结构优化和鲁棒性设计课件

结构优化和鲁棒性设计顾镭博士徐有忠博士奇瑞汽车公司奇瑞乘用车工程研究院Background:Analysisvs.DesignNumericalOptimizationMultidisciplinaryDesignOptimization(MDO)SafetyOptimizationBackground:SafetyScopeandChallengesCAEChallengesandSolutionTechnologiesStructuralOptimizationCrashPulseOptimizationMDOApplicationsTopologyOptimizationShapeOptimizationRestraintSystemOptimizationFutureDirectionsOutlineAnalysisandDesignOptimizationMethodsOptimalityCriteriaMethods(indirectmethods)OptimalitycriteriaaretheconditionsafunctionmustsatisfyatitsminimumpointStudyofoptimalityconditionsarenecessaryregardlessofthemethodused.SearchMethods(directsearchmethods)

Math.Programming

Mostgeneral

RequireF,h,g,dF/dx,dh/dxdg/dxxk+1=xk+ak

Skx1x2OptimizationinComputationalMechanicsF,g,&hareimplicitfunctionsofx.

ExactevaluationrequirescompleteFEA.SensitivitiesofF,g&hmayrequiremoreeffortsthananalysisitself.Numbersofconstraintsgi&xmaybeverylarge.FinddesignvariableXthatwillMinimizeF(X)Subjecttogi(X)£0,hj(X)=0,Xl

£

X£

XuApproximateOptimizationAnalysis+GradientsApproximationOptimizationInnerLoopOptimizationAnalysisOuterLoopAnalysisApproximationOptimizationDOEOuterLoopInnerLoopMultidisciplinaryDesignOptimization

(MDO)isamethodologyforimprovingdesignofengineeringsystems,e.g.,automobile,aircraft,orspacecraft,inwhicheverythinginfluenceseverythingelse.-ByDr.J.Sobieski-NASALangleyWhatisMDOMDO(continued)EffectiveIntegrationofIndividualDisciplines/SubsystemstoCapturetheInteractionsNovelSolutionProcedurestoEnableSystemLevelSolutionsCharacteristics:Large-Scale,NeedsDecomposition,ComputationIntensive,MultipleSimulationsCFDStructuresControlsLoadsDeformationControlSurfaceDeflnsStressPressureMomentsDesignspacediscipline1Designspacediscipline2DesignVariablesPerformanceMultidisciplinaryOptimalDesignDiscipline1OptimumFeasible

Design

SpaceSuboptimalDesignConventionalTradesMDOSearchDiscipline2OptimumSafetyCAEChallenges/SolutionTechnologiesSimulationToolNotRobustorImmatureVerificationandValidationMethodsHighlyUndeterministicRobustDesignComputationIntensive(Structure)ResponseSurfaceMethodHighlyNonlinearorEvenDiscontinuous(RestraintSystem)GeneticAlgorithmManyConflictingRequirementsOptimizationManydesignVariablesHighPerformanceComputing(HPC)?(nosolutionyet)StructuralOptimization

(DOE/ResponseSurfaceApproach)ConventionalApproachSOARApproachTooexpensiveComputationaffordableSequentialParallel/HighPerformanceComputationLocaloptimalGlobaloptimalSensitivitybasedOptimalLatinHyperCube/SurrogatemodelsSingleDisciplineMultidisciplinaryReliabilityBasedRobustDesignAccuracy/Convergence?RobustnessAssessment&Design(MonteCarloetc.)STOPAddNewPointstoReconstructRSDefineOptimizationProblem:Objective,Constraints,DesignVariables(DV)SelectSamplingMethod:2/3levelDOE,Supersaturated,LatinHypercube

etc.ReduceDVNo.(basedoncomputerresources)ConstructResponseSurface(RS):NN,EMARS,Polynomial,StepwiseRegressionetc.NumericalOptimizationbasedonRSConfirmationRunsforOptimalDesignsYesNoOptimizationandRobustDesignStrategyUniformLatinHypercubeSampling(ParallelSimulations)SecondOrderResponseSurfaceSubsetSelectionGlobalOptimization/MixedVariableAlgorithm/SQPReliabilityBasedRobustOptimization

(Guetal,“MultidisciplinaryDesignOptimizationofaFullVehiclewithHighPerformanceComputing”,AIAA-2001-1273)

UniformLatinHypercubeSamplingUniformLatinhypercubeseeksdesignpointsthatuniformlyscatteredonthedomain.(Fangetal,UniformDesign:TheoryandApplication,2000)MeasurementsofuniformityL2discrepancy(Warnock,1972)CenteredL2discrepancy(Hickernell,1998)

