外文翻译机械结构的可靠性优化设计.docx

外文翻译机械结构的可靠性优化设计.docx

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外文翻译机械结构的可靠性优化设计

外文翻译-机械结构的可靠性优化设计

英文原文

Optimizethereliabilityofmechanicalstructuredesign

Itisnowgenerallyrecognizedthatstructuralandmechanicalproblemsarenondeterministicand,consequently,engineeringoptimumdesignmustcopewithun-certainties，Reliabilitytechnologyprovidestoolsforformalassessmentandanalysisofsuchuncertainties，Thus,thecombinationofreliability-baseddesign

proceduresandoptimizationpromisestoprovideapracticaloptimumdesignsolution,i，e，,ade-signhavinganoptimumbalancebetweencostandrisk，However,

reliabilty-basedstructuraloptimizationprogramshavenotenjoyedthenamepopularityastheirdeterministiccounterparts，Somereasonsforthisaresuggested，

First,reliabilityanalysiscanbecomplicatedevenforsimplesystems，Thereare

variousmethodsforhandlingtheuncertaintyinsimilarsituations（e，g，,firstorder

secondmomentmethods,fulldistributionmethods），Lackingasinglemethod,

individualsarelikelytoadoptseparatestrategiesforhandlingtheuncertaintyintheirparticularproblems，Thissuggeststhepossibilityofdifferentreliabilitypredictionsinsimilarstructuraldesignsituations，Then,therearedivergingopinionsonmany

basicissues,fromtheverydefinitionofreliability-basedoptimization,includingthedefinitionoftheoptimumsolution,theobjectivefunctionandtheconstraints,toitsapplicationinstructuraldesignpractice，Thereisaneedtoformallyconsiderthese

itessinthemergerofpresentstructuraloptimizationresearchwithreliability-baseddesignphilosophy。

Ingeneral,anoptimizationproblemcanbestatedasfollows,Minimize

subjecttotheconstraints

whereXisan-dimensionalvectorcalledthedesignvector，f（X）iscalledthe

objectivefunctionand,"k（X）and}i（X）are,respectively,theinequalityandequalityconstraints，Thenumberofvariablesnandthenumberofconstraints，Lneednotbe

relatedinanyway，Thus,Lcouldbelessthan,equaltoorgreaterthanninagivenmathematicalprogrammingproblem，Insomeproblems,thevalueofLmightbe

zerowhichmeanstherearenoconstraintsontheproblem，Suchtypeofproblemsare

called"unconstrained"optimizationproblems，ThoseproblemsforwhichLisnot

equaltozeroareknownas"constrained"optimizationproblems。

Traditionallythedesignerassumestheloadingonanelementandthestrengthofthatelementtobeasinglevaluedcharacteristicordesignvalue，Perhapsitisequal

tosomemaximum（orminimum）anticipatedornominalvalue，Safetyisassuredby

introducingafactorofsafety,greaterthanone,usuallyappliedasareductionfactortostrength。

Probabilisticdesignispropose:

asanalternativetotheconventionalapproachwiththepromiseofproducing"betterengineered"systems，eachfactorinthedesign

processcanbedefinedandtreatedasarandomvariable，Usingmethod-ologyfrom

probabilistictheory,thedesignerdefinestheappropriatelimitstateandcomputestheprobabilityoffailureP}oftheelement，Thebasicdesignrequirementisthat，where

pfisthemaximumallowableprobabilityoffailure。

Advantagesofadoptingtheprobabilisticdesignapproacharewelldocumented（Wu,1984），Basicallytheargumentsforprobabilisticdesigncenteraroundthefactthat,relativetotheconventionalapproach,a）riskisamoremeaningfulindexofstructuralperformance,andb）areliabilityapproachtodesignofasys-tomcantendtoproducean"optimum"designbyensuringauniformriskinallcomponents。

Optimization,whichmaybeconsideredacomponentofoperationsresearch,istheprocessofobtainingthebestresultbyfindingconditionsthatproducethemaximumorminimumvalueofafunction，Table1，1illustratesareaofoperations

research。

Mathematicalprogrammingtechniques,alsoknownasoptimizationmethods,areusefulinfindingtheminimum（ormaximum）ofafunctionofseveralvariablesunderaprescribedsetofconstraints，Rao（1979）presentedadefinitionanddescriptionofsomeofthevariousmethodsofmathematicalprogramming，Stochas-ticprocess

techniquescanbeusedtoanalyzeproblemswhicharedescribedbyasetofrandomvariables，Statisticalmethodsenableonetoanalyzetheexperimentaldataandbuildempiricalmodelstoobtainthemostaccuraterepresentationsofphysicalbehavior。

OriginsofoptimizationtheorycanbetracedtothedaysofNewton,La-grangeandCauchyinthe1800'x，TheapplicationofdifferentialcalculustooptimizationwaspossiblebecauseofthecontributionsofNewtonandLeibnitz，Thefoundationsof

calculusofvariationswerelaidbyBernoulli,Euler,LagrangeandWeirstrass，The

methodofoptimizationforconstrainedproblems,whichinvolvestheadditionofunknownmultipliersbecameknownbythenameitsinventor,La-grange，Cauchy

presentedthefirstapplicationofthesteepestdescentmethodtosolveminimizationproblems。

