Structural Health Monitoring & Damage Detection, Volume 7: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017 PDF
Preview 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 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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthematerialisconcerned,specificallytherights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction onmicrofilms orinany other physical way, and transmission or informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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.
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