机械毕业设计英文外文翻译一种关于粗糙集改进注射模具浇道的报告.docx
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机械毕业设计英文外文翻译一种关于粗糙集改进注射模具浇道的报告.docx
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机械毕业设计英文外文翻译一种关于粗糙集改进注射模具浇道的报告
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AnImprovedRoughSetApproachtoDesignofGatingSchemeforInjectionMoulding
F.Shi,1Z.L.Lou,1J.G.Lu2andY.Q.Zhang11DepartmentofPlasticityEngineering,ShanghaiJiaotongUniversity,P.R.China;and2CenterofCAD,NanjingUniversityofChemicalTechnology,P.R.China
Thegateisoneofthemostimportantfunctionalstructuresinaninjectionmould,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;Knowledgeacquisition
1.Introduction
Themanufacturingindustryforplasticproductshasbeengrowingrapidlyinrecentyears,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.Alocalsearchwasusedtodeterminethenodesofthelocationofthegate[1].SaxenaandIraniproposedaframeforanon-manifoldtopology-basedenvironment.Aprototypesystemforgatelocationdesignwasdeveloped.Thecriteriaforevaluationwerebasedongeometry-relatedparameters[2].Linselectedtheinjectionlocationandsizeofthegateasthemajorcontrolparameters,andchosetheproductperformance(deformation)astheoptimisingparameter.Combiningthetechnologiesofabductivenetworksandsimulationannealingoptimisationalgorithms,theoptimalmodelforthelocationandsizeofthegatewasconstructed[3,4].Zhouetal.establishedarulesetfordeterminingthelocationofthegatebasedonanalysisoftheplasticparts.Thelocationofthegatewasdeterminedthroughreasoningwithrules[5].Pandelidisetal.developedasystemwhichcanoptimisegatelocationbasedontheinitialgatingplans.ThesystemusedMOLDFLOWsoftwareforflowanalysis,andcontrolledthetemperaturedifferentialandthenumberofelementsoverpackedwithanoptimisationstrategy[6].
DengusedID3anditsmodifiedalgorithmstogeneratetherulesetfortheselectionofthegatetypes[7].However,therearemanyfuzzyorvagueattributesintheselectionofthetypes,suchastheattributeoflossofpressurethathastwofuzzylinguisticvariablesi.e.canbehighandmustbelow.TheID3algorithmscannotdealwithfuzzyor“noise”informationefficiently.Itisalsodifficulttocontrolthesizeofthedecisiontreeextractedbythealgorithmsandsometimesverylargetreesaregenerated,makingcomprehensibilitydifficult[7,8].
Roughsettheoryprovidesanewmathematicalapproachtovagueanduncertaindataanalysis[9,10].Thispaperintroducesthetheoryofroughsetsforthedesignofagatingscheme.Theselectionofthetypeofgateisbasedonthetheoryofroughsets.Consideringthelimitationsofroughsets,thispaperproposesanimprovedapproachbasedonroughsettheoryforthedesignofthegatingscheme.Theimprovedroughsetapproachtotheschemedesignwillbegivenfirst.Afuzzyrough-set-basedinductivelearningalgorithm(FRILA),whichisappliedintheimprovedapproach,willthenbepresented.Anexampleofthedesignofagatewillfinallybegiven.
Table1.Classificationcriteria.
Conditionattributes
Fuzzylinguisticvariables
Styleofplasticparts(p)
(Deep,Middle,Shallow)Shell,(Deep,Middle,Shallow)Tube,(Deep,Middle,Shallow)
Ring
Numberofcavities(n)
Single-cavity,Multi-cavity
Lossofpressure(l)
Canbehigh,Mustbelow
Conditionofseparatinggatefromparts(q)
Mustbeeasy,Notrequestspecially
Machiningperformance(m)
Mustbeeasy,Notrequestspecially
2.ARoughSetApproachtoGatingSchemeDesign
2.1DesignoftheGatingScheme
Themodelofthegatingschemedesigncanbedescribedasfollows.Adecisiontablewith4-tuplescanberepresentedasT=(U,C,D,T).whereUistheuniverse.C={C1,C2,…,Ck}isthesetofconditionattributes,eachofwhichmeasuressomeimportantfeatureofanobjectintheuniverseU.T(Ck)={Tk1,T2k,...,TkSk}isthesetofdiscretelinguisticterms.Inotherwords,T(Ck)isthevaluesetoftheconditionattributes.D={D1,D2,…,Dl}isthesetofdecisionattributes,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=0.825
Fromtheaboverule,thegatingschemeofthestraightgatewillbeselectedisswithacertaintyfactorof0.825,ifthetypeofpartismiddleshellandthenumberofcavitiesissingleandtheconditionofseparatinggatefrompartisnotrequired.Theaboveisjustlikehumanlanguageandiseasytounderstand.
2.2BasicConceptsofRoughSets
Inrecentyears,theroughset(RS)theory,proposedbyPawlak,hasbeenattractingtheattentionoftheresearchers.ThebasicideaofRSistoclassifytheobjectsofinterestintosimilarityclasses(equivalentclasses)containingindiscernibleobjectsviatheanalysisofattributedependencyandattributereduction.Theruleinductionfromtheoriginaldatamodelisdata-drivenwithoutanyadditionalassumptions.Roughsetshavebeenappliedinmedicaldiagnosis,patternrecognition,machinelearning,andexpertsystems[10,11].
Adecisiontablewitha4-tuplecanberepresentedasT=,whereUistheuniverse,
CandDarethesetsofconditionanddecisionattributes,respectively,VisthevaluesetoftheattributeainA,andfisaninformationfunction.
Assumingasubsetofthesetofattributes,twoobjectsxandyinUareindiscerniblewithrespecttoPifandonlyif
.TheindiscernibilityrelationiswrittenasIND(P).U/IND(P)isusedtodenotethepartitionofUgiventheindiscernibilityrelationIND(P).
Aroughsetapproximatestraditionalsetsbyapairofsets,whicharethelowerandtheupperapproximationsofthesets.ThelowerandupperapproximationsofasetY.UgivenanequivalencerelationIND(P)aredefinedasfollows:
Thedefinitionofthelowerapproximationofasetinvolvesaninclusionrelationwherebytheobjectsinanequivalenceclassoftheattributesareentirelycontainedintheequivalenceclassforthedecisioncategory.Thisisthecaseofaperfectorunambiguousclassification.Fortheupperapproximation,theobjectsarepossiblyclassifiedusingtheinformationinattributesetP.
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