Table Of ContentConference Proceedings of the Society for Experimental Mechanics Series
Series Editor
Tom Proulx
Society for Experimental Mechanics, Inc.,
Bethel, CT, USA
For furthervolumes:
http://www.springer.com/series/8922
T. Simmermacher (cid:129) S. Cogan (cid:129) L.G. Horta (cid:129) R. Barthorpe
Editors
Topics in Model Validation
and Uncertainty Quantification,
Volume 4
Proceedings of the 30th IMAC, A Conference on Structural
Dynamics, 2012
Editors
T.Simmermacher S.Cogan
SandiaNationalLaboratories UniversityofFranche-Comte
Albuquerque,NM,USA Besanc¸on,France
L.G.Horta R.Barthorpe
NASALangleyResearchCenter UniversityofSheffield
Hampton,VA,USA Sheffield,UK
ISSN2191-5644 e-ISSN2191-5652
ISBN978-1-4614-2430-7 e-ISBN978-1-4614-2431-4
DOI10.1007/978-1-4614-2431-4
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2012934958
#TheSocietyforExperimentalMechanics,Inc.2012
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+Business
Media,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnection
withanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownor
hereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasan
expressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
TopicsinModelValidationandUncertaintyQuantificationrepresentsoneofsixvolumesoftechnicalpaperspresentedatthe
30thIMAC,AConferenceandExpositiononStructuralDynamics,2012organizedbytheSocietyforExperimentalMechanics,
andheldinJacksonville,Florida,January30–February2,2012.ThefullproceedingsalsoincludevolumesonDynamicsofCivil
Structures;SubstructuringandWindTurbineDynamics;NonlinearDynamics;andModalAnalysis,I&II.
Eachcollectionpresentsearlyfindingsfromexperimentalandcomputationalinvestigationsonanimportantareawithin
Structural Dynamics. This volume focuses on the importance of Model Validation and Uncertainty Quantification.
In keeping with the goals of encouraging advancement and application of model Verification and Validation (V&V) and
uncertainty quantification methods in Structural Dynamics, this volume includes tutorials on the use of the Bayesian and
Markov Chain Monte Carlo Methods. The Bayesian paradigm is of great interest to the engineering community as
itprovidesaprincipledframeworkforhandlinguncertaintiesincomplexsystems.TheMarkovChainMonteCarlomethod
is,inturn,ausefultoolforpracticalimplementationoftheBayesianparadigm.
Theorganizerswouldliketothanktheauthors,presenters,sessionorganizers,andsessionchairsfortheirparticipationin
thistrack.
Albuquerque,NM,USA T.Simmermacher
Besanc¸on,France S.Cogan
Hampton,VA,USA L.G.Horta
Sheffield,UK R.Barthorpe
v
Contents
1 OnAssessingtheRobustnessofStructuralHealthMonitoringTechnologies.................................... 1
ChristopherJ.Stull,Franc¸oisM.Hemez,andCharlesR.Farrar
2 DesignofUncertainPrestressedSpaceStructures:AnInfo-GapApproach..................................... 13
Aure´lienHot,ScottCogan,EmmanuelFolteˆte,GaetanKerschen,
FabriceBuffe,Je´roˆmeBuffe,andSte´phanieBehar
3 RobustControlDesignforUncertainNonlinearDynamicSystems............................................... 21
SeanP.Kenny,LuisG.Crespo,LindseyAndrews,andDanielGiesy
4 BayesianDamageLocalisationatHigherFrequencieswithGaussianProcessError........................... 39
ChristopheLecomte,J.J.Forster,B.R.Mace,andN.S.Ferguson
5 IdentificationofHystereticSystemsUsingNARXModels,PartI:EvolutionaryIdentification................ 49
K.WordenandR.J.Barthorpe
6 IdentificationofHystereticSystemsUsingNARXModels,PartII:ABayesianApproach..................... 57
K.Worden,R.J.Barthorpe,andJ.J.Hensman
7 BayesianMethodsforUncertaintyQuantificationinMulti-levelSystems ....................................... 67
ShankarSankararaman,KyleMcLemore,andSankaranMahadevan
8 SamplingTechniquesinBayesianFiniteElementModelUpdating............................................... 75
I.Boulkaibet,T.Marwala,L.Mthembu,M.I.Friswell,andS.Adhikari
9 BayesianModelUpdatingApproachforSystematicDamageDetectionofPlate-TypeStructures............. 85
