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外文资料--Neural network prediction.pdf

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外文资料--Neural network prediction.pdf

performancealjiceFrictionmaterialormanceThesmaterialssynergistandbytraining18differentneuralnetworkarchitectureswiththefivedifferentlearningalgorithms.TheoptimalneuralmodelofdiscbrakeoperationhasbeenshowntobevalidforpredictingthebrakefactorCvariationofthecolddiscbrakeoverawiderangeofbrakesoperatingregimesandfordifferenttypesingsystxandmanifold.berelatih,andhumiditygbrakeebrakdistance,pedalfeel,discwear,andbrakeinducedvibrations4.theeinofThesynergeticeffectsofallingredientsincludedinafrictionARTICLEINPRESSContentslistsavailableatScienceDirectsevier.com/locate/tribointTribologyIntTribologyInternational4220091074–1080ditions,iscomplicatedbythefactthatthetribologyatthefrictionEmailaddressdaleksendricmas.bg.ac.yuD.Aleksendric´.Forinstance,thevibrationsgeneratedattheinterfacebetweenthematerial,forthespecificmanufacturingconditions,determinethefinalfrictionmaterialcharacteristicsandaccordinglyaffectthebrakesystemsperformance.Improvementandcontrolofanautomotivebrakesperformance,underdifferentoperatingcon0301679X/seefrontmatter2009ElsevierLtd.Allrightsreserved.doi10.1016/j.triboint.2009.03.005C3Correspondingauthor.Tel.381113370346fax38113370364.foroverallperformanceofavehicle.Thisisbecauseitplayscrucialrolesinvariousaspectsofthebrakeperformancesuchasstoppingfrictionmaterialsandbrakingconditions11whichbothaffectthebrakingsystemsperformance.stablefrictioncoefficient,lowwearrate,nonoise,lowcost,andenvironmentfriendly3.Thefrictionmaterialintheautomotivebrakesystemhasbeenconsideredasoneofthekeycomponentsaffectedbythewidediversityinmechanicalpropertiesofcompositematerialsingredients7–10.Thatiswhy,achangfrictioncoefficientishighlydependentontheingredientsvaluesandstabilityofthefrictioncoefficientoverdifferentbrakesoperatingconditionsdefinedbychangingappliedpressureand/orslidingspeedand/ortemperature.Thefrictionbehaviourofautomotivebrakesisdeterminedbythecharacteroftheactivesurfacesofthediscandpadandthirdbodiesbetweenthesesurfaces2.Thebrakesrequirefrictionmaterialswithhigherandoperatingregimes.Therefore,thebrakesperformanceisprimarilyinfluencedbythecontactsituationbetweenacastironbrakediscandthecompositefrictionmaterial.Thecontactsituationisadditionallycomplicatedbythefactthatfrictionmaterialsarecomplexpolymercompositesandmaycontainover20differentingredients.Hencethecontactsituationcanbesignificantly1.IntroductionThedemandsimposedonabrakofoperatingconditions,arecomplethatthefrictioncoefficientshouldstablefrictionforce,reliablestrengtareneededirrespectiveoftemperature,wearandcorrosion,etc1.Thebrakinmostlydeterminedbythefoundationrequirementsimposedonautomotiv2009ElsevierLtd.Allrightsreserved.em,overawiderangeItisexpectedvelyhighbutalsogoodwearresistance,age,degreeofsystemperformanceisassembly.Thebasicesarerelatedtothetwobodiesinfrictionareresponsibleforvariousnoisessuchassquealing,juddering,hammering,hooting,etc5.Ontheotherhand,theperformancecriteriahaveincreasedandhavebecomemoresensitivetobraking6.Anautomotivebrakesfrictionbehaviourresultsfromthecomplexinterrelatedphenomenaoccurringatthecontactofthefrictionpairduringbraking.Thesecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalpropertiesofthecompositematerialasthefrictionelement,thebrakediscasthemetalliccounterface,andtheconditionsimposedbythebrakesoffrictionmaterial.NeuralnetworkpredictionofdiscbrakeDraganAleksendric´a,C3,DavidC.BartonbaAutomotiveDepartment,UniversityofBelgrade,FacultyofMechanicalEngineering,KrbSchoolofMechanicalEngineering,UniversityofLeeds,LS29JT,UKarticleinfoArticlehistoryReceived28November2007Receivedinrevisedform3March2009Accepted16March2009Availableonline24March2009KeywordsNeuralnetworkPredictionDiscbrakeperformanceabstractAnautomotivebrakesperfcontactofthefrictionpair.propertiesofthefrictionregimes.Inthispaper,thecompositionandmanufacturinvariationhavebeenmodelleparameters,determinedbyconditions5parameters,variation,havebeenpredicted.journalhomepagewww.elMarije16,11120Belgrade35,Serbiaresultsfromthecomplexinterrelatedphenomenaoccurringattheecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalingredients,thebrakediscproperties,andthebrakesoperatingiceffectsofthefrictionmaterialsproperties,definedbyitsgconditions,andthebrakesoperatingregimesonthediscbrakefactorCdbymeansofartificialneuralnetworks.Theinfluencesof26inputthefrictionmaterialcomposition18ingredients,itsmanufacturingthebrakesoperatingregimes3parametersonthebrakefactorCTheneuralmodelofthediscbrakecoldperformancehasbeendevelopedernationalARTICLEINPRESSnumberofneuronsinhiddenlayers,respectivelyIScalscaledinputvalueICurrcurrentinputvalueIMaxmaximuminputvalueIMinminimuminputvalueOLinlinearizedoutputvalueOCurrcurrentoutputvalueOMaxmaximumoutputvalueD.Aleksendric´,D.C.Barton/TribologyInternational4220091074–10801075interfacehasastochasticnatureaffectedbyvariationsoftherealcontactarea,transferlayerformation,changingpressure,temperature,andspeedconditions,aswellasdeformationandwearofthecomponents.Theareaofrealcontactbetweenthepadandthediscisfarfromconstant1,verysmallcomparedtothetotalcontactarea2,andhighlydependentonchangesofpressure,temperatures,deformation,andwear.Takingintoconsiderationthatverycomplexandhighlynonlinearphenomenaareinvolvedinthebrakingprocess2,11,completeanalyticalmodelsofbrakeoperationaredifficultifnotimpossibletoobtain.Incontrasttoclassicalanalyticalapproaches,itisarguedinthispaperthatartificialneuralnetworkscanbeusedtomodelthecomplexnonlinear,multidimensionalfactorsthatcaninfluenceabrakesperformance.Aspointedoutbymanyresearchers12–15,forexample,artificialneuralnetworksareapromisingfieldofresearchinpredictingexperimentaltrendsandarecapableofconsiderablesavingsintermsofcostandtimecomparedwithclassicalanalyticalmodels.Inordertoimproveabrakingsystemoperation,itisdesirablethatthebrakesshouldbemorepreciselycontrolledversuschangesofcoefficientofthefriction.Consequently,thebrakeperformanceshouldbecalibratedforthespecificbrakeoperatingregimesandafrictionpairscharacteristics15–17.Inthispaper,artificialneuralnetworkshavebeenusedformodellingandpredictingthediscbrakesfrictioncharacteristicsi.e.thebrakefactorCvariationtakingintoconsiderationthefollowinginfluencingfactorsifrictionmaterialcomposition,iimanufacturingparametersoffrictionmaterial,andiiibrakesoperatingconditions.Therearemanycomplexinfluencesoffrictionmaterialcomposition,itsmanufacturingconditions,andbrakeoperatingregimesonthewearresistanceandnoisypropensityofadiscFthenumberofoutputsfxactivationfunctionNomenclatureCbrakefactorTbrakingtorquepapplicationpressuredcpistondiameterreeffectivebrakediscradiusFtypeoffrictionmaterialFTtypeoffrictionmaterialusedforthetestdatasetAC–D–EBFneuralnetworkarchitectureAthenumberofinputsBthenumberofhiddenlayersC,D,EthebrakebutinthispaperourattentionhasbeenfocusedonpredictionofthediscbrakefactorCasoneofthemostimportantperformanceofthediscbrakeoperation.2.ExperimentalmethodsInordertobetaughtaboutthediscbrakeoperationi.e.brakeperformanceasafunctionofdifferenttypesoffrictionmaterialandbrakesoperatingconditions,theartificialneuralnetworkshavetobetrainedwithappropriatedata.Theprocessofmodellingofadiscbrakeoperationbymeansofartificialneuralnetworksisnottrivialandmanycriticalissueshavetoberesolved.Thefollowingoperationshavetobeconsiderediselectionofadatagenerator,iidefinitionoftherangesanddistributionofinputdata,iiidatageneration,ivdatapreprocessing,vselectionoftheneuralnetworksarchitectures,viselectionofthetrainingalgorithms,viitrainingoftheneuralnetworks,viiivalidationandaccuracyevaluation,andixtestingoftheartificialneuralnetworks.Thepreliminarystepindevelopmentoftheneuralmodelofadiscbrakeoperationistheidentificationofthemodelinputsandoutputs.Input/outputidentificationdependsonthemodelobjectivesandchoiceofthedatagenerator.Forthepurposesofthispaper,theinputparametersaredefinedbythefrictionmaterialcomposition,itsmanufacturingprocessconditions,andthediscbrakeoperatingconditions.ThebrakefactorChasbeentakenastheoutputparameterandusedforrepresentingthediscbrakeperformance.ThebrakefactorCcorrespondstochangesofthefrictioncoefficientinthecontactoffrictionpairduringbrakingC¼2m.ThebrakefactorCiscalculatedfromthemeasuredvariationofthebrakingtorqueandapplicationpressureduringthebrakingcycle,andknownvaluesofthepistondiameterandeffectivebrakediscradiusaccordingtoexpression1C¼4Tpd2cpre1Thetypeofdatageneratordependsontheapplicationandtheavailability.Inthiscase,thedatageneratorhasbeenasingleendfullscaleinertialdynamometer,developedatthelaboratoryforfrictionmechanismandbrakingsystemsFRIMEKSAutomotiveDepartment,FacultyofMechanicalEngineering,UniversityofBelgrade.Obviously,thetestingmethodologyneedstobechosenaccordingtotherangeanddistributionofdatathataregoingtobecollected.Table1presentsthetestingmethodologyusedfortheoutputdatageneration.Thebraketestingconditions,aftertheburnishingprocedure,havebeenchoseninordertoidentifytheinfluencesofappliedhydraulicpressureandinitialequivalentOMinminimumoutputvalueBRBayesianRegulationlearningalgorithmBRabcdneuralmodelBRBayesianRegulationlearningalgorithmathenumberofinputsbthenumberofneuronsinthefirsthiddenlayercthenumberofneuronsinthesecondhiddenlayerdthenumberofoutputsvehiclespeedonthefinalcoldperformanceofthediscbrakeforthedifferenttypesoffrictionmaterial18.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,andiiithebrakesoperationregimes.TherangesanddistributionofdatarelatedtothebrakesoperationregimesisdefinedbythetestingmethodologyTable1.Ontheotherhand,choiceoftherangesanddistributionofthemanufacturingandespeciallythecompositionparametersofthefrictionmaterialsisamuchmoredifficulttask.Forthetrainingandvalidationdatasetsformation,eachingredientinthecompositionofthefrictionmaterialanditsmanufacturingparametershavebeenselectedwithinarangeF1–F9aspresentedinTables2and3.FromTables2and3,itcanbeseenthatelevendifferenttypesoffrictionmaterialwereproducedasadiscpadassembly,mountedonthefrontbrakeaxlestaticweightof730kgofasmallpassengercarYugoFlorida1.4andtestedusingthesingleendfullscaleinertialdynamometer.Thediscpadswiththefrictionsurfaceareaof32.4cm2andpadthicknessof16.8mmweredesignedforthebrakewithaneffectivediscradiusof101mmandfloatingcalliperpistondiameterof48mm.Thecompositionandmanufacturingparametersforeachtypeoffrictionmaterial,aspresentedinTables2and3,werecompletelydifferentfromoneanother.ResultsobtainedduringbraketestingwithfrictionmaterialsF1–F8wereusedfortrainingtheneuralnetworks,whileresultswiththefrictionmaterialF9wereusedforvalidatingthecapabilitiesoftheartificialneuralnetworks.Thevolumepercentagesofthefrictionmaterialsingredients,usedfortheneuralnetworkstrainingandvalidationF1–F9overtherangespresentedinTable2,havebeenrandomlyselected.Thelearningalgorithmselected19,20.