σr standard deviation of random variable r

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1、AIAA-2000-4841ANITERATIVECONCURRENTSUBSPACEROBUSTDESIGNFRAMEWORKDhaneshPadmanabhanStephenM.Batill†DepartmentofAerospaceandMechanicalEngineeringUniversityofNotreDameNotreDame,IndianaAbstractKrVariance-CovarianceMatrixofrandomvectorrx¯MeanorcurrentDesig

2、nVariablesThepurposeofthispaperwastoevaluateaframe-y¯MeanorcurrentStateVariablesworkforobtainingrobustdesignsofcomplex,coupledp¯MeanorcurrentParameterssystems.ThisframeworkreferredtoasIterativeConcur-fMeritFunctionrentSubspaceRobustDesign(ICSRD),isbase

3、duponthegInequalityconstraintuseofglobalresponsesurfaceapproximationsofthede-erBiasinrandomvariablersignspace.ICSRDincorporatesarobustoptimizationaTrade-Offparameterformulation,usingalinearizationapproach.ItgeneratesbConfidencelimitsfortheapproximatesys

4、temapproximaterobustdesignsfromartificialNeuralNet-b0Confidencelimitsfortheactualsystemwork(NN)approximationsinaniterativefashion.Twobenchmarkproblemsarepresented,onebeinganana-lyticproblemwithtwodesignvariablesandtheotheracontrol-structuresproblem,which

5、ischaracterizedbyIntroductioncomplexdisciplinecoupling.Twovariationsofthelat-terproblemareconsidered,onewithmodifiedboundsTheICSRDframeworkisanextensionoftheCon-forcertaindesignvariablesandtheotherwithareducedcurrentSubspaceDesignFramework(CSD)1thatwasn

6、umberofdesignvariableswithoriginalbounds.Itisdevelopedformultidisciplinarydesignofacoupled,non-observedthattheNNtrainingplaysasignificantroleinhierarchicsystem,withthecapabilityofoptimizingsys-obtainingagoodrobustoptimum.Itisalsoobservedtemscharacterize

7、dbymixeddiscrete,blockandcontin-thatICSRDframeworkyieldsreasonablerobustdesignsuousdesignvariablesandasingleperformancefunction.forthetestcasesimplemented.TheICSRDframeworkincorporatesarobustoptimiza-tionformulationwhereasCSDframeworkdoesnot.Acomplexco

8、upledsystemcanbedecomposedintoNomenclatureContributingAnalyses(CAs)whoseoutputsarethesys-tem'sStateVariables(SVs).Inacoupledsystem,CAsµrMeanofRandomVariablerexchangeinformationwitheachother,oftennecessitat-srStandardDeviationofrandomvar