Inc.2017 1
C.Niezrecki(ed.),StructuralHealthMonitoring&DamageDetection,Volume7,ConferenceProceedings
oftheSocietyforExperimentalMechanicsSeries,DOI10.1007/978-3-319-54109-9_1
2 C.SmithandE.M.Hernandez
1.2 Method of Approach
The sensitivity approach is a popular and practical framework for finite model updating in structural dynamics [9]. The
sensitivitymatrixmapsmass,stiffnessand(or)dampingparameterstoassociatedchangesinsystemresponsecharacteristics,
typicallyvariationsineigenvectorsandeigenvalues[9].Inthispaper,weseekarelationshipbetweensmallchangesinthe
impulseresponsetosmallchangesintheparametersthatdefinethestiffnessmatrix.
Theimpulseresponseofalinearsystemdescribedby
Zt
h.t;(cid:2)/D C.(cid:2)/eA.(cid:2)/.t(cid:2)(cid:3)/B.(cid:2)/ı.(cid:3)/d(cid:3) DC.(cid:2)/eA.(cid:2)/tB.(cid:2)/CDı.t/ (1.1)
0
whereA,B,C,andDarethematricesthatdefinethestate-spacemodelofthesystem.Weseektofind
(cid:4)h.t/DS.t/(cid:4)(cid:2) (1.2)
where (cid:4)(cid:2)2Rp(cid:3)1 is a vector of changes in the p parameters that define the stiffness of the structure, S2Rmxp is the
impulse responsesensitivity matrix,(cid:4)h(t)2Rm(cid:3)1 is the correspondingchangein the impulse responsebetween damaged
andundamagedstates,andmisthenumberofoutputmultipliedtimesthenumberoftimesteps.
Werestrictourattentiontothecasewherethestiffnesscanbeexpressedas
Xp
KD Ei;Kfi.(cid:2)/ (1.3)
iD1
whereEisanelementaryinfluencematrixandf((cid:2))isadifferentiablefunction.BytakingthefirsttermoftheTaylorseries
i
expansionaroundtheparameterofinterest,thestiffnessanddampingmatricesmaybewrittenas
Xp
KD Ei;K(cid:2) (1.4)
iD1
where the sensitivity matrix is defined as the derivative of the impulse response with respect to a change in parameter (cid:2),
writtenas
(cid:2) (cid:3)
@h.t;(cid:2)/ @
S.t;(cid:2)/D D C.(cid:2)/eA.(cid:2)/tB.(cid:2)/CDı.t/ (1.5)
@(cid:2) @(cid:2)
ThematricesA,B,C,andDarewrittenas(foraccelerationmeasurements)
(cid:4) (cid:5) (cid:4) (cid:5)
AD (cid:3)M(cid:2)1K0.(cid:2)/ (cid:3)M(cid:2)1CdI.(cid:2)/ ; BD M(cid:2)10b2 ; CDc2(cid:6)(cid:3)M(cid:2)1K.(cid:2)/ (cid:3)M(cid:2)1Cd.(cid:2)/(cid:7); DDc2M(cid:2)1b2 (1.6)
b and c are respectively the input and output influence matrices, and MDMT2Rnxn, C DC T2Rnxn, and
2 2 d d
KDKT2Rnxn are the mass, damping and stiffness matrices. The derivative of the exponential mapping in Eq. (1.1) can
be found using results from Vetter [10] and Brewer [11]. Applyingthe chain rule from Vetter’s calculus the sensitivity is
writtenas
@h.t;(cid:2)/ @C (cid:8) (cid:9)@eAt (cid:8) (cid:8) (cid:9)(cid:9)@B @D
D eAtBC I ˝C BC I ˝ CeAt C (1.7)
@(cid:2) @(cid:2) p @(cid:2) p @(cid:2) @(cid:2)
Suchthat
(cid:4) (cid:5)
@A 0 I @C (cid:6) (cid:7) @B @D
@(cid:2)i D (cid:3)M(cid:2)1Ei;K (cid:3)M(cid:2)1Ei;Cd ; @(cid:2)i Dc2 (cid:3)M(cid:2)1(cid:2)i (cid:3)M(cid:2)1(cid:2)i ; @(cid:2)i D0;@(cid:2)i D0 (1.8)
1 ExploitingSpatialSparsityinVibration-BasedDamageDetection 3
