外文翻译--一种关于粗糙集改进注射模具浇道的报告.doc

附录附录1AnImprovedRoughSetApproachtoDesignofGatingSchemeforInjectionMouldingF.Shi,1Z.L.Lou,1J.G.Lu2andY.Q.Zhang11DepartmentofPlasticityEngineering,ShanghaiJiaotongUniversity,P.R.China；and2CenterofCAD,NanjingUniversityofChemicalTechnology,P.R.ChinaThegateisoneofthemostimportantfunctionalstructuresinaninjectionmould,asithasadirectinfluenceonthequalityoftheinjectionproducts.Thedesignofagatingschemeincludestheselectionofthetypesofgateandcalculationofthesizesanddeterminationofthelocation,whichdependsheavilyonpriorexperienceandknowledgeandinvolvesatrial-and-errorprocess.Duetothevaguenessanduncertaintyinthedesignofagatingscheme,classicalroughsettheoryisnoteffective.Inthispaper,afuzzyroughsetmodelisproposed,whichisnotbasedonequivalentrelationshipsbutonfuzzysimilarityrelationships.Aninductivelearningalgorithmbasedonthefuzzyroughsetmodel(FRILA)isthenpresented.Comparedtodecisiontreealgorithms,theproposedalgorithmcangeneratefewerclassificationrules；moreover,thegeneratedrulesaremoreconcise.Finally,anintelligentprototypesystemforthedesignofagatingschemebasedonaninducedfuzzyknowledgebaseisdeveloped.Anillustrativeexampleprovestheeffectivenessoftheproposedmethod.Keywords:Fuzzyroughset；Gatingscheme；Injectionmold；Intelligentdesign；Knowledgeacquisition1.IntroductionThemanufacturingindustryforplasticproductshasbeengrowingrapidlyinrecentyears,andplasticsareusedwidelytosubstituteformetals.Theinjectionmouldingprocessisthemostpopularmouldingprocessformakingthermoplasticparts.Thefeedingsystem,whichisoneoftheimportantfunctionalstructures,comprisesasprue,aprimaryrunner,asecondaryrunnerandagate.Themoltenplasticflowsfromthemachinenozzlethroughthesprueandrunnersystemandintothecavitiesthroughthegate.Actingastheconnectionbetweentherunnerandthecavity,thegatecaninfluencedirectlythemouldventing,theoccurrenceofjetting,thelocationofweldlines,andwarpage,shrinkageandresidualstresses.Hence,thegatedesignisimportantforassuringthequalityofthemould.Thedesignofagateincludestheselectionofthetypeofgate,calculationofthesizeanddeterminationofthelocation.Andthedesignofagateisbasedontheexperienceandknowledgeofthedesigners.Thedeterminationsofthelocationandsizesaremadebasedonatrial-and-errorprocess.Inrecentyears,afeature-modellingenvironmentandintelligenttechnologyhavebeenintroducedforgatedesign.LeeandKiminvestigatedgatelocationsusingtheevaluationcriteriaofwarpage,weldlinesandizodimpactstrength.Alocalsearchwasusedtodeterminethenodesofthelocationofthegate1.SaxenaandIraniproposedaframeforanon-manifoldtopology-basedenvironment.Aprototypesystemforgatelocationdesignwasdeveloped.Thecriteriaforevaluationwerebasedongeometry-relatedparameters2.Linselectedtheinjectionlocationandsizeofthegateasthemajorcontrolparameters,andchosetheproductperformance(deformation)astheoptimisingparameter.Combiningthetechnologiesofabductivenetworksandsimulationannealingoptimisationalgorithms,theoptimalmodelforthelocationandsizeofthegatewasconstructed3,4.Zhouetal.establishedarulesetfordeterminingthelocationofthegatebasedonanalysisoftheplasticparts.Thelocationofthegatewasdeterminedthroughreasoningwithrules5.Pandelidisetal.developedasystemwhichcanoptimisegatelocationbasedontheinitialgatingplans.ThesystemusedMOLDFLOWsoftwareforflowanalysis,andcontrolledthetemperaturedifferentialandthenumberofelementsoverpackedwithanoptimisationstrategy6.DengusedID3anditsmodifiedalgorithmstogeneratetherulesetfortheselectionofthegatetypes7.However,therearemanyfuzzyorvagueattributesintheselectionofthetypes,suchastheattributeoflossofpressurethathastwofuzzylinguisticvariablesi.e.canbehighandmustbelow.TheID3algorithmscannotdealwithfuzzyor“noise”informationefficiently.Itisalsodifficulttocontrolthesizeofthedecisiontreeextractedbythealgorithmsandsometimesverylargetreesaregenerated,makingcomprehensibilitydifficult7,8.Roughsettheoryprovidesanewmathematicalapproachtovagueanduncertaindataanalysis9,10.Thispaperintroducesthetheoryofroughsetsforthedesignofagatingscheme.Theselectionofthetypeofgateisbasedonthetheoryofroughsets.Consideringthelimitationsofroughsets,thispaperproposesanimprovedapproachbasedonroughsettheoryforthedesignofthegatingscheme.Theimprovedroughsetapproachtotheschemedesignwillbegivenfirst.Afuzzyrough-set-basedinductivelearningalgorithm(FRILA),whichisappliedintheimprovedapproach,willthenbepresented