Inspiteoftheseearlycontributions,verylittleprogresswasmadeuntilthemiddle

ofthetwentiethGentry,whenhigh-speeddigitalcomputersmadetheimplementationofoptimizationprocedurespossibleandstimulate,dfurtherresearchonnewmethods，Spectacularadvancesfollowed,producingam;}sssiveliteratureonoptimizationtechniques，Thisadvancementalsoresultedintheemergenceofseveralwell-definednewareasinoptimizationtheory。

ItisinterestingtonotethatmajordevelopmentsintheareaofnumericalmethodsofunconstrainedoptimizationhavebeenmadeintheTTnitedKingdomonlyinthe1960'x，ThedevelopmentofthesimplexmethodbyDantzig（1947）forlinearprogrammingandtheannunciationoftheprincipleofoptimalitybyBellman（195?

）fordynamicprogrammingproblemspavedthewa，;f}=developmentofthemethods

ofconstrainedoptimization，TheworkbyKuhnandTucker（1951）onnecessaryand

xuflicientconditionsfortheoptimalxolutionofprogrammingproblemslaidfoundationsforlaterresearchinnonlinearprogramming,theoptimizationareaofthisthesis。

Althoughnosingletechniquehasbeenfoundtobeuniversallyapplicablefornonlinearprogramming,theworksbyCacrol（1961）andFiaccoandMcCormic（1968）suggestedpracticalsolutionsbyemployingwell-knowntechniquesofunconxtrainedoptimization，GeometricprogrammingwasdevelopedbyDufhn,ZenerandPeterson（1960），Gomory（1963）pioneeredworkinintegerprogramming,whichisatthistimeanexcitingandrapidlydevelopingareaofoptimizationresearch，Many

"real-world"applicationscanbecastinthiscategoryofproblem，Dantzig（1955）and

CharnelandCooper（1959）developedstochasticprogrammingtechniquesandsolvedproblemsbyassumingdesignparameterstobeindependentandnormallydistributed。

Techniquesofnonlinearprogramming,employedinthisstudy,canbecategorized

1，one-dimensionalminimizationmethod

2，unconstrainedmultivariableminimization

A，gradientbasedmethod

B，nongradientbasedmethod

3，constrainedmultivariableminimization

A，gradientbasedmethod

B，gradientbasedmethod

Thegradientbasedmethodsrequirefunctionandderivativeevaluationswhilethenongradientbasedmethodsrequirefunctionevaluationsonly，Ingeneral,onewould

expectthegradientmethodstobemoreeffecti;re,duetotheaddedinformationprovided，However,ifanalyticalderivativesareavailable,thequestionofwhetherasearchtechniqueshouldbeusedatallispresented，Ifnumericalderivative

approximationsareutilized,theefficiencyofthegradientbasedmethodsshouldbeapproximatelythesameasthatofnongradientbasedmethods，Gradientbased

methodsincorporatingnumericalderivativeswouldbeexpectedtopresentsomenumericalproblemsinthevicinityoftheoptimum,i，e，,approximationstoslopes

wouldbecomesmall，Fig，1，1showsthe$owchartofgeneraliterativeschemeofoptimization（Rao,1979），

Noclaimismadethatsomemethodsarebetterthananyothers，Amethod

workswellononeproblemmayperformverypoorlyonanotherproblemofthesamegeneraltype，Onlyaftermuchexperienceusingallthemethodscanonejudgewhichmethodwouldbebetterforaparticularproblem（KuestersndMize,1973）.

Firstattemptstoapplyprobabilisticandstatisticalconceptsinstructuralanalysisdatebacktothebeginningofthiscentury，However,thesubjectaidnotreceive

muchattentionuntilaftertheWorldWarII，InOctober1945,ahistoricpaperwritten

byA，M，Freudenthalentitled"TheSafetyofStructures"appearedintheproceedingsoftheAmericanSocietyofCivilEngineers，Thepublication

ofthispapermarkedthegenesisofstructuralreliabilityintheU，S，A，，Professor

F:

eudenthalcontinuedformanyyearstobeintheforefrontofstructuralreliabilityandriskanalysis，

Duringthe1960'stherewasrapidgrowthofacademicinterestinstruc-totalreliabilitytheory，Classicaltheorybecamewelldevelopedandwidelyknown

throughafewinfluentialpublicationssuchasthatofFreudenthal,Garrelts,andShi-nouzuka（1966）,Pugsley（1966）,KececiogluandCormier（1964）,Ferry-BorgesandCastenheta（1971,andHaugen（1968），However,professionalacceptancewas

lowforseveralreasons，Probabilisticdesignseemedcumbersome,thetheory,

particularlysystemanalysis,seemedmathematicallyintractible，Littledatawere

available,andmodelingerrorwasanissuewhichneededtobeaddressed，

Buttherewereearlyeffortstocircumventtheselimitations，Turkstra（l070）

Yr}}ntedstructuraldesignasaproblemofdecisionmakingunderuncertaintyandrisk，Lind,Turkstra,andWright（1965）definedtheproblemofrationaldesignofacodeasfindingasetofbestvaluesoftheloadandresistancefactors，Cornell（1967）

suggestedtheuseofasecondmomentformat,andsubsequentlyit