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外文资料--Neural network prediction.pdf

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外文资料--Neural network prediction.pdf

performancealjiceFrictionmaterialormanceThesmaterial’ssynergistandbytraining18differentneuralnetworkarchitectureswiththefivedifferentlearningalgorithms.TheoptimalneuralmodelofdiscbrakeoperationhasbeenshowntobevalidforpredictingthebrakefactorCvariationofthecolddiscbrakeoverawiderangeofbrake’soperatingregimesandfordifferenttypesingsystxandmanifold.berelatih,andhumiditygbrakeebrakdistance,pedalfeel,discwear,andbrakeinducedvibrations[4].theeinofThesynergeticeffectsofallingredientsincludedinafrictionARTICLEINPRESSContentslistsavailableatScienceDirectsevier.com/locate/tribointTribologyIntTribologyInternational4220091074–1080ditions,iscomplicatedbythefactthatthetribologyatthefrictionE-mailaddressdaleksendricmas.bg.ac.yuD.Aleksendric.Forinstance,thevibrationsgeneratedattheinterfacebetweenthematerial,forthespecificmanufacturingconditions,determinethefinalfrictionmaterialcharacteristicsandaccordinglyaffectthebrakesystem’sperformance.Improvementandcontrolofanautomotivebrake’sperformance,underdifferentoperatingcon-0301-679X/-seefrontmatter2009ElsevierLtd.Allrightsreserved.doi10.1016/j.triboint.2009.03.005C3Correspondingauthor.Tel.381113370346;fax38113370364.foroverallperformanceofavehicle.Thisisbecauseitplayscrucialrolesinvariousaspectsofthebrakeperformancesuchasstoppingfrictionmaterialsandbrakingconditions[11]whichbothaffectthebrakingsystem’sperformance.stablefrictioncoefficient,lowwearrate,nonoise,lowcost,andenvironmentfriendly[3].Thefrictionmaterialintheautomotivebrakesystemhasbeenconsideredasoneofthekeycomponentsaffectedbythewidediversityinmechanicalpropertiesofcompositematerial’singredients[7–10].Thatiswhy,achangfrictioncoefficientishighlydependentontheingredientsvaluesandstabilityofthefrictioncoefficientoverdifferentbrake’soperatingconditionsdefinedbychangingappliedpressureand/orslidingspeedand/ortemperature.Thefrictionbehaviourofautomotivebrakesisdeterminedbythecharacteroftheactivesurfacesofthediscandpadandthirdbodiesbetweenthesesurfaces[2].Thebrakesrequirefrictionmaterialswithhigherandoperatingregimes.Therefore,thebrake’sperformanceisprimarilyinfluencedbythecontactsituationbetweenacastironbrakediscandthecompositefrictionmaterial.Thecontactsituationisadditionallycomplicatedbythefactthatfrictionmaterialsarecomplexpolymercompositesandmaycontainover20differentingredients.Hencethecontactsituationcanbesignificantly1.IntroductionThedemandsimposedonabrakofoperatingconditions,arecomplethatthefrictioncoefficientshouldstablefrictionforce,reliablestrengtareneededirrespectiveoftemperature,wearandcorrosion,etc[1].Thebrakinmostlydeterminedbythefoundationrequirementsimposedonautomotiv2009ElsevierLtd.Allrightsreserved.em,overawiderangeItisexpectedvelyhighbutalsogoodwearresistance,age,degreeofsystemperformanceisassembly.Thebasicesarerelatedtothetwobodiesinfrictionareresponsibleforvariousnoisessuchassquealing,juddering,hammering,hooting,etc[5].Ontheotherhand,theperformancecriteriahaveincreasedandhavebecomemoresensitivetobraking[6].Anautomotivebrake’sfrictionbehaviourresultsfromthecomplexinterrelatedphenomenaoccurringatthecontactofthefrictionpairduringbraking.Thesecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalpropertiesofthecompositematerialasthefrictionelement,thebrakediscasthemetalliccounterface,andtheconditionsimposedbythebrake’soffrictionmaterial.NeuralnetworkpredictionofdiscbrakeDraganAleksendrica,C3,DavidC.BartonbaAutomotiveDepartment,UniversityofBelgrade,FacultyofMechanicalEngineering,KrbSchoolofMechanicalEngineering,UniversityofLeeds,LS29JT,UKarticleinfoArticlehistoryReceived28November2007Receivedinrevisedform3March2009Accepted16March2009Availableonline24March2009KeywordsNeuralnetworkPredictionDiscbrakeperformanceabstractAnautomotivebrake’sperfcontactofthefrictionpair.propertiesofthefrictionregimes.Inthispaper,thecompositionandmanufacturinvariationhavebeenmodelleparameters,determinedbyconditions5parameters,variation,havebeenpredicted.journalhomepagewww.elMarije16,11120Belgrade35,Serbiaresultsfromthecomplexinterrelatedphenomenaoccurringattheecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalingredients,thebrakediscproperties,andthebrake’soperatingiceffectsofthefrictionmaterial’sproperties,definedbyitsgconditions,andthebrake’soperatingregimesonthediscbrakefactorCdbymeansofartificialneuralnetworks.Theinfluencesof26inputthefrictionmaterialcomposition18ingredients,itsmanufacturingthebrake’soperatingregimes3parametersonthebrakefactorCTheneuralmodelofthediscbrakecoldperformancehasbeendevelopedernationalARTICLEINPRESSnumberofneuronsinhiddenlayers,respectively;IScalscaledinputvalueICurrcurrentinputvalueIMaxmaximuminputvalueIMinminimuminputvalueOLinlinearizedoutputvalueOCurrcurrentoutputvalueOMaxmaximumoutputvalueD.Aleksendric,D.C.Barton/TribologyInternational4220091074–10801075interfacehasastochasticnatureaffectedbyvariationsoftherealcontactarea,transferlayerformation,changingpressure,tem-perature,andspeedconditions,aswellasdeformationandwearofthecomponents.Theareaofrealcontactbetweenthepadandthediscisfarfromconstant[1],verysmallcomparedtothetotalcontactarea[2],andhighlydependentonchangesofpressure,temperatures,deformation,andwear.Takingintoconsiderationthatverycomplexandhighlynon-linearphenomenaareinvolvedinthebrakingprocess[2,11],completeanalyticalmodelsofbrakeoperationaredifficultifnotimpossibletoobtain.Incontrasttoclassicalanalyticalapproaches,itisarguedinthispaperthatartificialneuralnetworkscanbeusedtomodelthecomplexnon-linear,multidimensionalfactorsthatcaninfluenceabrake’sperformance.Aspointedoutbymanyresearchers[12–15],forexample,artificialneuralnetworksareapromisingfieldofresearchinpredictingexperimentaltrendsandarecapableofconsiderablesavingsintermsofcostandtimecomparedwithclassicalanalyticalmodels.Inordertoimproveabrakingsystemoperation,itisdesirablethatthebrakesshouldbemorepreciselycontrolledversuschangesofcoefficientofthefriction.Consequently,thebrakeperformanceshouldbecalibratedforthespecificbrakeoperatingregimesandafrictionpair’scharacteristics[15–17].Inthispaper,artificialneuralnetworkshavebeenusedformodellingandpredictingthediscbrake’sfrictioncharacteristicsi.e.thebrakefactorCvariationtakingintoconsiderationthefollowinginfluen-cingfactorsifrictionmaterialcomposition,iimanufacturingparametersoffrictionmaterial,andiiibrake’soperatingconditions