performancealjiceFrictionmaterialormanceThesmaterialssynergistandbytraining18differentneuralnetworkarchitectureswiththefivedifferentlearningalgorithms.TheoptimalneuralmodelofdiscbrakeoperationhasbeenshowntobevalidforpredictingthebrakefactorCvariationofthecolddiscbrakeoverawiderangeofbrakesoperatingregimesandfordifferenttypesingsystxandmanifold.berelatih,andhumiditygbrakeebrakdistance,pedalfeel,discwear,andbrakeinducedvibrations4.theeinofThesynergeticeffectsofallingredientsincludedinafrictionARTICLEINPRESSContentslistsavailableatScienceD/locate/tribointTribologyIntTribologyInternational42(2009)10741080ditions,iscomplicatedbythefactthatthetribologyatthefrictionE-mailaddress:daleksendricmas.bg.ac.yu(D.Aleksendric).Forinstance,thevibrationsgeneratedattheinterfacebetweenthematerial,forthespecificmanufacturingconditions,determinethefinalfrictionmaterialcharacteristicsandaccordinglyaffectthebrakesystemsperformance.Improvementandcontrolofanautomotivebrakesperformance,underdifferentoperatingcon-0301-679X/$-seefrontmatter&2009ElsevierLtd.Allrightsreserved.doi:10.1016/j.triboint.2009.03.005C3Correspondingauthor.Tel.:+381113370346；fax:+38113370364.foroverallperformanceofavehicle.Thisisbecauseitplayscrucialrolesinvariousaspectsofthebrakeperformancesuchasstoppingfrictionmaterialsandbrakingconditions11whichbothaffectthebrakingsystemsperformance.stablefrictioncoefficient,lowwearrate,nonoise,lowcost,andenvironmentfriendly3.Thefrictionmaterialintheautomotivebrakesystemhasbeenconsideredasoneofthekeycomponentsaffectedbythewidediversityinmechanicalpropertiesofcompositematerialsingredients710.Thatiswhy,achangfrictioncoefficientishighlydependentontheingredientsvaluesandstabilityofthefrictioncoefficientoverdifferentbrakesoperatingconditionsdefinedbychangingappliedpressureand/orslidingspeedand/ortemperature.Thefrictionbehaviourofautomotivebrakesisdeterminedbythecharacteroftheactivesurfacesofthediscandpadandthirdbodiesbetweenthesesurfaces2.Thebrakesrequirefrictionmaterialswithhigherandoperatingregimes.Therefore,thebrakesperformanceisprimarilyinfluencedbythecontactsituationbetweenacastironbrakediscandthecompositefrictionmaterial.Thecontactsituationisadditionallycomplicatedbythefactthatfrictionmaterialsarecomplexpolymercompositesandmaycontainover20differentingredients.Hencethecontactsituationcanbesignificantly1.IntroductionThedemandsimposedonabrakofoperatingconditions,arecomplethatthefrictioncoefficientshouldstablefrictionforce,reliablestrengtareneededirrespectiveoftemperature,wearandcorrosion,etc1.Thebrakinmostlydeterminedbythefoundationrequirementsimposedonautomotiv&2009ElsevierLtd.Allrightsreserved.em,overawiderangeItisexpectedvelyhighbutalsogoodwearresistance,age,degreeofsystemperformanceisassembly.Thebasicesarerelatedtothetwobodiesinfrictionareresponsibleforvariousnoisessuchassquealing,juddering,hammering,hooting,etc5.Ontheotherhand,theperformancecriteriahaveincreasedandhavebecomemoresensitivetobraking6.Anautomotivebrakesfrictionbehaviourresultsfromthecomplexinterrelatedphenomenaoccurringatthecontactofthefrictionpairduringbraking.Thesecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalpropertiesofthecompositematerialasthefrictionelement,thebrakediscasthemetalliccounterface,andtheconditionsimposedbythebrakesoffrictionmaterial.NeuralnetworkpredictionofdiscbrakeDraganAleksendrica,C3,DavidC.BartonbaAutomotiveDepartment,UniversityofBelgrade,FacultyofMechanicalEngineering,KrbSchoolofMechanicalEngineering,UniversityofLeeds,LS29JT,UKarticleinfoArticlehistory:Received28November2007Receivedinrevisedform3March2009Accepted16March2009Availableonline24March2009Keywords:NeuralnetworkPredictionDiscbrakeperformanceabstractApertiesofthefrictionregimes.Inthispaper,thecompositionandmanufacturinvariationhavebeenmodelleparameters,determinedbyconditions(5parameters),variation,havebeenpredicted.journalhomepage:www.elMarije16,11120Belgrade35,Serbiaresultsfromthecomplexinterrelatedphenomenaoccurringattheecomplexbrakingphenomenaaremostlyaffectedbythetribochemicalingredients,thebrakediscproperties,andthebrakesoperatingiceffectsofthefrictionmaterialsproperties,definedbyitsgconditions,andthebrakesoperatingregimesonthediscbrakefactorCdbymeansofartificialneuralnetworks.Theinfluencesof26inputthefrictionmaterialcomposition(18ingredients),itsmanufacturingthebrakesoperatingregimes(3parameters)onthebrakefactorCTheneuralmodelofthediscbrakecoldperformancehasbeendevelopedernationalARTICLEINPRESSnumberofneuronsinhiddenlayers,respectively；IScalscaledinputvalueICurrcurrentinputvalueIMaxmaximuminputvalueIMinminimuminputvalueOLinlinearizedoutputvalueOCurrcurrentoutputvalueOMaxmaximumoutputvalueD.Aleksendric,D.C.Barton/TribologyInternational42(2009)107410801075interfacehasastochasticnatureaffectedbyvariationsoftherealcontactarea,transferlayerformation,changingpressure,tem-perature,andspeedconditions,aswellasdeformationandwearofthecomponents.Theareaofrealcontactbetweenthepadandthediscisfarfromconstant1,verysmallcomparedtothetotalcontactarea2,andhighlydependentonchangesofpressure,temperatures,deformation,andwear.Takingintoconsiderationthatverycomplexandhighlynon-linearphenomenaareinvolvedinthebrakingprocess2,11,completeanalyticalmodelsofbrakeoperationaredifficultifnotimpossibletoobtain.Incontrasttoclassicalanalyticalapproaches,itisarguedinthispaperthatartificialneuralnetworkscanbeusedtomodelthecomplexnon-linear,multidimensionalfactorsthatcaninfluenceabrakesperformance.Aspointedoutbymanyresearchers(1215,forexample),artificialneuralnetworksareapromisingfieldofresearchinpredictingexperimentaltrendsandarecapableofconsiderablesavingsintermsofcostandtimecomparedwithclassicalanalyticalmodels.Inordertoimproveabrakingsystemoperation,itisdesirablethatthebrakesshouldbemorepreciselycontrolledversuschangesofcoefficientofthefriction.Consequently,thebrakeperformanceshouldbecalibratedforthespecificbrakeoperatingregimesandafrictionpairscharacteristics1517.Inthispaper,artificialneuralnetworkshavebeenusedformodellingandpredictingthediscbrakesfrictioncharacteristicsi.e.thebrakefactorCvariationtakingintoconsiderationthefollowinginfluen-cingfactors:(i)frictionmaterialcomposition,(ii)manufacturingparametersoffrictionmaterial,and(iii)brakesoperatingconditions.Therearemanycomplexinfluencesoffrictionmaterialcomposition,itsmanufacturingconditions,andbrakeoperatingregimesonthewearresistanceandnoisypropensityofadiscFthenumberofoutputs)f(x)activationfunctionNomenclatureCbrakefactorTbrakingtorquepapplicationpressuredcpistondiameterreeffectivebrakediscradiusFtypeoffrictionmaterialFTtypeoffrictionmaterialusedforthetestdatasetACDEBFneuralnetworkarchitecture(Athenumberofinputs；Bthenumberofhiddenlayers；C,D,EthebrakebutinthispaperourattentionhasbeenfocusedonpredictionofthediscbrakefactorCasoneofthemostimportantperformanceofthediscbrakeoperation.2.ExperimentalmethodsInordertobetaughtaboutthediscbrakeoperationi.e.brakeperformanceasafunctionofdifferenttypesoffrictionmaterialandbrakesoperatingconditions,theartificialneuralnetworkshavetobetrainedwithappropriatedata.Theprocessofmodellingofadiscbrakeoperationbymeansofartificialneuralnetworksisnottrivialandmanycriticalissueshavetoberesolved.Thefollowingoperationshavetobeconsidered:(i)selectionofadatagenerator,(ii)definitionoftherangesanddistributionofinputdata,(iii)datageneration,(iv)datapre-processing,(v)selectionoftheneuralnetworksarchitectures,(vi)selectionofthetrainingalgorithms,(vii)trainingoftheneuralnetworks,(viii)validationandaccuracyevaluation,and(ix)testingoftheartificialneuralnetworks.Thepreliminarystepindevelopmentoftheneuralmodelofadiscbrakeoperationistheidentificationofthemodelinputsandoutputs.Input/outputidentificationdependsonthemodelobjectivesandchoiceofthedatagenerator.Forthepurposesofthispaper,theinputparametersaredefinedbythefrictionmaterialcomposition,itsmanufacturingprocessconditions,andthediscbrakeoperatingconditions.ThebrakefactorChasbeentakenastheoutputparameterandusedforrepresentingthediscbrakeperformance.ThebrakefactorCcorrespondstochangesofthefrictioncoefficientinthecontactoffrictionpairduringbraking(C2m).ThebrakefactorCiscalculatedfromthemeasuredvariationofthebrakingtorqueandapplicationpressureduringthebrakingcycle,andknownvaluesofthepistondiameterandeffectivebrakediscradiusaccordingtoexpression(1):C4Tpd2cpre(1)Thetypeofdatageneratordependsontheapplicationandtheavailability.Inthiscase,thedatageneratorhasbeenasingle-endfull-scaleinertialdynamometer,developedatthelaboratoryforfrictionmechanismandbrakingsystemsFRIMEKS(AutomotiveDepartment,FacultyofMechanicalEngineering,UniversityofBelgrade).Obviously,thetestingmethodologyneedstobechosenaccordingtotherangeanddistributionofdatathataregoingtobecollected.Table1presentsthetestingmethodologyusedfortheoutputdatageneration.Thebraketestingconditions,aftertheburnishingprocedure,havebeenchoseninordertoidentifytheinfluencesofappliedhydraulicpressureandinitialequivalentOMinminimumoutputvalueBRBayesianRegulationlearningalgorithmBRabcdneuralmodel(BRBayesianRegulationlearningalgorithm；athenumberofinputs；bthenumberofneuronsinthefirsthiddenlayer；cthenumberofneuronsinthesecondhiddenlayer；dthenumberofoutputs)vehiclespeedonthefinalcoldperformanceofthediscbrakeforthedifferenttypesoffrictionmaterial18.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)107410801076Table2Theselectionandrangesofrawmaterialsforthefrictionmaterialcompositions(%vol).RawmaterialsF1F9(trainingandvalidationdataset)FT1(testdataset)FT2(testdataset)Phenolicresin17252517Ironoxide3553Barites26151526Calciumcarbonate1331Brasschips1331Aramid2662Mineralfibre1016109Vermiculite4884Steelfibre4114Glassfibre2442Brasspowder1221Copperpowder1331Graphite7337Frictiondust5225MolybdenumDisulphide1331Aluminiumoxide2332Silica1221Magnesiumoxide8228Table3Rangesofmanufacturingparametersforthefrictionmaterials.threegroupsofinputdata:(i)thefrictionmaterialcomposition,(ii)itsmanufacturingconditions,and(iii)thebrakesoperationregimes.Therangesanddistributionofdatarelatedtothebrakesoperationregimesisdefinedbythetestingmethodology(Table1).Ontheotherhand,choiceoftherangesanddistributionofthemanufacturingandespeciallythecompositionparametersofthefrictionmaterialsisamuchmoredifficulttask.Forthetrainingandvalidationdatasetsformation,eachingredientinthecompositionofthefrictionmaterialanditsmanufacturingparametershavebeenselectedwithinarange(F1F9)aspresentedinTables2and3.FromTables2and3,itcanbeseenthatelevendifferenttypesoffrictionmaterialwereproducedasadiscpadassembly,mountedonthefrontbrake(axlestaticweightof730kg)ofasmallpassengercar(YugoFlorida1.4)andtestedusingthesingleendfull-scaleinertialdynamometer.Thediscpadswiththefrictionsurfaceareaof32.4cm2andpadthicknessof16.8mmweredesignedforthebrakewithaneffectivediscradiusof101mmandfloatingcalliperpistondiameterof48mm.Thecompositionandmanufacturingparametersforeachtypeoffrictionmaterial,aspresentedinTables2and3,werecompletelydifferentfromoneanother.ResultsobtainedduringbraketestingwithfrictionmaterialsF1F8wereusedfortrainingtheneuralnetworks,whileresultswiththefrictionmaterialF9wereusedforvalidatingthecapabilitiesoftheartificialneuralnetworks.Thevolumepercentagesofthefrictionmaterialsingredients,usedfortheneuralnetworkstrainingandvalidation(F1F9)overtherangespresentedinTable2,havebeenrandomlyselected.Thelearningalgorithmselected19,20.ThelearningabilityoftheManufacturingparametersF1F9(trainingandvalidationdataset)FT1(testdataset)FT2(testdataset)Specificmouldingpressure(MPa)45654070Mouldingtemperature(1C)155170170155Mouldingtime(min)611116Heattreatmenttemperature(1C)200250200250Heattreatmenttime(h)125125neuralnetworktoextenditspredictivepowerfordataoutsideofthetrainingdatasetisessentialinimplementationoftheartificialneuralnetworksforpredictingdiscbrakeperformance.