.Anexampleofthedesignofagatewillfinallybegiven.Table1.Classicationcriteria.ConditionattributesFuzzylinguisticvariablesStyleofplasticparts(p)(Deep,Middle,Shallow)Shell,(Deep,Middle,Shallow)Tube,(Deep,Middle,Shallow)RingNumberofcavities(n)Single-cavity,Multi-cavityLossofpressure(l)Canbehigh,MustbelowConditionofseparatinggatefromparts(q)Mustbeeasy,NotrequestspeciallyMachiningperformance(m)Mustbeeasy,Notrequestspecially2.ARoughSetApproachtoGatingSchemeDesign2.1DesignoftheGatingSchemeThemodelofthegatingschemedesigncanbedescribedasfollows.Adecisiontablewith4-tuplescanberepresentedasT=（U,C,D,T）.whereUistheuniverse.C=C1,C2,Ckisthesetofconditionattributes,eachofwhichmeasuressomeimportantfeatureofanobjectintheuniverseU.T(Ck)=Tk1,T2k,.,TkSkisthesetofdiscretelinguisticterms.Inotherwords,T(Ck)isthevaluesetoftheconditionattributes.D=D1,D2,Dlisthesetofdecisionattributes,thatis,eachobjectintheuniverseisclassifiedbythesetD.Generally,theconditionattributescanbeclassifiedasfivesets,includingstyleofplasticparts,numberofcavities,lossofpressure,conditionofseparatinggatefrompartsandmachineperformance.ThedetailsofthefiveconditionattributesandcorrespondingvariablesofthefuzzylinguisticareshowninTable1.Fromthetable,itcanbeseenthatmostoftheattributesarevaguesincetheyrepresentahumanperceptionanddesire.Forinstance,shell,tubeandringareselectedfortheclassificationofplasticpartsandtheirfuzzylinguisticvaluesare“deep”,“middle”and“shallow”,respectively.Fortheattributelossofpressure,“canbehigh”and“mustbelow”areselectedtoapproximatethefuzzyattribute.Afuzzyruleforgatingschemedesigncanbewritteninthefollowingform:IF(C1isT1i1)AND(CkisTik)THEN(DisDj)(1)whereTkikisthelinguistictermofconditionattributeCk,andDjisaclasstermofthedecisionattributeD.FuzzyruleswiththeformofEq.(1)areusedtoperformmin-maxfuzzyinference.LetckbethemembershipvalueofanobjectinTkanddbetheforecastvalueofDj,whered=ikmin(ck)andministheminimumoperator.Iftwoormoreruleshavethesameconclusion,theconclusionwiththelargestvalueofd,whichisalsonamedthecertaintyfactorischosen.Fortheproblemofthegatingschemedesign,afuzzydesignrulecanbedescribedasfollows.IF(Typeofplasticpart=middleshell)AND(Numberofcavities=single)AND(Conditionofseparatinggatefrompart=notrequestespecially)(2)THEN(Gatingscheme=straightgate)CF=0.825Fromtheaboverule,thegatingschemeofthestraightgatewillbeselectedisswithacertaintyfactorof0.825,ifthetypeofpartismiddleshellandthenumberofcavitiesissingleandtheconditionofseparatinggatefrompartisnotrequired.Theaboveisjustlikehumanlanguageandiseasytounderstand.2.2BasicConceptsofRoughSetsInrecentyears,theroughset(RS)theory,proposedbyPawlak,hasbeenattractingtheattentionoftheresearchers.ThebasicideaofRSistoclassifytheobjectsofinterestintosimilarityclasses(equivalentclasses)containingindiscernibleobjectsviatheanalysisofattributedependencyandattributereduction.Theruleinductionfromtheoriginaldatamodelisdata-drivenwithoutanyadditionalassumptions.Roughsetshavebeenappliedinmedicaldiagnosis,patternrecognition,machinelearning,andexpertsystems10,11.Adecisiontablewitha4-tuplecanberepresentedasT=<U,A,V,f>,whereUistheuniverse,CandDarethesetsofconditionanddecisionattributes,respectively,VisthevaluesetoftheattributeainA,andfisaninformationfunction.Assumingasubsetofthesetofattributes,twoobjectsxandyinUareindiscerniblewithrespecttoPifandonlyif,.TheindiscernibilityrelationiswrittenasIND(P).U/IND(P)isusedtodenotethepartitionofUgiventheindiscernibilityrelationIND(P).Aroughsetapproximatestraditionalsetsbyapairofsets,whicharethelowerandtheupperapproximationsofthesets.ThelowerandupperapproximationsofasetY.UgivenanequivalencerelationIND(P)aredefinedasfollows:Thedefinitionofthelowerapproximationofasetinvolvesaninclusionrelationwherebytheobjectsinanequivalenceclassoftheattributesareentirelycontainedintheequivalenceclassforthedecisioncategory.Thisisthecaseofaperfectorunambiguousclassification.Fortheupperapproximation,theobjectsarepossiblyclassifiedusingtheinformationinattributesetP.Attributereductionisimportantforroughsettheory.Basedontheabovedefinitions,theconceptofreduction,denotedbyRED(P),isdefinedasfollows:Q.PisareductionofPifandonlyifIND(P)=IND(Q).2.3AnImprovedRoughSetApproachInthedesignofthegatingscheme,itiscrucialtoacquirethefuzzyrulesefficiently.Knowledgeacquisitionisthebottleneck.Aroughsetisappliedtosolvetheproblemforthe