UniformLatinHypercubeSamplingMin.num.ofsimulations=3num.ofdesignvariablesFactorialDesignLatinHypecubeUniformLatinHypecubeGoal:within45simulationsforeachcrashmode.SubsetRegressionSecondorderresponsesurfaceRegressionbysubsetselection(A.J.Miller,SubsetSelectioninRegression,ChapmanandHall,1990)E.g.HIC=359.4-2.83x1+76.3x2x10-34.84x9x9+0.3x3-3.87x4x10+2.7x4+0.2x5QualityoftheresponsesurfaceismeasuredbyResidualSumofSquares(RSS)Stepwiseregression(Efroymsonalgorithm)SequentialReplacementAlgorithmSequentialReplacementAlgorithm(SRA) Startingsubset:y=a0+a1x1+…+an

xnReplacementcandidates:x12,x22,…,xn2,x1x2,x1x3,…,x1xn,x2x3,…,xn-1xn Startingsubset:y=a0+a1x1+…+an

xn

RSS0

Iteration1:y=a0+a1x12+…+an

xn

RSS1

Iteration2:y=a0+a1x22+…+an

xn RSS2 …………Iterationm:y=a0+a1

xn-1xn+…+an

xn RSSm

LetRSSk

=Min{RSSi},thenStartingsubset:y=a0+a1

pk(x)+a2x2+…+an

xn

…………Application:FrontEndOptimization35mphFrontimpactintoaRigidWall40mphFrontOffsetImpactintoaDeformableBarrierApplication:VehicleFrontEndOptimizationSummaryofFrontEndOptimizationDesignVariables(10):GagesandMaterialsofRail,Shotgun,Subframe,Brace,Cross-member,Rocker,Sill,etc.TotalNumberofSimulations:72CPUofEachSimulation:70hrsonSGIOrigin2000(front)and100hrs(Offset)FEMmodels:C.O’Connor,M.El-BkallyandT.QuExampleofOptimizationandRobustnessAssessmentRisksof“Optimized”Design:ActiveConstraints

–uncertainty,variationleadstofaileddesignsOptimizationXYFeasibleInfeasible(safe)(failed)InitialDesignOptimizationXYFeasibleInfeasible(safe)(failed)InitialDesignSensitive“peak”solutions–smallchangesininputsresultsinsignificantlossofperformanceEffectofUncertainty:PerformanceVariationSearchforreliablestructuraldesigns:feasiblewithrespecttodeterministicconstraintsmeetadesiredminimumlevelofReliabilitydonotexceedamaximumProbabilityofFailureHastheeffectofpullingdeterministicoptimizationsolutionsawayfromtheconstraintsInitialProbabilityofFailure,PfY1Robust,ReliableSolutionconstraintReliabilityBasedDesignoptimization:BenefitsOptimalSolutionReliability“Shift”andRobust“Shrink”SafetyFactor?Optimization?OrRobust?Focus:AddressingUncertainty,DesigningforQualityImplementation: SixSigmaBasedRobustDesignOptimization(iSIGHT)

PerformanceMeasureApproach(PMA)ReliabilityBasedDesignOptimizationSourcesofVariabilityMaterialrelatedMaterialpropertiesThicknessManufacturingrelatedFormingprocessesMachiningprocessesAssemblyprocessesTestconditionsEnvironmentsHumanFactorsActualvs.expecteduseModelingTechniquesNumericalalgorithmscontrolsConstitutivemodelsComputerhardwareReliabilityBasedDesignOptimizationMethodologiesMinimize Costf(x)Subjectto P[Gi(x)0]

Pfi,i=1-mSQP+MonteCarloMethodSingleLoopSingleVector(SLSV)MeanValueMethodPerformanceMeasureApproach(PMA) (K.K.Choi,Univ.ofIowa)RobustDesignMinimize Variationoff(x)( )Subjectto P[Gi(x)0]

Pfi,i=1-mSQP+MonteCarloMethodSingleLoopSingleVector(SLSV)MeanValueMethodHasofer-LindMethod(DoubleLoop)Inputm(k)xLoopforeachGjtocomputerbj.OptimizationLoopforcostfunctiontoupdatemx

Converge?stopyesnoStartNumberofFunctionEvaluationSingleLoopSingleVectorMethod(Chenetal,1997)startComputermConstraintDerivativesComputera(0)janda*(0)Computerm(0)x=x(0)+b0sxa

*(0)CallOptimizer(SQP)toupdatemx

Computerx(k)=m(k)