Table Of ContentConference Proceedings of the Society for Experimental Mechanics Series
Christopher Niezrecki · Javad Baqersad Editors
Structural Health Monitoring,
Photogrammetry & DIC,
Volume 6
Proceedings of the 36th IMAC, A Conference and Exposition
on Structural Dynamics 2018
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
SeriesEditor
KristinB.Zimmerman,Ph.D.
SocietyforExperimentalMechanics,Inc.,
Bethel,CT,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/8922
Christopher Niezrecki • Javad Baqersad
Editors
Structural Health Monitoring,
Photogrammetry & DIC, Volume 6
Proceedings of the 36th IMAC, A Conference and Exposition
on Structural Dynamics 2018
123
Editors
ChristopherNiezrecki JavadBaqersad
DepartmentofMechanicalEngineering KetteringUniversity
UniversityofMassachusetts Flint,MI,USA
Lowell,MA,USA
ISSN2191-5644 ISSN2191-5652 (electronic)
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
ISBN978-3-319-74475-9 ISBN978-3-319-74476-6 (eBook)
https://doi.org/10.1007/978-3-319-74476-6
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Preface
StructuralHealthMonitoring,Photogrammetry&DICrepresentsoneofninevolumesoftechnicalpaperspresentedatthe
36thIMAC,AConferenceandExpositiononStructuralDynamics,organizedbytheSocietyforExperimentalMechanics,
and held in Orlando, Florida, February 12–15, 2018. The full proceedings also include volumes on Nonlinear Dynamics;
DynamicsofCivilStructures;ModelValidationandUncertaintyQuantification;DynamicsofCoupledStructures;Special
Topics inStructural Dynamics; Rotating Machinery, Vibro-Acoustics and Laser Vibrometry; Sensors and Instrumentation,
Aircraft/AerospaceandEnergyHarvesting;andTopicsinModalAnalysisandTesting.
Eachcollectionpresentsearlyfindingsfromexperimentalandcomputationalinvestigationsonanimportantareawithin
structuraldynamics.
Theorganizerswouldliketothanktheauthors,presenters,sessionorganizers,andsessionchairsfortheirparticipationin
thistrack.
UniversityofMassachusettsatLowell,Lowell,MA,USA ChristopherNiezrecki
KetteringUniversity,Flint,MI,USA JavadBaqersad
v
Contents
1 AModificationtoUnifiedMatrixPolynomialApproach(UMPA)forModalParameterIdentification ...... 1
SeyedEhsanHajiAghaMohammadZarbafandRandallAllemang
2 OrthogonalProjection-BasedHarmonicSignalRemovalforOperationalModalAnalysis .................... 9
S.Gres,P.Andersen,C.Hoen,andL.Damkilde
3 Identifying Mode Shapes of Turbo-Machinery Blades Using Principal Component Analysis
andSupportVectorMachines.......................................................................................... 23
AlexLa,JohnSalmon,andJaronEllingson
4 Full-FieldModalAnalysisUsingaDSLRCamera .................................................................. 27
JakaJavh,JankoSlavicˇ,andMihaBoltežar
5 EnhancingStandardGVTMeasurementswithDigitalImageCorrelation....................................... 31
S.Manzato,E.Di Lorenzo,andP.Mäckel
6 AMulti-viewDICApproachtoExtractOperatingModeShapesofStructures................................. 43
VanshajSrivastava,KiranPatil,JavadBaqersad,andJamesZhang
7 DevelopmentofaSemi-autonomousDroneforStructuralHealthMonitoringofStructuresUsing
DigitalImageCorrelation(DIC)....................................................................................... 49
SeanCatt,BenjaminFick,MatthewHoskins,JosephPraski,andJavadBaqersad
8 Experimental Examples for Identification of Structural Systems Using Neural Network
andDOF-BasedReductionMethod ................................................................................... 59
HeejunSungandMaenghyoCho
9 ActiveControlofFlexibleCylindersUndergoingVortex-InducedVibrationsUsingPiezoStripe
Actuators ................................................................................................................. 63
ErsegunDenizGedikli,DavidChelidze,andJasonDahl
10 ExtractingNaturalFrequenciesofLayeredBeamsUsingaContinuousVariationModelandModal
Analysis................................................................................................................... 67
ArnaldoJ.Mazzei,JavadBaqersad,andYaominDong
11 ExtendedAbstract:DynamicBehaviorofaCompliantMechanismDrivenbyStackedPiezoelectric
Actuators ................................................................................................................. 77
