模糊滑模控制ppt课件.ppt

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 Zi Ki whereKiisthecomplexityfactorfortheitssubsystem 1 Multiplefunctionalrelationshipswiththeothergroups 2 Numberofcomponentscomprisingsubsystem 6 2 2 Cost 成本 Foralargesystem thecostincrementforreliabilityimprovementisrelativelyhigh Thedemonstrationofahighreliabilityvalueforacostlysystemmaybeextremelyuneconomical Hence Zi Coi whereCoiisthecostfactorfortheitssubsystem 2 3 State of the art 工艺状态 Whenthecomponenthasbeenavailableforalongtime itisquitedifficulttofurtherimprovethereliabilityofacomponentevenifthereliabilityisconsiderablylowerthandesired Hence Zi 1 Si whereSiisthestate of the artfactorfortheitssubsystem 7 2 4 Criticality 临界值 Criticalityisanotherveryimportantfactorinreliabilityallocation Itislogical higherreliabilitytargetshouldbeallocatedtothefunctionallycriticalsub systemsandthusZiisproportionaltocriticality Hence Zi 1 Cri whereCriisthecriticalityfactorfortheitssubsystem 2 5 Timeofoperation 运行时间 Theremaybesomesubsystemswhicharerequiredtobeoperatedforaperiodlessthanthemissiontime So forthesubsystemswithoperatingtimelessthanthemissiontime itisonlylogicaltoallocaterelativelylowerreliability Hence Zi 1 Ti whereTiisthetimeofoperationfactorfortheithsubsystem 2 6 Maintenance 维护 Acomponentwhichisperiodicallymaintainedoronewhichisregularlymonitoredorcheckedandrepairedasnecessarywillhave onanaveragehigheravailabilitythanonewhichisnotmaintainedHence Zi Mi 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 Aggregatetheteammember ssubjectiveopinionsonallocationfactorsfortheithsubsystemfori 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 Thetransceiversubs