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performancealjiceFrictionmaterialormanceThesmaterial’ssynergistandbytraining18differentneuralnetworkarchitectureswiththefivedifferentlearningalgorithms.TheoptimalneuralmodelofdiscbrakeoperationhasbeenshowntobevalidforpredictingthebrakefactorCvariationofthecolddiscbrakeoverawiderangeofbrake’soperatingregimesandfordifferenttypesingsystxandmanifold.berelatih,andhumiditygbrakeebrakdistance,pedalfeel,discwear,andbrakeinducedvibrations[4].theeinofThesynergeticeffectsofallingredientsincludedinafrictionARTICLEINPRESSContentslistsavailableatScienceDirectsevier.com/locate/tribointTribologyIntTribologyInternational42(2009)1074–1080ditions,iscomplicatedbythefactthatthetribologyatthefrictionE-mailaddress:[email protected](D.Aleksendric´).Forinstance,thevibrationsgeneratedattheinterfacebetweenthematerial,forthespecificmanufacturingconditions,determinethefinalfrictionmaterialcharacteristicsandaccordinglyaffectthebrakesystem’sperformance.Improvementandcontrolofanautomotivebrake’sperformance,underdifferentoperatingcon-0301-679X/$-seefrontmatter&2009ElsevierLtd.Allrightsreserved.doi:10.1016/j.triboint.2009.03.005C3Correspondingauthor.Tel.:+381113370346;fax:+38113370364.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].Thebrakinmostlydeterminedbythefoundationrequirementsimposedonautomotiv&2009ElsevierLtd.Allrightsreserved.em,overawiderangeItisexpectedvelyhighbutalsogoodwearresistance,age,degreeofsystemperformanceisassembly.Thebasicesarerelatedtothetwobodiesinfrictionareresponsibleforvariousnoisessuchassquealing,juddering,hammering,hooting,etc[5].Ontheotherhand,theperformancecriteriahaveincreasedandhavebecomemoresensitivetobraking[6].Anautomotivebrake’sfrictionbehaviourresultsfromthecomplexinterrelatedphenomenaoccurringatthecontactofthefrictionpairduringbraking.Thesecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalpropertiesofthecompositematerialasthefrictionelement,thebrakediscasthemetalliccounterface,andtheconditionsimposedbythebrake’soffrictionmaterial.NeuralnetworkpredictionofdiscbrakeDraganAleksendric´a,C3,DavidC.BartonbaAutomotiveDepartment,UniversityofBelgrade,FacultyofMechanicalEngineering,KrbSchoolofMechanicalEngineering,UniversityofLeeds,LS29JT,UKarticleinfoArticlehistory:Received28November2007Receivedinrevisedform3March2009Accepted16March2009Availableonline24March2009Keywords:NeuralnetworkPredictionDiscbrakeperformanceabstractAnautomotivebrake’sperfcontactofthefrictionpair.propertiesofthefrictionregimes.Inthispaper,thecompositionandmanufacturinvariationhavebeenmodelleparameters,determinedbyconditions(5parameters),variation,havebeenpredicted.journalhomepage:www.elMarije16,11120Belgrade35,Serbiaresultsfromthecomplexinterrelatedphenomenaoccurringattheecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalingredients,thebrakediscproperties,andthebrake’soperatingiceffectsofthefrictionmaterial’sproperties,definedbyitsgconditions,andthebrake’soperatingregimesonthediscbrakefactorCdbymeansofartificialneuralnetworks.Theinfluencesof26inputthefrictionmaterialcomposition(18ingredients),itsmanufacturingthebrake’soperatingregimes(3parameters)onthebrakefactorCTheneuralmodelofthediscbrakecoldperformancehasbeendevelopedernationalARTICLEINPRESSnumberofneuronsinhiddenlayers,respectively;IScalscaledinputvalueICurrcurrentinputvalueIMaxmaximuminputvalueIMinminimuminputvalueOLinlinearizedoutputvalueOCurrcurrentoutputvalueOMaxmaximumoutputvalueD.Aleksendric´,D.C.Barton/TribologyInternational42(2009)1074–10801075interfacehasastochasticnatureaffectedbyvariationsoftherealcontactarea,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-cingfactors:(i)frictionmaterialcomposition,(ii)manufacturingparametersoffrictionmaterial,and(iii)brake’soperatingconditions.Therearemanycomplexinfluencesoffrictionmaterialcomposition,itsmanufacturingconditions,andbrakeoperatingregimesonthewearresistanceandnoisypropensityofadiscF—thenumberofoutputs)f(x)activationfunctionNomenclatureCbrakefactorTbrakingtorquepapplicationpressuredcpistondiameterreeffectivebrakediscradiusFtypeoffrictionmaterialFTtypeoffrictionmaterialusedforthetestdatasetA[C–D–E]BFneuralnetworkarchitecture(A—thenumberofinputs;B—thenumberofhiddenlayers;C,D,E—thebrakebutinthispaperourattentionhasbeenfocusedonpredictionofthediscbrakefactorCasoneofthemostimportantperformanceofthediscbrakeoperation.2.ExperimentalmethodsInordertobetaughtaboutthediscbrakeoperationi.e.brakeperformanceasafunctionofdifferenttypesoffrictionmaterialandbrake’soperatingconditions,theartificialneuralnetworkshavetobetrainedwithappropriatedata.Theprocessofmodellingofadiscbrakeoperationbymeansofartificialneuralnetworksisnottrivialandmanycriticalissueshavetoberesolved.Thefollowingoperationshavetobeconsidered:(i)selectionofadatagenerator,(ii)definitionoftherangesanddistributionofinputdata,(iii)datageneration,(iv)datapre-processing,(v)selectionoftheneuralnetwork’sarchitectures,(vi)selectionofthetrainingalgorithms,(vii)trainingoftheneuralnetworks,(viii)validationandaccuracyevaluation,and(ix)testingoftheartificialneuralnetworks.Thepreliminarystepindevelopmentoftheneuralmodelofadiscbrakeoperationistheidentificationofthemodelinputsandoutputs.Input/outputidentificationdependsonthemodelobjectivesandchoiceofthedatagenerator.Forthepurposesofthispaper,theinputparametersaredefinedbythefrictionmaterialcomposition,itsmanufacturingprocessconditions,andthediscbrakeoperatingconditions.ThebrakefactorChasbeentakenastheoutputparameterandusedforrepresentingthediscbrakeperformance.ThebrakefactorCcorrespondstochangesofthefrictioncoefficientinthecontactoffrictionpairduringbraking(C¼2m).ThebrakefactorCiscalculatedfromthemeasuredvariationofthebrakingtorqueandapplicationpressureduringthebrakingcycle,andknownvaluesofthepistondiameterandeffectivebrakediscradiusaccordingtoexpression(1):C¼4Tpd2cpre(1)Thetypeofdatageneratordependsontheapplicationandtheavailability.Inthiscase,thedatageneratorhasbeenasingle-endfull-scaleinertialdynamometer,developedatthelaboratoryforfrictionmechanismandbrakingsystems—FRIMEKS(AutomotiveDepartment,FacultyofMechanicalEngineering,UniversityofBelgrade).Obviously,thetestingmethodologyneedstobechosenaccordingtotherangeanddistributionofdatathataregoingtobecollected.Table1presentsthetestingmethodologyusedfortheoutputdatageneration.Thebraketestingconditions,aftertheburnishingprocedure,havebeenchoseninordertoidentifytheinfluencesofappliedhydraulicpressureandinitialequivalentOMinminimumoutputvalueBRBayesianRegulationlearningalgorithmBRabcdneuralmodel(BR—BayesianRegulationlearningalgorithm;a—thenumberofinputs;b—thenumberofneuronsinthefirsthiddenlayer;c—thenumberofneuronsinthesecondhiddenlayer;d—thenumberofoutputs)vehiclespeedonthefinalcoldperformanceofthediscbrakeforthedifferenttypesoffrictionmaterial[18].Thesedatahavebeenusedfortraining,validation,andtestingoftheneuralnetworksinordertoestablishthefunctionalrelationshipbetweenthediscbrakeoperatingconditions,thetypeofthefrictionmaterial,andthebrakefactorCvariationastheoutput.Itisobviousthattherangesanddistributionoftheinputsdatafortraining,validation,andtestinghavetobepredefined.TheneuralmodelofdiscbrakeoperationtakesintoconsiderationtheTable1Testingmethodology.TestconditionsAppliedpressure(bar)Initialspeed(km/h)Temperature(1C)NumberofbrakingeventsInitialburnishing4090o100150Brakingregimes20,40,60,80,10020,40,60,80,100o10025ARTICLEINPRESSD.Aleksendric´,D.C.Barton/TribologyInternational42(2009)1074–10801076Table2Theselectionandrangesofrawmaterialsforthefrictionmaterialcompositions(%vol).RawmaterialsF1–F9(trainingandvalidationdataset)FT1(testdataset)FT2(testdataset)Phenolicresin17–252517Ironoxide3–553Barites26–151526Calciumcarbonate1–331Brasschips1–331Aramid2–662Mineralfibre10–16109Vermiculite4–884Steelfibre4–114Glassfibre2–442Brasspowder1–221Copperpowder1–331Graphite7–337Frictiondust5–225MolybdenumDisulphide1–331Aluminiumoxide2–332Silica1–221Magnesiumoxide8–228Table3Rangesofmanufacturingparametersforthefrictionmaterials.threegroupsofinputdata:(i)thefrictionmaterialcomposition,(ii)itsmanufacturingconditions,and(iii)thebrake’soperationregimes.Therangesanddistributionofdatarelatedtothebrake’soperationregimesisdefinedbythetestingmethodology(Table1).Ontheotherhand,choiceoftherangesanddistributionofthemanufacturingandespeciallythecompositionparametersofthefrictionmaterialsisamuchmoredifficulttask.Forthetrainingandvalidationdatasetsformation,eachingredientinthecompositionofthefrictionmaterialanditsmanufacturingparametershavebeenselectedwithinarange(F1–F9)aspresentedinTables2and3.FromTables2and3,itcanbeseenthatelevendifferenttypesoffrictionmaterialwereproducedasadiscpadassembly,mountedonthefrontbrake(axlestaticweightof730kg)ofasmallpassengercar(YugoFlorida1.4)andtestedusingthesingleendfull-scaleinertialdynamometer.Thediscpadswiththefrictionsurfaceareaof32.4cm2andpadthicknessof16.8mmweredesignedforthebrakewithaneffectivediscradiusof101mmandfloatingcalliperpistondiameterof48mm.Thecompositionandmanufacturingparametersforeachtypeoffrictionmaterial,aspresentedinTables2and3,werecompletelydifferentfromoneanother.ResultsobtainedduringbraketestingwithfrictionmaterialsF1–F8wereusedfortrainingtheneuralnetworks,whileresultswiththefrictionmaterialF9wereusedforvalidatingthecapabilitiesoftheartificialneuralnetworks.Thevolumepercentagesofthefrictionmaterial’singredients,usedfortheneuralnetworks’trainingandvalidation(F1–F9)overtherangespresentedinTable2,havebeenrandomlyselected.Thelearningalgorithmselected[19,20].ThelearningabilityoftheManufacturingparametersF1–F9(trainingandvalidationdataset)FT1(testdataset)FT2(testdataset)Specificmouldingpressure(MPa)45–654070Mouldingtemperature(1C)155–170170155Mouldingtime(min)6–11116Heattreatmenttemperature(1C)200–250200250Heattreatmenttime(h)12–5125neuralnetworktoextenditspredictivepowerfordataoutsideofthetrainingdatasetisessentialinimplementationoftheartificialneuralnetworksforpredictingdiscbrakeperformance.Itisaclearthatsufficientinput/targetpairshavetobestoredinthetrainingdataset.Input/outputdatahavebeenobtainedbyformulation,manufacturing,anddynamometertestingofelevendifferentfrictionmaterialsrepresentingalargedatasetthatcanbeusedfortraining,validation,andtestingtheneuralnetwork.Thetotalnumberofoutputresults,obtainedbythedynamometertestingforeachtypeoffrictionmaterial,is25accordingtotheadoptedtestingmethodology(Table1).Thismeansthat275input/outputpairsareavailablefortheneuralnetworktraining,validation,andtesting.Thetotalnumberof275input/outputpairshasbeendividedintothreesets,200input/outputpairsfortheneuralnetworktraining,25pairsforvalidation,and50pairsfortheneuralnetworktesting.Sincethebestneuralnetworkarchitectureandalearningalgorithmareunknowninadvance,atrailanderrormethodhasbeenemployedtofindoutthebestnetworkcharacteristicsformatchingtheparticularinput/outputrelationship.BasedonMatLab6.5Rel.13,thefollowingnetworksarchitectureshavebeeninvestigatedinthisapplication:(i)one-layeredstructures26[1]11,26[2]11,26[3]11,26[5]11,26[8]11,(ii)two-layeredstructures26[1–1]21,26[2–2]21,26[3–2]2manufacturingparameters,presentedinTable3,havebeenalsorandomlyselectedinthecaseoffrictionmaterialsdenotedasF1–F9.Furthermore,theaccuracyofthetrainedneuralnetworksforpredictingthediscbrakeperformancehasbeentestedusingtheinput/outputdatastoredinthetestdataset.Thetestdatasethavebeenobtainedbyproducingtwonewtypesoffrictionmaterials(FT1andFT2)whoseinputparameterswerecompletelydifferentfromthosestoredinthetrainingandvalidationtestdatasets.Thevolumepercentageofingredients,presentedinTable2,usedforthecompositionoffrictionmaterialsFT1andFT2weremostlyselectedtocorrespondtotheupperandlowerboundvaluesofthespecifiedranges.ThemanufacturingparametersofthefrictionmaterialsFT1andFT2havebeenalsosimilarlyselectedregardingtherangesspecifiedinTable3.Theonlydifferenceisrelatedtothespecificmouldingpressureswhich,inthecaseoffrictionmaterialsFT1andFT2,wereoutoftherangeusedformanufactur-ingthefrictionmaterialsdenotedasF1–F9(seeTable3).Thesevalueswereselectedinordertotesttheneuralmodelabilitiestoextenditspredictivepowerfordataeitherattheendsoftherangesorcompletelyoutsideoftherangesusedforthetrainingdatasetcreation.3.NeuralnetworkmodellingBasedonTables1–3,neuralmodellingofthediscbrakeoperationhasbeenperformedfor26inputparameters(18parametersrelatedtothefrictionmaterial’scomposition,5parametersrelatedtothemanufacturingconditions,and3parametersrelatedtothebraketestingconditions),andoneoutputparameter(brakefactorC).Neuralmodellingofthediscbrakeoperationisacomplextaskandtheappropriatearchitec-tureoftheneuralnetworkaswellasthelearningalgorithmneedtobeproperlydetermined.Thearchitectureofanartificialneuralnetworkconsistsofadescriptionofhowmanylayersanetworkhas,thenumberofneuronsineachlayer,eachlayer’stransferfunctionandhowthelayersareconnectedtoeachother.Thebestarchitecturetousedependsonthekindofproblemtoberepresentedbythenetwork.Thebestneuralnetworksetisaffectedbytherepresentationalpowerofthenetworkandthe1,26[5–2]21,26[8–2]21,26[8–4]21,26[10–5]21,and(iii)three-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-ingtrainingalgorithms:Levenberg–Marquardt,BayesianRegula-tion,ResilientBackpropagation,ScaledConjugateGradient,andGradientDecent.Thesigmoidactivationfunctionhasbeenusedbetweentheinputandhiddenlayers(seeexpression(2)):fðxÞ¼11þeC0x(2)Alinearactivationfunction(f(x)¼1x)wasemployedbetweenthehiddenandoutputlayer.Pre-processingoftheinputparameterswascarriedoutbeforetheneuralnetworktraining.Thus,18parametersrelatedtothefrictionmaterialformulationwerepresentedtothenetworkinpercentbyvolume,and5manufacturingparametersand3testingconditionswerescaledintherangeof0–1accordingtoexpression(3):ðICurrC0IMaxÞtwotypesoffrictionmaterials(FT1andFT2)havebeenfirstlyproducedandtestedusingtheinertialfull-scalebrakedynam-between20and60barand60and100bar,inordertobetterillustratethecomplexityofrealchangesofdiscbrakeperformanceinfluencedbythefrictionmaterialFT1underthespecifieddiscbrakeoperationregimes.FromFig.1,thegeneraltrendofthediscbrakeperformanceisevidentforappliedpressuresbetween20and60barandinitialspeedsbetween20and100km/h.ThebrakefactorCincreasesintherangeof20–40barforinitialspeedsbetween20and60km/h.Thediscbrakeperformanceisrelativelyconstantoverthewholerangeofinitialspeeds(20–100km/h)forfurtherincreasesofappliedpressurefrom40to60bar,seeFig.1.Forinitialspeedsbetween80and100km/h,thebrakefactorChasbeenrelativelyconstantinthesamerangeofappliedpressures(20–60bar).Contrarytorelativelyconstantdiscbrakeperformance,intherangeofappliedpressuresbetween40and60barandinitialspeedsbetween20and100km/h,thediscbrakeperformancehasbeendecreasedbyfurtherincreasingofappliedpressureto100bar(Fig.2).Obviously,themeasureddiscbrakeperformancehasbeendifferentlyaffectedbythefrictionmaterialpropertiesinsynergywithchangesofthebrakeoperationregimes(Figs.1and2).FromFigs.1and2,itcanbeseenthreedifferentrangesofdiscbrakeoperationversusappliedpressuresandinitialspeedsexist:(a)between20and40bar,(b)between40and60bar,and(c)between60and100bar.AccordingtoFigs.1and2,themeasureddiscbrakeperfor-ARTICLEINPRESS0.840.860.880.90.920.940.96BrakefactorCv=20v=40v=60v=80v=100Fig.3.Predicteddiscbrakeperformanceversusappliedpressures(20–60bar)andinitialspeeds(20–100km/h)—frictionmaterialFT1.D.Aleksendric´,D.C.Barton/TribologyInternational42(2009)1074–10801077ometer.ThecompositionandmanufacturingparametersoffrictionmaterialsFT1andFT2havebeencompletelyunknowntotheneuralmodels.TheperformanceofthediscbrakeequippedwiththefrictionmaterialFT1isshowninFigs.1and2versusapplicationpressureandinitialspeedchanges.Themeasureddiscbrakeperformance,expressedasthebrakefactorCvariation,hasbeendividedintotworangesdependingonappliedpressure,0.840.860.880.90.920.940.960.98120Pressureapplication(bar)BrakefactorCv=20v=40v=60v=80v=10060504030Fig.1.Measureddiscbrakeperformanceversusappliedpressures(20–60bar)andIScal¼1þðIMaxC0IMinÞ(3)Ontheotherhand,theoutputparameter(brakefactorC)hasbeenlinearizedbyexpression(4):OLin¼0:75þ0:2ðOCurrC0OMaxÞðOMaxC0OMinÞ(4)4.ResultsanddiscussionAftertheirtrainingandvalidation,theneuralnetworkshavebeenemployedforpredictingtheperformanceofthediscbrakeequippedwiththetwonewtypesofdiscpads(FT1andFT2).Intotal90differentneuralmodelshavebeentested(18differentneuralnetworkstrainedbythefivelearningalgorithms)inordertoevaluatetheircapabilitiesforpredictingthediscbrakefactorCvariationasinfluencedbythedifferenttypesoffrictionmaterialsunderthespecificbrakingregimes.Asmentionedabovethenewinitialspeeds(20–100km/h)—frictionmaterialFT1.0.840.860.880.90.920.940.960.98160Pressureapplication(bar)BrakefactorCv=20v=40v=60v=80v=100100908070Fig.2.Measureddiscbrakeperformanceversusappliedpressures(60–100bar)andinitialspeeds(20–100km/h)—frictionmaterialFT1.0.98120Pressureapplication(bar)60504030mancehasbeenstronglyaffectedbytheoperatingconditionsfor
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