A.Koyuncu,M.S¸ahin,andH. N.Özgüven
12 Detection of Natural Frequency and Mode Shape Correspondence Using Phase-Based Video
MagnificationinLarge-ScaleStructures.............................................................................. 81
AralSarrafi,PeymanPoozesh,ChristopherNiezrecki,andZhuMao
13 RelatingVibrationandThermalLossesUsingtheDampingHeatCoefficient................................... 89
MarkoMihalec,JankoSlavicˇ,JakaJavh,FilippoCianetti,MicheleMoretti,GianlucaRossi,andMihaBoltežar
vii
viii Contents
14 PredictingGeometricToleranceThresholdsinaFive-AxisMachiningCentre .................................. 93
T.Rooker,N.Dervilis,J.Stammers,K.Worden,P.Hammond,G.Potts,T.Brown,andK.Kerrigan
15 LightFieldImagingofThree-DimensionalStructuralDynamics ................................................. 101
Benjamin Chesebrough, Sudeep Dasari, Andre Green, Yongchao Yang, Charles R. Farrar,
andDavidMascareñas
16 AdaptiveObserversforStructuralHealthMonitoringofHigh-Rate,Time-VaryingDynamicSystems...... 109
B. S.Joyce,J.Hong,J. C.Dodson,J. C.Wolfson,andS.Laflamme
17 ProbabilisticRobustnessAnalysisofanActivelyControlledStructurethatOperatesinHarshand
UncertainEnvironments................................................................................................ 121
ChristopherJ.D’Angelo,DanielG.Cole,andJohnC.Collinger
18 ImplementationofPiezoelectricShapeSensorsUsingDigitalImageCorrelation............................... 133
JasonTranandJayantSirohi
19 VariableAmplitudeFatigueTestingApparatusandItsDynamicalCharacterization .......................... 137
HewenxuanLiandDavidChelidze
20 AnEfficientLikelihood-FreeBayesianComputationforModelSelectionandParameterEstimation
AppliedtoStructuralDynamics ....................................................................................... 141
A.BenAbdessalem,N.Dervilis,D.Wagg,andK.Worden
21 Investigation on the Performance of a Velocity Feedback Control Unit for Structural Vibration
Control:TheoryandExperiments..................................................................................... 153
S.Camperi,M.Ghandchi-Tehrani,andS.J.Elliott
22 ExperimentalImplementationofaNonlinearFeedbackControllerforaStrokeLimitedInertial
Actuator .................................................................................................................. 163
M.DalBorgo,M.GhandchiTehrani,andS. J.Elliott
23 Bio-inspiredNonlinearControlofArtificialHairCells............................................................. 179
SheydaDavaria,V. V. N.SriramMalladi,andPabloA.Tarazaga
24 TransientExcitationSuppressionCapabilitiesofElectromagneticActuatorsinRotor-ShaftSystems ....... 185
NitishSharma,ShivangShekhar,andJayantaKumarDutt
25 ActiveVehicleSuspensionwithaWeightedMultitoneOptimalController:ConsiderationsofEnergy
Consumption............................................................................................................. 195
WaldemarRa˛czka,MarekSibielak,andJarosławKonieczny
26 SlidingModeControllerforVehicleBodyRollReductionUsingActiveSuspensionSystem................... 199
JarosławKonieczny,MarekSibielak,andWaldemarRa˛czka
27 ApplyingConceptsofComplexitytoStructuralHealthMonitoring .............................................. 205
BrianM.West,WilliamR.Locke,TravisC.Andrews,AlexScheinker,andCharlesR.Farrar
Chapter 1
A Modification to Unified Matrix Polynomial Approach (UMPA)
for Modal Parameter Identification
SeyedEhsanHajiAghaMohammadZarbafandRandallAllemang
Abstract Inthispaper,amodificationtoUnifiedMatrixPolynomialApproach(UMPA)formodalparameteridentification
of mechanical systems is suggested. Following the proposed modification, the measured Frequency Response Functions
(FRF)/ImpulseResponseFunctions(IRF)matricesofthesystemaremanipulatedsothatthevibrationalmodesofthesystem
can be identified at smaller model orders. A multi degree of freedom numerical case study and the experimental data of a
circular plate are then employed to investigate the enhancement in performance of UMPA framework due to the proposed
modification.Itwillbeshownthatfollowingtheproposeddatamanipulation,matriceswithlargevaluesofconditionnumber
canbeavoidedinmodalparameterestimation.