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,thefollowingnetworksarchitectureshavebeeninvestigatedinthisapplicationionelayeredstructures26111,26211,26311,26511,26811,iitwolayeredstructures261–121,262–221,263–22manufacturingparameters,presentedinTable3,havebeenalsorandomlyselectedinthecaseoffrictionmaterialsdenotedasF1–F9.Furthermore,theaccuracyofthetrainedneuralnetworksforpredictingthediscbrakeperformancehasbeentestedusingtheinput/outputdatastoredinthetestdataset.ThetestdatasethavebeenobtainedbyproducingtwonewtypesoffrictionmaterialsFT1andFT2whoseinputparameterswerecompletelydifferentfromthosestoredinthetrainingandvalidationtestdatasets.Thevolumepercentageofingredients,presentedinTable2,usedforthecompositionoffrictionmaterialsFT1andFT2weremostlyselectedtocorrespondtotheupperandlowerboundvaluesofthespecifiedranges.ThemanufacturingparametersofthefrictionmaterialsFT1andFT2havebeenalsosimilarlyselectedregardingtherangesspecifiedinTable3.Theonlydifferenceisrelatedtothespecificmouldingpressureswhich,inthecaseoffrictionmaterialsFT1andFT2,wereoutoftherangeusedformanufacturingthefrictionmaterialsdenotedasF1–F9seeTable3.Thesevalueswereselectedinordertotesttheneuralmodelabilitiestoextenditspredictivepowerfordataeitherattheendsoftherangesorcompletelyoutsideoftherangesusedforthetrainingdatasetcreation.3.NeuralnetworkmodellingBasedonTables1–3,neuralmodellingofthediscbrakeoperationhasbeenperformedfor26inputparameters18parametersrelatedtothefrictionmaterialscomposition,5parametersrelatedtothemanufacturingconditions,and3parametersrelatedtothebraketestingconditions,andoneoutputparameterbrakefactorC.Neuralmodellingofthediscbrakeoperationisacomplextaskandtheappropriatearchitectureoftheneuralnetworkaswellasthelearningalgorithmneedtobeproperlydetermined.Thearchitectureofanartificialneuralnetworkconsistsofadescriptionofhowmanylayersanetworkhas,thenumberofneuronsineachlayer,eachlayerstransferfunctionandhowthelayersareconnectedtoeachother.Thebestarchitecturetousedependsonthekindofproblemtoberepresentedbythenetwork.Thebestneuralnetworksetisaffectedbytherepresentationalpowerofthenetworkandthe1,265–221,268–221,268–421,2610–521,andiiithreelayeredstructures263–2–231,264–3–231,264–2–231,265–2–231,268–2–231,268–4–231.ThesenetworkarchitectureshavebeentrainedbythefollowingtrainingalgorithmsLevenberg–Marquardt,BayesianRegulation,ResilientBackpropagation,ScaledConjugateGradient,andGradientDecent.Thesigmoidactivationfunctionhasbeenusedbetweentheinputandhiddenlayersseeexpression2fðxÞ¼11þeC0x2Alinearactivationfunctionfx¼1xwasemployedbetweenthehiddenandoutputlayer.Preprocessingoftheinputparameterswascarriedoutbeforetheneuralnetworktraining.Thus,18parametersrelatedtothefrictionmaterialformulationwerepresentedtothenetworkinpercentbyvolume,and5manufacturingparametersand3testingconditionswerescaledintherangeof0–1accordingtoexpression3ðICurrC0IMaxÞtwotypesoffrictionmaterialsFT1andFT2havebeenfirstlyproducedandtestedusingtheinertialfullscalebrakedynambetween20and60barand60and100bar,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,themeasureddiscbrakeperforARTICLEINPRESS0.840.860.880.90.920.940.96BrakefactorCv20v40v60v80v100Fig.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.Measureddiscbrakeperformanceversusappliedpressures20–60barandIScal¼1þðIMaxC0IMinÞ3Ontheotherhand,theoutputparameterbrakefactorChasbeenlinearizedbyexpression4OLin¼075þ02ðOCurrC0OMaxÞðOMaxC0OMinÞ44.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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