MasahiroKurata,JeromeP.Lynch,KinchoH.Law,andLimingW.Salvino
10 OntheLegitimacyofModelCalibrationinStructuralDynamics................................................ 95
Franc¸oisM.HemezandChristopherJ.Stull
11 PossibilisticInterpretationofMistuninginBladedDisksbyFuzzyAlgebra..................................... 109
H.C¸ag˘larKaratas¸,EnderCig˘erog˘lu,andH.NevzatO¨zg€uven
12 FEMSensitivityTechniqueforDynamicResponseUncertaintyAnalyses....................................... 117
RobertN.Coppolino
13 UncertaintyQuantificationofWeightedResidualMethodinLoadsEstimation ................................ 125
ColinM.Haynes,MichaelD.Todd,andKevinL.Napolitano
14 RapidStructuralConditionAssessmentUsingTransmissibilitywithQuantified
ConfidenceforDecisionMaking..................................................................................... 133
ZhuMaoandMichaelTodd
vii
viii Contents
15 SimulatingUnbalanceforFutureIVHMApplications............................................................. 141
RyanWalker,SureshkumarPerinpanayagam,andIanJennions
16 InverseEigensensitivityApproachinModelUpdatingofAvionicComponents................................. 149
ElvioBonisoli,CarloRosso,CristianaDelprete,andFabioStratta
17 ShapeOptimizationofPlatesforDesiredNaturalFrequenciesfromCoarseGridResults..................... 167
EduardoB.M.R.GermanoandRodrigoNicoletti
18 ModelUpdatingofComplexAssemblyStructuresBasedonSubstructures-JointParameters................. 175
MortezaH.Sadeghi,ParivashSoleimanian,andHamedSamandari
Chapter 1
On Assessing the Robustness of Structural
Health Monitoring Technologies
ChristopherJ.Stull,Franc¸oisM.Hemez,andCharlesR.Farrar
Abstract AsStructuralHealthMonitoring(SHM)continuestogainpopularity,bothasanareaofresearchandasatoolfor
useinindustrialapplications,thenumberoftechnologiesassociatedwithSHMwillalsocontinuetogrow.Asaresult,the
engineer tasked with developing a SHM system is faced with myriad hardware and software technologies from which to
choose, often adopting an ad hoc qualitative approach based on physical intuition or past experience to making such
decisions,andofferinglittleinthewayofjustificationforaparticulardecision.Thepresentpaperoffersaframeworkthat
aimstoprovidetheengineerwithaqualitativeapproachforchoosingfromamongasuiteofcandidateSHMtechnologies.
The framework is outlined for the general case, where a supervised learning approach to SHM is adopted, and is then
demonstratedonaproblemcommonlyencounteredwhendevelopingSHMsystems:selectionofadamageclassifier,where
theengineermustselectfromamongasuiteofcandidateclassifiers,theonemostappropriateforthetaskathand.Thedata
employedfortheseproblemsaretakenfromapreliminarystudythatexaminedthefeasibilityofapplyingSHMtechnologies
totheRAPidTelescopesforOpticalResponseobservatorynetwork.(ApprovedforunlimitedpublicreleaseonSeptember
20,2011,LA-UR11-05398,Unclassified)
Keywords Structural health monitoring • Info-gap decision theory • Decision making • Model selection • Uncertainty
•Autoregressivemodel
1.1 Introduction
At the most general level, Structural Health Monitoring (SHM) often employs a model to approximate the changes in
behaviorofaphysicalsystemthatresultfromdamage.AnincreasedinterestinSHMbythecivil,aerospaceandmechanical
engineering communities has led to a relative explosion of technologies proposed to both improve upon and extend the
applicationoftheseresearchfields.Asthesetechnologiesarebroughtonline,theengineertaskedwithdevelopingaSHM
systemisnotonlyfacedwiththedifficultyofchoosingfromamongthesetechnologies,butmustalsodosodefensibly.
Offeringsuchdefensibleapproaches,tworecentresearchefforts[1,2]adoptedBayesianmodelselectionframeworksto
selectfromamongafamilyofmodels,themodelthatmostprobablyrepresentedasystemforwhichdataexist.Whereas[1]
focused more generally on the problem of selecting a model that approximates a physical system, [2] focused more
specifically on the determining the most probable order of an autoregressive model with exogenous inputs (ARX).
Ingeneral,theseapproachesemployBayes’theoremas[3]
PðMjDÞ/PðDjMÞPðMÞ: (1.1)
i i i
C.J.Stull(*)•C.R.Farrar
EngineeringInstitute,LosAlamosNationalLaboratory,POBox1663,MailStopT001,LosAlamos,NM87545,USA
e-mail:[email protected]
F.M.Hemez
X-TheoreticalDesignDivision,LosAlamosNationalLaboratory,POBox1663,MailStopT087,LosAlamos,NM87545,USA
T.Simmermacheretal.(eds.),TopicsinModelValidationandUncertaintyQuantification,Volume4, 1
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries29,
DOI10.1007/978-1-4614-2431-4_1,#TheSocietyforExperimentalMechanics,Inc.2012
2 C.J.Stulletal.
Here, PðMÞ is the prior probability assigned to the model M, or the probability that the model M is the true
i i i
model before observing the data. PðDjMÞ is the model evidence, or the probability that the data D will be observed
i
given the model M. PðDjMÞ is also referred to as the marginal likelihood, as it is essentially a likelihood function
i i
associated with model M, where the effects of the model parameters are removed by randomly sampling from the
i
prior probabilities associated with the model parameters [3]. Lastly, the term PðMjDÞ is the posterior probability of
i
themodelM,ortheprobabilitythatmodelM isthetruemodelafterobservingthedataD.Withrespecttotheworkof[1],
i i
the M in (1.1) corresponded to different model classes employed to approximate the dynamic behavior of
i
structures subjected to seismic excitations. For [2], the M corresponded to the parameters that define different orders
i
ofanARXmodel.
WhensolvingBayesianmodelcomparisonproblems,modelsaretypicallyassignedequalpriorprobabilitiestorepresent
theanalyst’signoranceastowhichmodelisthetruemodelforthedataathand.Oncetheposteriorprobabilitiesassociated
withthemodelsareestimated,theseestimationsmaybeusedtocomputeinformationcriteria(e.g.Akaike,Schwartz[3])as
ameansofevaluatingtherelativemeritofeachmodel.Whilethisframeworkoffersaprincipledtreatmentoftheanalyst’s
uncertaintyaboutthemodelselectionproblem,itisconditionedondataD.Assuch,concernariseswhenitisadmittedthat
these data are subject to variability (aleatoric and epistemic), as such changes have the potential to introduce additional
uncertaintiesintothemodelselectionproblem.
1.1.1 Overview of Proposed Framework
Thepresentpaperoffersanalternativeframeworkwithwhichtoaddressthemodelselectionproblemwithinthecontextof
SHM.AnchoredinInformation-GapDecisionTheory(IGDT)[4],thisframeworkassumesanon-probabilisticdescription
of the engineer’s lack of knowledge about the data. Using this as a point of departure, the proposed framework aims to
informtheengineerastotherobustness,orinsensitivitytothisignorance,ofaparticulardecision(i.e.SHMtechnology).
IGDThasbeenappliedinanumberofresearchtopics,andthereaderisdirectedto[5]foranexhaustivelistofreferences.
A recent application of IGDT to SHM is found in [6] where the authors assessed the robustness of an artificial neural
network’sabilitytodetectdamage,givenvariabilityintheinthenetworkinputs.Whileasimilarstrategyisadoptedherein,
an attempt has been madeby the authors togeneralize the approach inorder totackle broader classes ofproblems within
SHM.Tothisend,thefour-partstatisticalpatternrecognitionparadigmdiscussedin[7]ispresented:
(i) OperationalEvaluation;
(ii) DataAcquisition,Normalization,andCleansing;
(iii) FeatureSelectionandInformationCondensation;and
(iv) StatisticalModelDevelopmentforFeatureDiscrimination.
ThefocushereinwillbeondecisionsrelatedtoPart(iv)ofthisparadigm,andassuch,itwillbeassumedforthepurposes
ofthispaperthatthetechnologies,data,etc.associatedwithParts(i),(ii),and(iii)havebeendefinedandarefixedatthis
pointintheSHMsystemdesignprocess.Itisnotedhowever,thattheproposedframeworkisgeneral,inthatitcouldalsobe
appliedtodecisionsassociatedwithParts(i),(ii),and(iii).
1.1.2 Paper Organization
Theremainderofthispaperisorganizedaroundtwomainsections.Section1.2isdevotedtoformulatingtheproblemofhow
toassessSHMtechnologies,insupportofdesigningSHMsystemsthatarerobusttovariabilityinthedataandhence,the
damage-sensitivefeaturesextractedfromthesedata.First,theproblemiscastwithinthecontextofIGDT.Then,important
quantities relevant to this application of IGDT are defined, which feed into the definitions of the info-gap models of
uncertainty and the robustness function. Section 1.3 then demonstrates the application of IGDT to an aspect of an SHM
design, related to Part (iv) of the paradigm outlined above. The paper concludes with a summary of the work performed,
improvementstotheSHMdevelopmentprocess,andideasforfuturedirectionsofresearch.
