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1、StructMultidiscOptim(2009)37:475492DOI10.1007/s00158-008-0239-2RESEARCHPAPERReliability-basedrobustdesignoptimizationusingtheeigenvectordimensionreduction(EDR)methodByengD.Youn·ZhiminXiReceived:16March2007/Revised:14November2007/Accepted:23January200
2、8/Publishedonline:15March2008?Springer-Verlag2008AbstractThispaperpresentsaneffectivemethod-KeywordsDerivative-free·Reliability·ologyforreliability-basedrobustdesignoptimiza-Quality·Designoptimization·tion(RBRDO).TheeigenvectordimensionreductionEigen
3、vectordimensionreduction(EDR)methodplaysapivotalroleinmakingRBRDOeffectivebecausetheEDRmethodturnsouttobeveryef?cientandaccurateforprobabilityanalysis.TheuseoftheEDRmethodprovidesthreebene?tsto1IntroductionRBRDO.First,anapproximateresponsesurfacefaci
4、-litatessensitivitycalculationofreliabilityandqualityProbabilityanalysisisanessentialtooltoobservethewheretheresponsesurfaceisconstructedusingtheeffectofuncertainty(e.g.,manufacturingvariabilityeigenvectorsamples.Thus,sensitivityanalysisbecomesandloa
5、ds)inengineeringsystems.However,acommonveryef?cientandsimple.Second,oneEDRexecutionchallengeinprobabilityanalysisisamultidimensionalevaluatesasetofquality(objective)andreliabilityintegrationtoquantifytheprobabilisticnatureofthe(constraint)functions.I
6、ngeneral,theEDRrequiressystemresponses.Itisalmostimpossibletoconductthe2N+1or4N+1simulationrunswhereNisthemultidimensionalintegrationanalyticallyandnumeri-totalnumberofrandomvariables.TheEDRexe-cally.Otherthandirectintegrationapproach,theexist-cution
7、doesnotrequireaniterativeprocess,sotheingapproximationmethodsforprobabilityanalysiscanproposedRBRDOmethodologyhasasingle-loopbecategorizedintofourgroups:(1)samplingmethod;structure.Moreover,theEDRexecutiontimecanbe(2)expansionmethod;(3)themostprobabl
8、epointmuchshorterbytakingadvantageofaparallelcom-(MPP)-basedmethod;and(4)approximateintegrationputingpower,andRBRDOcanbefarmoreef?cient.method.Third,theEDRmethodallowssolvingproblemswithThesamplingmethodismostcomprehensivebutstatisticallycorrelatedan