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-layeredstructures26111,26211,26311,26511,26811,(ii)two-layeredstructures261121,262221,26322manufacturingparameters,presentedinTable3,havebeenalsorandomlyselectedinthecaseoffrictionmaterialsdenotedasF1F9.Furthermore,theaccuracyofthetrainedneuralnetworksforpredictingthediscbrakeperformancehasbeentestedusingtheinput/outputdatastoredinthetestdataset.Thetestdatasethavebeenobtainedbyproducingtwonewtypesoffrictionmaterials(FT1andFT2)whoseinputparameterswerecompletelydifferentfromthosestoredinthetrainingandvalidationtestdatasets.Thevolumepercentageofingredients,presentedinTable2,usedforthecompositionoffrictionmaterialsFT1andFT2weremostlyselectedtocorrespondtotheupperandlowerboundvaluesofthespecifiedranges.ThemanufacturingparametersofthefrictionmaterialsFT1andFT2havebeenalsosimilarlyselectedregardingtherangesspecifiedinTable3.Theonlydifferenceisrelatedtothespecificmouldingpressureswhich,inthecaseoffrictionmaterialsFT1andFT2,wereoutoftherangeusedformanufactur-ingthefrictionmaterialsdenotedasF1F9(seeTable3).Thesevalueswereselectedinordertotesttheneuralmodelabilitiestoextenditspredictivepowerfordataeitherattheendsoftherangesorcompletelyoutsideoftherangesusedforthetrainingdatasetcreation.3.NeuralnetworkmodellingBasedonTables13,neuralmodellingofthediscbrakeoperationhasbeenperformedfor26inputparameters(18parametersrelatedtothefrictionmaterialscomposition,5parametersrelatedtothemanufacturingconditions,and3parametersrelatedtothebraketestingconditions),andoneoutputparameter(brakefactorC).Neuralmodellingofthediscbrakeoperationisacomplextaskandtheappropriatearchitec-tureoftheneuralnetworkaswellasthelearningalgorithmneedtobeproperlydetermined.Thearchitectureofanartificialneuralnetworkconsistsofadescriptionofhowmanylayersanetworkhas,thenumberofneuronsineachlayer,eachlayerstransferfunctionandhowthelayersareconnectedtoeachother.Thebestarchitecturetousedependsonthekindofproblemtoberepresentedbythenetwork.Thebestneuralnetworksetisaffectedbytherepresentationalpowerofthenetworkandthe1,265221,268221,268421,2610521,and(iii)three-layeredstructures2632231,2643231,2642231,2652231,2682231,2684231.Thesenetworkarchitectureshavebeentrainedbythefollow-ingtrainingalgorithms:LevenbergMarquardt,BayesianRegula-tion,ResilientBackpropagation,ScaledConjugateGradient,andGradientDecent.Thesigmoidactivationfunctionhasbeenusedbetweentheinputandhiddenlayers(seeexpression(2):fx11eC0x(2)Alinearactivationfunction(f(x)1x)wasemployedbetweenthehiddenandoutputlayer.Pre-processingoftheinputparameterswascarriedoutbeforetheneuralnetworktraining.Thus,18parametersrelatedtothefrictionmaterialformulationwerepresentedtothenetworkinpercentbyvolume,and5manufacturingparametersand3testingconditionswerescaledintherangeof01accordingtoexpression(3):ICurrC0IMaxtwotypesoffrictionmaterials(FT1andFT2)havebeenfirstlyproducedandtestedusingtheinertialfull-scalebrakedynam-between20and60barand60and100bar,inordertobetterillustratethecomplexityofrealchangesofdiscbrakeperformanceinfluencedbythefrictionmaterialFT1underthespecifieddiscbrakeoperationregimes.FromFig.1,thegeneraltrendofthediscbrakeperformanceisevidentforappliedpressuresbetween20and60barandinitialspeedsbetween20and100km/h.ThebrakefactorCincreasesintherangeof2040barforinitialspeedsbetween20and60km/h.Thediscbrakeperformanceisrelativelyconstantoverthewholerangeofinitialspeeds(20100km/h)forfurtherincreasesofappliedpressurefrom40to60bar,seeFig.1.Forinitialspeedsbetween80and100km/h,thebrakefactorChasbeenrelativelyconstantinthesamerangeofappliedpressures(2060bar).Contrarytorelativelyconstantdiscbrakeperformance,intherangeofappliedpressuresbetween40and60barandinitialspeedsbetween20and100km/h,thediscbrakeperformancehasbeendecreasedbyfurtherincreasingofappliedpressureto100bar(Fig.2).Obviously,themeasureddiscbrakeperformancehasbeendifferentlyaffectedbythefrictionmaterialpropertiesinsynergywithchangesofthebrakeoperationregimes(Figs.1and2).FromFigs.1and2,itcanbeseenthreedifferentrange