.Therearemanycomplexinfluencesoffrictionmaterialcomposition,itsmanufacturingconditions,andbrakeoperatingregimesonthewearresistanceandnoisypropensityofadiscFthenumberofoutputsfxactivationfunctionNomenclatureCbrakefactorTbrakingtorquepapplicationpressuredcpistondiameterreeffectivebrakediscradiusFtypeoffrictionmaterialFTtypeoffrictionmaterialusedforthetestdatasetA[C–D–E]BFneuralnetworkarchitectureAthenumberofinputs;Bthenumberofhiddenlayers;C,D,EthebrakebutinthispaperourattentionhasbeenfocusedonpredictionofthediscbrakefactorCasoneofthemostimportantperformanceofthediscbrakeoperation.2.ExperimentalmethodsInordertobetaughtaboutthediscbrakeoperationi.e.brakeperformanceasafunctionofdifferenttypesoffrictionmaterialandbrake’soperatingconditions,theartificialneuralnetworkshavetobetrainedwithappropriatedata.Theprocessofmodellingofadiscbrakeoperationbymeansofartificialneuralnetworksisnottrivialandmanycriticalissueshavetoberesolved.Thefollowingoperationshavetobeconsiderediselectionofadatagenerator,iidefinitionoftherangesanddistributionofinputdata,iiidatageneration,ivdatapre-processing,vselectionoftheneuralnetwork’sarchitectures,viselectionofthetrainingalgorithms,viitrainingoftheneuralnetworks,viiivalidationandaccuracyevaluation,andixtestingoftheartificialneuralnetworks.Thepreliminarystepindevelopmentoftheneuralmodelofadiscbrakeoperationistheidentificationofthemodelinputsandoutputs.Input/outputidentificationdependsonthemodelobjectivesandchoiceofthedatagenerator.Forthepurposesofthispaper,theinputparametersaredefinedbythefrictionmaterialcomposition,itsmanufacturingprocessconditions,andthediscbrakeoperatingconditions.ThebrakefactorChasbeentakenastheoutputparameterandusedforrepresentingthediscbrakeperformance.ThebrakefactorCcorrespondstochangesofthefrictioncoefficientinthecontactoffrictionpairduringbrakingC2m.ThebrakefactorCiscalculatedfromthemeasuredvariationofthebrakingtorqueandapplicationpressureduringthebrakingcycle,andknownvaluesofthepistondiameterandeffectivebrakediscradiusaccordingtoexpression1C4Tpd2cpre1Thetypeofdatageneratordependsontheapplicationandtheavailability.Inthiscase,thedatageneratorhasbeenasingle-endfull-scaleinertialdynamometer,developedatthelaboratoryforfrictionmechanismandbrakingsystemsFRIMEKSAutomotiveDepartment,FacultyofMechanicalEngineering,UniversityofBelgrade.Obviously,thetestingmethodologyneedstobechosenaccordingtotherangeanddistributionofdatathataregoingtobecollected.Table1presentsthetestingmethodologyusedfortheoutputdatageneration.Thebraketestingconditions,aftertheburnishingprocedure,havebeenchoseninordertoidentifytheinfluencesofappliedhydraulicpressureandinitialequivalentOMinminimumoutputvalueBRBayesianRegulationlearningalgorithmBRabcdneuralmodelBRBayesianRegulationlearningalgorithm;athenumberofinputs;bthenumberofneuronsinthefirsthiddenlayer;cthenumberofneuronsinthesecondhiddenlayer;dthenumberofoutputsvehiclespeedonthefinalcoldperformanceofthediscbrakeforthedifferenttypesoffrictionmaterial[18].Thesedatahavebeenusedfortraining,validation,andtestingoftheneuralnetworksinordertoestablishthefunctionalrelationshipbetweenthediscbrakeoperatingconditions,thetypeofthefrictionmaterial,andthebrakefactorCvariationastheoutput.Itisobviousthattherangesanddistributionoftheinputsdatafortraining,validation,andtestinghavetobepredefined.TheneuralmodelofdiscbrakeoperationtakesintoconsiderationtheTable1Testingmethodology.TestconditionsAppliedpressurebarInitialspeedkm/hTemperature1CNumberofbrakingeventsInitialburnishing4090o100150Brakingregimes20,40,60,80,10020,40,60,80,100o10025ARTICLEINPRESSD.Aleksendric,D.C.Barton/TribologyInternational4220091074–10801076Table2Theselectionandrangesofrawmaterialsforthefrictionmaterialcompositionsvol.RawmaterialsF1–F9trainingandvalidationdatasetFT1testdatasetFT2testdatasetPhenolicresin17–252517Ironoxide3–553Barites26–151526Calciumcarbonate1–331Brasschips1–331Aramid2–662Mineralfibre10–16109Vermiculite4–884Steelfibre4–114Glassfibre2–442Brasspowder1–221Copperpowder1–331Graphite7–337Frictiondust5–225MolybdenumDisulphide1–331Aluminiumoxide2–332Silica1–221Magnesiumoxide8–228Table3Rangesofmanufacturingparametersforthefrictionmaterials.threegroupsofinputdataithefrictionmaterialcomposition,iiitsmanufacturingconditions,andiiithebrake’soperationregimes.Therangesanddistributionofdatarelatedtothebrake’soperationregimesisdefinedbythetestingmethodologyTable1.Ontheotherhand,choiceoftherangesanddistributionofthemanufacturingandespeciallythecompositionparametersofthefrictionmaterialsisamuchmoredifficulttask.Forthetrainingandvalidationdatasetsformation,eachingredientinthecompositionofthefrictionmaterialanditsmanufacturingparametershavebeenselectedwithinarangeF1–F9aspresentedinTables2and3.FromTables2and3,itcanbeseenthatelevendifferenttypesoffrictionmaterialwereproducedasadiscpadassembly,mountedonthefrontbrakeaxlestaticweightof730kgofasmallpassengercarYugoFlorida1.4andtestedusingthesingleendfull-scaleinertialdynamometer.Thediscpadswiththefrictionsurfaceareaof32.4cm2andpadthicknessof16.8mmweredesignedforthebrakewithaneffectivediscradiusof101mmandfloatingcalliperpistondiameterof48mm.Thecompositionandmanufacturingparametersforeachtypeoffrictionmaterial,aspresentedinTables2and3,werecompletelydifferentfromoneanother.ResultsobtainedduringbraketestingwithfrictionmaterialsF1–F8wereusedfortrainingtheneuralnetworks,whileresultswiththefrictionmaterialF9wereusedforvalidatingthecapabilitiesoftheartificialneuralnetworks.Thevolumepercentagesofthefrictionmaterial’singredients,usedfortheneuralnetworks’trainingandvalidationF1–F9overtherangespresentedinTable2,havebeenrandomlyselected.Thelearningalgorithmselected[19,20].ThelearningabilityoftheManufacturingparametersF1–F9trainingandvalidationdatasetFT1testdatasetFT2testdatasetSpecificmouldingpressureMPa45–654070Mouldingtemperature1C155–170170155Mouldingtimemin6–11116Heattreatmenttemperature1C200–250200250Heattreatmenttimeh12–5125neuralnetworktoextenditspredictivepowerfordataoutsideofthetrainingdatasetisessentialinimplementationoftheartificialneuralnetworksforpredictingdiscbrakeperformance.Itisaclearthatsufficientinput/targetpairshavetobestoredinthetrainingdataset.Input/outputdatahavebeenobtainedbyformulation,manufacturing,anddynamometertestingofelevendifferentfrictionmaterialsrepresentingalargedatasetthatcanbeusedfortraining,validation,andtestingtheneuralnetwork.Thetotalnumberofoutputresults,obtainedbythedynamometertestingforeachtypeoffrictionmaterial,is25accordingtotheadoptedtestingmethodologyTable1.Thismeansthat275input/outputpairsareavailablefortheneuralnetworktraining,validation,andtesting.Thetotalnumberof275input/outputpairshasbeendividedintothreesets,200input/outputpairsfortheneuralnetworktraining,25pairsforvalidation,and50pairsfortheneuralnetworktesting.Sincethebestneuralnetworkarchitectureandalearningalgorithmareunknowninadvance,atrailanderrormethodhasbeenemployedtofindoutthebestnetworkcharacteristicsformatchingtheparticularinput/outputrelationship.BasedonMatLab6.5Rel.13,thefollowingnetworksarchitectureshavebeeninvestigatedinthisapplicationione-layeredstructures26[1]11,26[2]11,26[3]11,26[5]11,26[8]11,iitwo-layeredstructures26[1–1]21,26[2–2]21,26[3–2]2manufacturingparameters,presentedinTable3,havebeenalsorandomlyselectedinthecaseoffrictionmaterialsdenotedasF1–F9.Furthermore,theaccuracyofthetrainedneuralnetworksforpredictingthediscbrakeperformancehasbeentestedusingtheinput/outputdatastoredinthetestdataset.ThetestdatasethavebeenobtainedbyproducingtwonewtypesoffrictionmaterialsFT1andFT2whoseinputparameterswerecompletelydifferentfromthosestoredinthetrainingandvalidationtestdatasets.Thevolumepercentageofingredients,presentedinTable2,usedforthecompositionoffrictionmaterialsFT1andFT2weremostlyselectedtocorrespondtotheupperandlowerboundvaluesofthespecifiedranges.ThemanufacturingparametersofthefrictionmaterialsFT1andFT2havebeenalsosimilarlyselectedregardingtherangesspecifiedinTable3.Theonlydifferenceisrelatedtothespecificmouldingpressureswhich,inthecaseoffrictionmaterialsFT1andFT2,wereoutoftherangeusedformanufactur-ingthefrictionmaterialsdenotedasF1–F9seeTable3.Thesevalueswereselectedinordertotesttheneuralmodelabilitiestoextenditspredictivepowerfordataeitherattheendsoftherangesorcompletelyoutsideoftherangesusedforthetrainingdatasetcreation.3.NeuralnetworkmodellingBasedonTables1–3,neuralmodellingofthediscbrakeoperationhasbeenperformedfor26inputparameters18parametersrelatedtothefrictionmaterial’scomposition,5parametersrelatedtothemanufacturingconditions,and3parametersrelatedtothebraketestingconditions,andoneoutputparameterbrakefactorC.Neuralmodellingofthediscbrakeoperationisacomplextaskandtheappropriatearchitec-tureoftheneuralnetworkaswellasthelearningalgorithmneedtobeproperlydetermined.Thearchitectureofanartificialneuralnetworkconsistsofadescriptionofhowmanylayersanetworkhas,thenumberofneuronsineachlayer,eachlayer’stransferfunctionandhowthelayersareconnectedtoeachother.Thebestarchitecturetousedependsonthekindofproblemtoberepresentedbythenetwork.Thebestneuralnetworksetisaffectedbytherepresentationalpowerofthenetworkandthe1,26[5–2]21,26[8–2]21,26[8–4]21,26[10–5]21,andiiithree-layeredstructures26[3–2–2]31,26[4–3–2]31,26[4–2–2]31,26[5–2–2]31,26[8–2–2]31,26[8–4–2]31.Thesenetworkarchitectureshavebeentrainedbythefollow-ingtrainingalgorithmsLevenberg–Marquardt,BayesianRegula-tion,ResilientBackpropagation,ScaledConjugateGradient,andGradientDecent.Thesigmoidactivationfunctionhasbeenusedbetweentheinputandhiddenlayersseeexpression2fx11eC0x2Alinearactivationfunctionfx1xwasemployedbetweenthehiddenandoutputlayer.Pre-processingoftheinputparameterswascarriedoutbeforetheneuralnetworktraining.Thus,18parametersrelatedtothefrictionmaterialformulationwerepresentedtothenetworkinpercentbyvolume,and5manufacturingparametersand3testingconditionswerescaledintherangeof0–1accordingtoexpression3ICurrC0IMaxtwotypesoffrictionmaterialsFT1andFT2havebeenfirstlyproducedandtestedusingtheinertialfull-scalebrakedynam-between20and60barand60and100bar,inordertobetterillustratethecomplexityofrealchangesofdiscbrakeperformanceinfluencedbythefrictionmaterialFT1underthespecifieddiscbrakeoperationregimes.FromFig.1,thegeneraltrendofthediscbrakeperformanceisevidentforappliedpressuresbetween20and60barandinitialspeedsbetween20and100km/h.ThebrakefactorCincreasesintherangeof20–40barforinitialspeedsbetween20and60km/h.Thediscbrakeperformanceisrelativelyconstantoverthewholerangeofinitialspeeds20–100km/hforfurtherincreasesofappliedpressurefrom40to60bar,seeFig.1.Forinitialspeedsbetween80and100km/h,thebrakefactorChasbeenrelativelyconstantinthesamerangeofappliedpressures20–60bar.Contrarytorelativelyconstantdiscbrakeperformance,intherangeofappliedpressuresbetween40and60barandinitialspeedsbetween20and100km/h,thediscbrakeperformancehasbeendecreasedbyfurtherincreasingofappliedpressureto100barFig.2.Obviously,themeasureddiscbrakeperformancehasbeendifferentlyaffectedbythefrictionmaterialpropertiesinsynergywithchangesofthebrakeoperationregimesFigs.1and2.FromFigs.1and2,itcanbeseenthreedifferentrangesofdiscbrakeoperationversusappliedpressuresandinitialspeedsexistabetween20and40bar,bbetween40and60bar,andcbetween60and100bar.AccordingtoFigs.1and2,themeasureddiscbrakeperfor-ARTICLEINPRESS0.840.860.880.90.920.940.96BrakefactorCv20v40v60v80v100Fig.3.Predicteddiscbrakeperformanceversusappliedpressures20–60barandinitialspeeds20–100km/hfrictionmaterialFT1.D.Aleksendric,D.C.Barton/TribologyInternational4220091074–10801077ometer.ThecompositionandmanufacturingparametersoffrictionmaterialsFT1andFT2havebeencompletelyunknowntotheneuralmodels.TheperformanceofthediscbrakeequippedwiththefrictionmaterialFT1isshowninFigs.1and2versusapplicationpressureandinitialspeedchanges.Themeasureddiscbrakeperformance,expressedasthebrakefactorCvariation,hasbeendividedintotworangesdependingonappliedpressure,0.840.860.880.90.920.940.960.98120PressureapplicationbarBrakefactorCv20v40v60v80v10060504030Fig.1.Measureddiscbrakeperformanceversusappliedpressures20–60barandIScal1IMaxC0IMin3Ontheotherhand,theoutputparameterbrakefactorChasbeenlinearizedbyexpression4OLin07502OCurrC0OMaxOMaxC0OMin44.ResultsanddiscussionAftertheirtrainingandvalidation,theneuralnetworkshavebeenemployedforpredictingtheperformanceofthediscbrakeequippedwiththetwonewtypesofdiscpadsFT1andFT2.Intotal90differentneuralmodelshavebeentested18differentneuralnetworkstrainedbythefivelearningalgorithmsinordertoevaluatetheircapabilitiesforpredictingthediscbrakefactorCvariationasinfluencedbythedifferenttypesoffrictionmaterialsunderthespecificbrakingregimes.Asmentionedabovethenewinitialspeeds20–100km/hfrictionmaterialFT1.0.840.860.880.90.920.940.960.98160PressureapplicationbarBrakefactorCv20v40v60v80v100100908070Fig.2.Measureddiscbrakeperformanceversusappliedpressures60–100barandinitialspeeds20–100km/hfrictionmaterialFT1.0.98120Pressureapplicationbar60504030mancehasbeenstronglyaffectedbytheoperatingconditionsfor

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