where˝istheKroneckerproduct.InthecasethatCisafunctionof(cid:2),thenEq.(1.7)isreducedto
@h.t;(cid:2)/ @C (cid:8) (cid:9)@eAt
D eAtBC I ˝C B (1.9)
@(cid:2) @(cid:2) p @(cid:2)
ApplyingBrewer’sderivativeofamatrixexponentialweobtain
(
@e@A(cid:2).(cid:2)/t DX2n X2n (cid:8)I1˝˛k(cid:5)k(cid:4)(cid:9)@@A(cid:2) (cid:8)Ip˝˛l(cid:5)l(cid:4)(cid:9)fkl.t/; fkl.t/D tee(cid:6)(cid:6)ltk(cid:2)te(cid:6)kt iiff(cid:6)(cid:6)k D¤(cid:6)(cid:6)l (1.10)
k l (cid:6)l(cid:2)(cid:6)k k l
where˛istheeigenvectorsofAand(cid:5) istheeigenvectorsofAT whicharenormalizedsuchthat
(cid:5)(cid:4)˛ D1 (1.11)
k k
Inordertobeconsistentwiththespectralbandwidthoftheidentifiedimpulseresponseusedtocompute(cid:4)hthesensitivity
matrix is truncated at the maximumnumber of identified frequencies. Using the spectral representationof an exponential
mapping,thetruncationatthespecifiedeigenvalue(cid:6) ,wherer<n,isdefinedas
r
X2r
eAt D ˛ (cid:5)(cid:4)e(cid:6)kt (1.12)
k k
kD1
where˛and(cid:5) arenormalizedaccordingtoEq.(1.11).
1.3 LASSORegularization
In1996,R. Tibshiraniproposeda newmethod(LASSOregression)forestimatinglinearmodelswhichseeksto minimize
thefollowingresidualfunction
1
min ky(cid:3)Axk2C(cid:6)kxk (1.13)
x2Rp 2 2 1
with regularization parameter (cid:6)(cid:4)0 [12]. LASSO typically recovers sparse solution due to the l -norm constraint. For
1
experimental demonstrations we use the Matlab package, Lasso and Elastic-Net Regularized Generalized Linear Models
(glmnet),anefficientprocedureforfittingthelassoregularizationpathforlinearregression[13].Thealgorithmusescyclical
coordinatedescentcomputedalongaregularizationpathtooptimizetheobjectivefunctionovereachparameterwithothers
fixed,andcyclesrepeatedlyuntilconvergence[13].
The choice of the regularization parameter is subject to the user, where larger values of (cid:6) tend to sparse solutions. To
excludeuserbiastotheknownsolution,weusetheglmnet’sbuiltincrossvalidationalgorithmtoselectavalueof(cid:6).The
cross validation uses tenfold. We constrain the maximum number of nonzero elements in x to about 20% the number of
degreesofthesystemofinterest.
1.4 SimulationsandVerification
The simulated experimentshall validate our methodologythat seeking small localized damages with a sparsity prior will
yieldmoreaccurateandillustrativeresultsthanwithout(i.e.l regularization).Thesimulationisanidealcasebecausethe
2
modelusedtogeneratethedataisalsotheoneusedtoimplementthealgorithm.
The simulated model is a 21 degree of freedom, non-uniform shear beam with degrees of freedom enumerated from
1 the first mass closest to the support, to 21 the free end. The spring stiffness are as follows: k D ::: D k D 1000,
1 7
k D ::: Dk D750,andk D ::: Dk D500,andthemasses:m D ::: Dm D1,m D ::: Dm D0.75,and
8 14 15 21 1 7 8 14
m D ::: Dm D0.5.Thestructureisclassicallydampedwithadampingcoefficientof0.01.Thefundamentalfrequency
15 21
is0.436Hz.
4 C.SmithandE.M.Hernandez
a b
0.03
0.03
n n
o o
cti0.025 cti0.025
u u
d d
e 0.02 e
r r 0.02
s s
s s
e e
n0.015 n0.015
stiff stiff
d 0.01 d 0.01
e e
at at
m m
sti0.005 sti0.005
E E
0 0
5 10 15 20 5 10 15 20
Element Element
Fig.1.1 Estimatedstiffnessreductionforeveryelement.Inthiscase,onlythestiffnessofEl.6wasreducedby1%.(a)Thel -basedsolution,and
1
(b)thel -basedsolution
2
StiffnessistheonlydamagesensitiveparameterandthesensitivitymatrixisdefinedbyEq.(1.9).Thechangeinimpulse
response between the damaged and undamaged system contain only the specified lower frequencies, which are typically
the only ones that can be identified from structural vibrations. The input sensor is fixed at El. 21 and the output sensor
fixedatEl.3forallsubsequentexperiments.Ourobjectiveis:(1)toshowhowtheLASSOregularizationcomparestothe
Tikhonovregularizationindetectingchangesinstiffness,(2)presenttheminimumnumberoffrequenciesrequiredtodetect
areductioninstiffnessataspecifiedlocation,and(3)showtheeffectsofidentificationerrors(noise)ontheprobabilityof
detection(POD).
In the first simulation, the stiffness of El. 6 is reducedby 1% and the lowest four frequenciesare identified within the
impulseresponsesoftheoriginalsystemandthedamagedsystem.Nopriorinformationaboutthequantityormagnitudeof
damagesareknownexceptthatthesolutionissparse.Asdescribedabove,thesystemissingleinputandsingleoutput,and
the sensitivity matrix is truncatedaccordingto the numberof identified frequencies(Eqs. (1.10)and(1.12)).The LASSO
regularization (Eq. (1.13)) is used to estimate the reduction in stiffness and its location. The results are compared to the
solutionoftheTikhonovregularization(Fig.1.1).
Itisimmediatelyclearthatthel constrainedsolutionidentifiesthetruedamagedelement,andestimatesthemagnitude
1
of the reduction in stiffness precisely. In stark contrast, no information is gained about the damaged element when the
regularizationissubjectedtothel constrainedparameternoristhesolutionsparse.ThesolutiontotheLASSOhasonlyone
2
non-zeroelementandhenceissparse.
Theperformanceofthel constrainedregularizationmethodindetectinga1%stiffnessreductioninanysingleelement
1
takenseparatelyisconsidered.Figure1.2apresentstheminimumnumberoffrequenciesrequiredtoidentifythisreduction
atanysingleelement.Theimpulseresponsesensitivitymethodandfrequencysensitivitymethodarecompared.Frequencies
areselectedsequentiallyfromthelowestinincrementsofoneuntilaproperdetectionisobtained.Figure1.2bpresentsthe
estimatedstiffnessreductionbythel regularizationforthecasewhereonlyfourfrequencieswereidentified.We compare
1
thesparsesensitivitymethodwithfrequencyshiftsfrom[5],tothesparsesensitivitymethodwithimpulseresponses.Clearly,
thenumberofidentifiablefrequenciesrequiredtodetectasingledamageisfarlessintheimpulsemethod.
We consider now the case with multiple damage locations and varying percent reduction in stiffness. In this case, the
impulseresponseandsensitivitymatrixweretruncatedatthesixthfrequency.Figure1.3presentsthefollowingscenarios:
(1)thestiffnessofEl.6reducedby1%andEl.15by1%,(2)stiffnessofEl.6reducedby1%andEl.15by3%,and(3)El.6
reduced by 1% and El. 15 by 5%. In cases (1) and (2) damages were correctly located, and their reductions in stiffness
accuratelyestimated.Incase(3)afalsepositiveisobtainedatEl.19andtheestimatedmagnitudesofthestiffnessreduction
at the true damage locations shrink in value. This may be due to the greater reduction in stiffness which drives the error
betweenthe linearapproximationandthe truenonlinearityofthe sensitivity.We requiresmallchangesin stiffnessso that
thechangesinimpulseresponsearecontainedwithinthelinearspanofthesensitivitymatrix.