Keywords Unifiedmatrixpolynomialapproach(UMPA) · High-ordermodalparameteridentification · Condition
number · Rationalfractionpolynomialmethod · Polyreferencetimedomainmethod
1.1 Introduction
Modalparameterestimationisabranchofsystemidentificationwhereexperimentallymeasuredresponseofthesystemis
used to identify the modal parameters of the system employing a model in terms of modal parameters. There are several
typesofsystemresponsesintime/frequencydomainthatcanbeusedtoextractthemodalpropertieslikeImpulseResponse
Functions(IRF)andFrequencyResponseFunction(FRF).Thesystemcanbeexcitedusingdifferentexcitationmethods[1,2]
oritcanbelefttobeexcitedbyworking/environmentalconditions[3–8].Thesystemresponsesmeasuredatdifferentpoints
on the structure can be processed individually or simultaneously [9]. Consequently, there are many system identification
methods developed to identify the modal properties of systems using several types of systems responses [10–15]. In
1998, Allemang and Brown reformulated different modal parameter identification methods into a consistent mathematical
formulation and named it Unified Matrix Polynomial Approach (UMPA) [16]. In UMPA framework, a polynomial of a
generalized frequency variable with matrix coefficients is considered as the characteristic equation of the system where
the model order is the highest order of the generalized frequency variable. The methods in which there is no limitation
on the value of model order such as Complex Exponential (CE) [17], Least Squares Complex Exponential (LSCE) [18],
PolyreferenceTimeDomain(PTD)[19],andRationalFractionPolynomial(RFP)[20]arecalledhigh-ordermethodswhile
the methods with model order 1 (Ibrahim Time Domain (ITD) [21] and Eigensystem Realization Algorithm (ERA) [22])
or2(PolyreferenceFrequencyDomain(PFD)[23])arecalledlow-ordermethods.Foreachmodalparameteridentification
method,datamatricesintime/frequencydomainaremanipulatedaccordinglytocalculatetheunknowncoefficientmatrices
of matrix polynomial equation. Employing acquired coefficient matrices in a two-stage linear procedure, complex-valued
natural frequencies, modal participation vectors, modal vectors, and modal scaling factors (modal A/modal mass) are
identified[16].
Large condition number of data matrices involved in high order modal parameter identification methods is a challenge
especiallyforfrequencydomainmethodRFPwherethedatamatrixisofVandermondeform[24]andhence,thecondition
number of data matrix increases with model order and makes the identification method more sensitive to noise in data.
Minimizing the frequency range of the data and the order of the model [25], scaling the frequencies [26], and using
S.E.HajiAghaMohammadZarbaf((cid:2))·R.Allemang
StructuralDynamicsResearchLaboratory,SchoolofDynamicSystems,CollegeofEngineeringandAppliedScience,UniversityofCincinnati,
Cincinnati,OH,USA
e-mail:[email protected]
©TheSocietyforExperimentalMechanics,Inc.2019 1
C.Niezrecki,J.Baqersad(eds.),StructuralHealthMonitoring,Photogrammetry&DIC,Volume6,
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries,https://doi.org/10.1007/978-3-319-74476-6_1
2 S.E.HajiAghaMohammadZarbafandR.Allemang
orthogonalpolynomialslikeForsythepolynomials[27,28]andChebyshevpolynomials[29]insteadofpowerpolynomials
intheformulationofRFPhavebeenproposedovertheyearstodealwithill-conditioningofdatamatrixinhigh-ordermodal
parameteridentificationmethods.
In this paper, a data manipulation based on UMPA framework is suggested so that smaller model orders are required
to identify the vibrational modes of a system. First, UMPA framework for modal parameter identification of mechanical
systemsisreviewed.Second,amodificationtoUMPAframeworkissuggestedtoreducethemodelorderrequiredtoidentify
thevibrationalmodesofthesystemandhence,matriceswithlargeconditionnumberscanbeavoided.Finally,twohigh-order
modalparameteridentificationmethodsPTDandRFPareimplementedinUMPAframeworktoinvestigatetheenhancement
inperformanceofhighordermodalparameteridentificationmethodsinUMPAframeworkduetotheproposedmodification.
