《模糊滑模控制》PPT课件

Fuzzyarithmeticbasedreliabilityallocationapproachduringearlydesignanddevelopment初期阶段的设计和发展中基于模糊算法的可靠度分配方法,V.Sriramdas,S.K.Chaturvedi,H.Gargama,1.Introduction2.Factorsbasedconventionalreliabilityallocationmethod3.Fuzzynumbersandarithmetic4.Themethodology5.Illustrativeexample6.Conclusions,1.IntroductionReliabilityallocationisanimportantanditerativetaskduringthedesignanddevelopmentactivitiesofanyengineeringsystem.Itisalsodifficulttaskbecauseoftheobscuredandincompletedesigndetailsandanumberoffactorshavetoconsiderindesignprocess.Duringthedesignphaseofasystemwithaspecifiedtargetreliabilitylevel,thereliabilitylevelsofthesubsystemsaffecttheoverallsystemreliability.Therefore,aproperreliabilityallocationmethodneedstobeadoptedtoallocatethetargetsystemreliabilitytoitsconstituentsubsystemsproportionately.,4,2.Factorsbasedconventionalreliabilityallocationmethod,Inthisallocationmethod,thetargetreliabilitybasedonthereliabilityfactorsisapportionedtosubsystemsforwhichnopredictedreliabilityvaluesareknown.TherelationshipbetweenapportionedreliabilityofithsubsystemRi（子系统可靠度）andtargetsystemreliabilityR*（总系统可靠度）isdefinedwithaweightagefactorwi.,Ri=(R*)wi,(1),whereweightagefactorwi（权重因子）canbeexpressedwithproportionalityfactorZi（比例因子）as：,wi=Zi/Zi,(2),5,2.1.Complexity（复杂度）,Thecomplexityfactorvariesfromsubsystemtosubsystemwithinasystemandismeasuredintermsofnumberofactivecomponentsthatasubsystemiscomposedof.Thenumberofcomponentsinasubsystemhasadirectbearingonthereliabilityofthesubsystem.Thus,complexityhasastrongimpactonthereliabilityallocation.Thefailurerateofthesubsystemwithhighcomplexityisgenerallygoingtobehigh.So,thefailurerateisallocatedproportionaltothecomplexityofthesubsystem.Hence,ZiKi,whereKiisthecomplexityfactorfortheitssubsystem.,1.Multiplefunctionalrelationshipswiththeothergroups.2.Numberofcomponentscomprisingsubsystem.,6,2.2.Cost（成本）,Foralargesystem,thecostincrementforreliabilityimprovementisrelativelyhigh.Thedemonstrationofahighreliabilityvalueforacostlysystemmaybeextremelyuneconomical.Hence,ZiCoi,whereCoiisthecostfactorfortheitssubsystem.,2.3.State-of-the-art（工艺状态）,Whenthecomponenthasbeenavailableforalongtime,itisquitedifficulttofurtherimprovethereliabilityofacomponentevenifthereliabilityisconsiderablylowerthandesired.Hence,Zi1/Si,whereSiisthestate-of-the-artfactorfortheitssubsystem.,7,2.4.Criticality（临界值）,Criticalityisanotherveryimportantfactorinreliabilityallocation.Itislogical,higherreliabilitytargetshouldbeallocatedtothefunctionallycriticalsub-systemsandthusZiisproportionaltocriticality.Hence,Zi1/Cri,whereCriisthecriticalityfactorfortheitssubsystem.,2.5.Timeofoperation（运行时间）,Theremaybesomesubsystemswhicharerequiredtobeoperatedforaperiodlessthanthemissiontime.So,forthesubsystemswithoperatingtimelessthanthemissiontime,itisonlylogicaltoallocaterelativelylowerreliability.Hence,Zi1/Ti,whereTiisthetimeofoperationfactorfortheithsubsystem,2.6.Maintenance（维护）,Acomponentwhichisperiodicallymaintainedoronewhichisregularlymonitoredorcheckedandrepairedasnecessarywillhave,onanaveragehigheravailabilitythanonewhichisnotmaintainedHence,ZiMi,whereMiisthemaintenancefactorfortheitssubsystem.Theprocessofallocationofrelativescalesiscarriedoutasateamexercise,comprisingofexperiencedmembersfromtheeachofthesubsystemidentified.Fromthepreviousdiscussionsinthissection,afterconsiderationofvariousfactors,formulaforproportionalityfactor(Zi)as:,3.Fuzzynumbersandarithmetic,Definition:Afuzzynumberisafuzzysubsetthatisbothconvex,andnormal.Themostcommonlyusedfuzzynumbersaretriangularandtrapezoidalfuzzynumbers,parameterizedby(a,b,c),and(a,b,c,d),respectively,themembershipfunctionsofthesenumbersaredefinedbelow:,Thenthestandardoperationsontrapezoidalfuzzynumbersareexpressedas:,Addition:,Subtraction:,Multiplication:,Division:,Defuzzification（解模糊化）istheunderlyingreasonthatonecannotcomparefuzzynumbersdirectly.Althoughmanyauthorsproposedtheirfavoritemethods,thereisnouniversalconsensus.Eachmethodincludescomputingacrispvalue,tobeusedforcomparison.Thisassignmentofarealvaluetoafuzzynumberiscalleddefuzzification.Itcantakemanyforms,butthemoststandarddefuzzificationisthroughcomputingthecentroid(计算模糊重心).,3.1.Fuzzydivisionbyusinglinearprogramming,Letbetwotrapezoidalfuzzynumbersparameterizedby(l1,c1,c11,r1),and(l2,c2,c22,r2),wherel1andl2,c1andc2,c11andc22,andr1andr2denotesleftendpoints,leftcenterpoints,rightcenterpoints,andrightendpoints,respectively.Theresultingfuzzynumberscanbewrittenasfollows:,Theconstraintsandobjectivefunctionofthelinearprogrammingproblemforthetrapezoidalfuzzydivisionaredefinedasfollows:,Thefirstconstraintisconstructedbasedontheleftspreads.Theleftspreadvalueovercentervalueforshouldbeequaltoorlessthandivisionofthesameratioscalculatedfor,Inasimilarmanner,thesecondconstraintisconstructedasfollows:,Thethirdandfourthconstraintscanbedefinedbasedonthedefinitionoffuzzynumbers.Theleftendpointofafuzzynumbershouldbelessthantheleftcentervalue.Themathematicalexpressionforthethirdconstraintisgivenbelow:,Therightendpointofafuzzynumbershouldbegreaterthantherightcentervalue.Themathematicalexpressionforthefourthconstraintisgivenbelow:,Theobjectivefunctionisgivenbelow:,4.Themethodology,ItcanbeverywellarguedthatitisnoteasytoevaluateallocationfactorsK,Co,Cr,M,TandSinaprecisemanner.SimilarkindofproblemhasbeenobservedinFailureModeEffectandCriticalityAnalysis,whileevaluatingtheriskfactors.Significanteffortshavebeenmadetoevaluateriskfactorsinalinguisticwayusingfuzzylogic.Inthisstudy,similarefforthasbeenmadetoevaluatetheallocationfactorsinlinguisticway,Supposetherearensubsystems,Ui(i=1,.,n)beevaluatedandallocatedbyasystemdesignandanalysisteamconsistingofmmembers,TMj(j=1,.,m).,Lethj(j=1,.,m)betherelativeimportanceweightsofthemteammembers,satisfying,Basedontheseassumptions,thensubsystemscanbeallocatedbyfollowingsteps:,(a)Aggregatetheteammemberssubjectiveopinionsonallocationfactorsfortheithsubsystemfori=1,.,n,as:,(b)Defineandcomputethefuzzyallocationproportionalityfactor(FZ)ofeachsubsystemas,Now,FZofeachsubsystemcanbecomputedbycombiningfuzzymultiplicationanddivision.FuzzymultiplicationhasbeenperformedbyusingEq.(6)andthefuzzydivisionhasbeenperformedbyusinglinerprogramming,whichisexplainedinSection3.1.,(c)DefuzzifytheFZbyusingEq.(8).(d)EvaluatetheweightageofeachsubsystemusingtheEq.(2)bythesolutionoftrapezoidalcentroiddefuzzificationvalues.(e)EvaluatetheallocatereliabilitiesoftheeachsubsystemusingtheEq.(1).,5.Illustrativeexample,Inthissection,weprovideanumericalexampletoillustratethepotentialapplicationsoftheproposedfuzzyallocationmethod.Ateamconsistingofthethreemembersidentifiesfoursubsystemsinatransceiverandneedstoallocatereliabilitytoeachsubsysteminordertoachievetargetreliability.Thetransceiversubsy