1.2 UMPA
ThegoverningdifferentialequationofmotionofasystemwithNDegreesofFreedom(DOFs)canbewrittenasEq.(1.1),
ŒM(cid:2)fxR.t/gCŒC(cid:2)fxP.t/gCŒK(cid:2)fx.t/gDff.t/g (1.1)
where [M], [C], and [K] – RN(cid:2)N are the mass, damping, and stiffness matrices of the system and fx(t)g and ff(t)g are the
systemresponsevectorandexcitationvector.TakingtheLaplacetransformofbothsidesofEq.(1.1)resultsin,
(cid:2) (cid:3)
ŒM(cid:2)s2CŒC(cid:2)sCŒK(cid:2) fX.s/gDfF.s/g (1.2)
where s is a general frequency variable and fX(s)g and fF(s)g are the Laplace transforms of fx(t)g and ff(t)g respectively.
AssumingthefreevibrationconditionforEq.(1.1),ff(t)gD0,thecharacteristicequationofthesystemiscalculatedasEq.
(1.3):
(cid:2) (cid:3)
det ŒM(cid:2)s2CŒC(cid:2)sCŒK(cid:2) D0 (1.3)
Partitioning[M],[C],and[K]intosub-matrices[M ],[C ],and[K ],i,jD1,2,3, :::,n,Eq.(1.3)canbeexpandedas
ij ij ij
below,
02 3 2 3 2 31
ŒM11(cid:2) ŒM12(cid:2) (cid:2)(cid:2)(cid:2) ŒM1n(cid:2) ŒC11(cid:2) ŒC12(cid:2) (cid:2)(cid:2)(cid:2) ŒC1n(cid:2) ŒK11(cid:2) ŒK12(cid:2) (cid:2)(cid:2)(cid:2) ŒK1n(cid:2)
detBBB@6664 ŒM:::21(cid:2)ŒM:::22(cid:2) (cid:2)::(cid:2):(cid:2) ŒM:::2n(cid:2)7775s2C6664 ŒC:::21(cid:2)ŒC:::22(cid:2) (cid:2)::(cid:2):(cid:2) ŒC:::2n(cid:2)7775sC6664 ŒK:::21(cid:2)ŒK:::22(cid:2) (cid:2)::(cid:2):(cid:2) ŒK:::2n(cid:2)7775CCCAD0 (1.4)
ŒMn1(cid:2)ŒMn2(cid:2) (cid:2)(cid:2)(cid:2) ŒMnn(cid:2) ŒCn1(cid:2)ŒCn2(cid:2) (cid:2)(cid:2)(cid:2) ŒCnn(cid:2) ŒKn1(cid:2)ŒKn2(cid:2) (cid:2)(cid:2)(cid:2) ŒKnn(cid:2)
Thesecond-ordermatrixpolynomialofEq.(1.4)canalsobewrittenasahigherordermatrixpolynomialwiththesame
roots:
Œ’2n(cid:2)s2nCŒ’2n(cid:3)1(cid:2)s2n(cid:3)1C(cid:2)(cid:2)(cid:2)CŒ’1(cid:2)sCŒ’0(cid:2)D0 (1.5)
InUMPAframework,thepolynomialmodelofEq.(1.6)isemployedtocalculatetheunknowncoefficientmatrices[’]in
Eq.(1.5):
P
H .¨/D “n.j¨/nC“n(cid:3)1.j¨/n(cid:3)1C(cid:2)(cid:2)(cid:2)C“1.j¨/1C“0 D PnkD0“k.j¨/k (1.6)
pq ’m.j¨/mC’m(cid:3)1.j¨/m(cid:3)1C(cid:2)(cid:2)(cid:2)C’1.j¨/1C’0 mkD0’k.j¨/k
where H (¨) is the FRF of the system measured at DOF p while the system is being excited at DOF q, ¨ is the angular
pq
frequencyinrad/sec,andmisthemodelorder.Eq.(1.6)canberewrittenas,
Xm Xn
’ .j¨/kH .¨/D “ .j¨/k (1.7)
k pq k
kD0 kD0
