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PERFORMANCEALJICEFRICTIONMATERIALORMANCETHESMATERIAL’SSYNERGISTANDBYTRAINING18DIFFERENTNEURALNETWORKARCHITECTURESWITHTHEFIVEDIFFERENTLEARNINGALGORITHMSTHEOPTIMALNEURALMODELOFDISCBRAKEOPERATIONHASBEENSHOWNTOBEVALIDFORPREDICTINGTHEBRAKEFACTORCVARIATIONOFTHECOLDDISCBRAKEOVERAWIDERANGEOFBRAKE’SOPERATINGREGIMESANDFORDIFFERENTTYPESINGSYSTXANDMANIFOLDBERELATIH,ANDHUMIDITYGBRAKEEBRAKDISTANCE,PEDALFEEL,DISCWEAR,ANDBRAKEINDUCEDVIBRATIONS4THEEINOFTHESYNERGETICEFFECTSOFALLINGREDIENTSINCLUDEDINAFRICTIONARTICLEINPRESSCONTENTSLISTSAVAILABLEATSCIENCEDIRECTSEVIERCOM/LOCATE/TRIBOINTTRIBOLOGYINTTRIBOLOGYINTERNATIONAL4220091074–1080DITIONS,ISCOMPLICATEDBYTHEFACTTHATTHETRIBOLOGYATTHEFRICTIONEMAILADDRESSDALEKSENDRICMASBGACYUDALEKSENDRICFORINSTANCE,THEVIBRATIONSGENERATEDATTHEINTERFACEBETWEENTHEMATERIAL,FORTHESPECIFICMANUFACTURINGCONDITIONS,DETERMINETHEFINALFRICTIONMATERIALCHARACTERISTICSANDACCORDINGLYAFFECTTHEBRAKESYSTEM’SPERFORMANCEIMPROVEMENTANDCONTROLOFANAUTOMOTIVEBRAKE’SPERFORMANCE,UNDERDIFFERENTOPERATINGCON0301679X/SEEFRONTMATTER2009ELSEVIERLTDALLRIGHTSRESERVEDDOI101016/JTRIBOINT200903005C3CORRESPONDINGAUTHORTEL381113370346;FAX38113370364FOROVERALLPERFORMANCEOFAVEHICLETHISISBECAUSEITPLAYSCRUCIALROLESINVARIOUSASPECTSOFTHEBRAKEPERFORMANCESUCHASSTOPPINGFRICTIONMATERIALSANDBRAKINGCONDITIONS11WHICHBOTHAFFECTTHEBRAKINGSYSTEM’SPERFORMANCESTABLEFRICTIONCOEFFICIENT,LOWWEARRATE,NONOISE,LOWCOST,ANDENVIRONMENTFRIENDLY3THEFRICTIONMATERIALINTHEAUTOMOTIVEBRAKESYSTEMHASBEENCONSIDEREDASONEOFTHEKEYCOMPONENTSAFFECTEDBYTHEWIDEDIVERSITYINMECHANICALPROPERTIESOFCOMPOSITEMATERIAL’SINGREDIENTS7–10THATISWHY,ACHANGFRICTIONCOEFFICIENTISHIGHLYDEPENDENTONTHEINGREDIENTSVALUESANDSTABILITYOFTHEFRICTIONCOEFFICIENTOVERDIFFERENTBRAKE’SOPERATINGCONDITIONSDEFINEDBYCHANGINGAPPLIEDPRESSUREAND/ORSLIDINGSPEEDAND/ORTEMPERATURETHEFRICTIONBEHAVIOUROFAUTOMOTIVEBRAKESISDETERMINEDBYTHECHARACTEROFTHEACTIVESURFACESOFTHEDISCANDPADANDTHIRDBODIESBETWEENTHESESURFACES2THEBRAKESREQUIREFRICTIONMATERIALSWITHHIGHERANDOPERATINGREGIMESTHEREFORE,THEBRAKE’SPERFORMANCEISPRIMARILYINFLUENCEDBYTHECONTACTSITUATIONBETWEENACASTIRONBRAKEDISCANDTHECOMPOSITEFRICTIONMATERIALTHECONTACTSITUATIONISADDITIONALLYCOMPLICATEDBYTHEFACTTHATFRICTIONMATERIALSARECOMPLEXPOLYMERCOMPOSITESANDMAYCONTAINOVER20DIFFERENTINGREDIENTSHENCETHECONTACTSITUATIONCANBESIGNIFICANTLY1INTRODUCTIONTHEDEMANDSIMPOSEDONABRAKOFOPERATINGCONDITIONS,ARECOMPLETHATTHEFRICTIONCOEFFICIENTSHOULDSTABLEFRICTIONFORCE,RELIABLESTRENGTARENEEDEDIRRESPECTIVEOFTEMPERATURE,WEARANDCORROSION,ETC1THEBRAKINMOSTLYDETERMINEDBYTHEFOUNDATIONREQUIREMENTSIMPOSEDONAUTOMOTIV2009ELSEVIERLTDALLRIGHTSRESERVEDEM,OVERAWIDERANGEITISEXPECTEDVELYHIGHBUTALSOGOODWEARRESISTANCE,AGE,DEGREEOFSYSTEMPERFORMANCEISASSEMBLYTHEBASICESARERELATEDTOTHETWOBODIESINFRICTIONARERESPONSIBLEFORVARIOUSNOISESSUCHASSQUEALING,JUDDERING,HAMMERING,HOOTING,ETC5ONTHEOTHERHAND,THEPERFORMANCECRITERIAHAVEINCREASEDANDHAVEBECOMEMORESENSITIVETOBRAKING6ANAUTOMOTIVEBRAKE’SFRICTIONBEHAVIOURRESULTSFROMTHECOMPLEXINTERRELATEDPHENOMENAOCCURRINGATTHECONTACTOFTHEFRICTIONPAIRDURINGBRAKINGTHESECOMPLEXBRAKINGPHENOMENAAREMOSTLYAFFECTEDBYTHETRIBOCHEMICALPROPERTIESOFTHECOMPOSITEMATERIALASTHEFRICTIONELEMENT,THEBRAKEDISCASTHEMETALLICCOUNTERFACE,ANDTHECONDITIONSIMPOSEDBYTHEBRAKE’SOFFRICTIONMATERIALNEURALNETWORKPREDICTIONOFDISCBRAKEDRAGANALEKSENDRICA,C3,DAVIDCBARTONBAAUTOMOTIVEDEPARTMENT,UNIVERSITYOFBELGRADE,FACULTYOFMECHANICALENGINEERING,KRBSCHOOLOFMECHANICALENGINEERING,UNIVERSITYOFLEEDS,LS29JT,UKARTICLEINFOARTICLEHISTORYRECEIVED28NOVEMBER2007RECEIVEDINREVISEDFORM3MARCH2009ACCEPTED16MARCH2009AVAILABLEONLINE24MARCH2009KEYWORDSNEURALNETWORKPREDICTIONDISCBRAKEPERFORMANCEABSTRACTANAUTOMOTIVEBRAKE’SPERFCONTACTOFTHEFRICTIONPAIRPROPERTIESOFTHEFRICTIONREGIMESINTHISPAPER,THECOMPOSITIONANDMANUFACTURINVARIATIONHAVEBEENMODELLEPARAMETERS,DETERMINEDBYCONDITIONS5PARAMETERS,VARIATION,HAVEBEENPREDICTEDJOURNALHOMEPAGEWWWELMARIJE16,11120BELGRADE35,SERBIARESULTSFROMTHECOMPLEXINTERRELATEDPHENOMENAOCCURRINGATTHEECOMPLEXBRAKINGPHENOMENAAREMOSTLYAFFECTEDBYTHETRIBOCHEMICALINGREDIENTS,THEBRAKEDISCPROPERTIES,ANDTHEBRAKE’SOPERATINGICEFFECTSOFTHEFRICTIONMATERIAL’SPROPERTIES,DEFINEDBYITSGCONDITIONS,ANDTHEBRAKE’SOPERATINGREGIMESONTHEDISCBRAKEFACTORCDBYMEANSOFARTIFICIALNEURALNETWORKSTHEINFLUENCESOF26INPUTTHEFRICTIONMATERIALCOMPOSITION18INGREDIENTS,ITSMANUFACTURINGTHEBRAKE’SOPERATINGREGIMES3PARAMETERSONTHEBRAKEFACTORCTHENEURALMODELOFTHEDISCBRAKECOLDPERFORMANCEHASBEENDEVELOPEDERNATIONALARTICLEINPRESSNUMBEROFNEURONSINHIDDENLAYERS,RESPECTIVELY;ISCALSCALEDINPUTVALUEICURRCURRENTINPUTVALUEIMAXMAXIMUMINPUTVALUEIMINMINIMUMINPUTVALUEOLINLINEARIZEDOUTPUTVALUEOCURRCURRENTOUTPUTVALUEOMAXMAXIMUMOUTPUTVALUEDALEKSENDRIC,DCBARTON/TRIBOLOGYINTERNATIONAL4220091074–10801075INTERFACEHASASTOCHASTICNATUREAFFECTEDBYVARIATIONSOFTHEREALCONTACTAREA,TRANSFERLAYERFORMATION,CHANGINGPRESSURE,TEMPERATURE,ANDSPEEDCONDITIONS,ASWELLASDEFORMATIONANDWEAROFTHECOMPONENTSTHEAREAOFREALCONTACTBETWEENTHEPADANDTHEDISCISFARFROMCONSTANT1,VERYSMALLCOMPAREDTOTHETOTALCONTACTAREA2,ANDHIGHLYDEPENDENTONCHANGESOFPRESSURE,TEMPERATURES,DEFORMATION,ANDWEARTAKINGINTOCONSIDERATIONTHATVERYCOMPLEXANDHIGHLYNONLINEARPHENOMENAAREINVOLVEDINTHEBRAKINGPROCESS2,11,COMPLETEANALYTICALMODELSOFBRAKEOPERATIONAREDIFFICULTIFNOTIMPOSSIBLETOOBTAININCONTRASTTOCLASSICALANALYTICALAPPROACHES,ITISARGUEDINTHISPAPERTHATARTIFICIALNEURALNETWORKSCANBEUSEDTOMODELTHECOMPLEXNONLINEAR,MULTIDIMENSIONALFACTORSTHATCANINFLUENCEABRAKE’SPERFORMANCEASPOINTEDOUTBYMANYRESEARCHERS12–15,FOREXAMPLE,ARTIFICIALNEURALNETWORKSAREAPROMISINGFIELDOFRESEARCHINPREDICTINGEXPERIMENTALTRENDSANDARECAPABLEOFCONSIDERABLESAVINGSINTERMSOFCOSTANDTIMECOMPAREDWITHCLASSICALANALYTICALMODELSINORDERTOIMPROVEABRAKINGSYSTEMOPERATION,ITISDESIRABLETHATTHEBRAKESSHOULDBEMOREPRECISELYCONTROLLEDVERSUSCHANGESOFCOEFFICIENTOFTHEFRICTIONCONSEQUENTLY,THEBRAKEPERFORMANCESHOULDBECALIBRATEDFORTHESPECIFICBRAKEOPERATINGREGIMESANDAFRICTIONPAIR’SCHARACTERISTICS15–17INTHISPAPER,ARTIFICIALNEURALNETWORKSHAVEBEENUSEDFORMODELLINGANDPREDICTINGTHEDISCBRAKE’SFRICTIONCHARACTERISTICSIETHEBRAKEFACTORCVARIATIONTAKINGINTOCONSIDERATIONTHEFOLLOWINGINFLUENCINGFACTORSIFRICTIONMATERIALCOMPOSITION,IIMANUFACTURINGPARAMETERSOFFRICTIONMATERIAL,ANDIIIBRAKE’SOPERATINGCONDITIONSTHEREAREMANYCOMPLEXINFLUENCESOFFRICTIONMATERIALCOMPOSITION,ITSMANUFACTURINGCONDITIONS,ANDBRAKEOPERATINGREGIMESONTHEWEARRESISTANCEANDNOISYPROPENSITYOFADISCFTHENUMBEROFOUTPUTSFXACTIVATIONFUNCTIONNOMENCLATURECBRAKEFACTORTBRAKINGTORQUEPAPPLICATIONPRESSUREDCPISTONDIAMETERREEFFECTIVEBRAKEDISCRADIUSFTYPEOFFRICTIONMATERIALFTTYPEOFFRICTIONMATERIALUSEDFORTHETESTDATASETAC–D–EBFNEURALNETWORKARCHITECTUREATHENUMBEROFINPUTS;BTHENUMBEROFHIDDENLAYERS;C,D,ETHEBRAKEBUTINTHISPAPEROURATTENTIONHASBEENFOCUSEDONPREDICTIONOFTHEDISCBRAKEFACTORCASONEOFTHEMOSTIMPORTANTPERFORMANCEOFTHEDISCBRAKEOPERATION2EXPERIMENTALMETHODSINORDERTOBETAUGHTABOUTTHEDISCBRAKEOPERATIONIEBRAKEPERFORMANCEASAFUNCTIONOFDIFFERENTTYPESOFFRICTIONMATERIALANDBRAKE’SOPERATINGCONDITIONS,THEARTIFICIALNEURALNETWORKSHAVETOBETRAINEDWITHAPPROPRIATEDATATHEPROCESSOFMODELLINGOFADISCBRAKEOPERATIONBYMEANSOFARTIFICIALNEURALNETWORKSISNOTTRIVIALANDMANYCRITICALISSUESHAVETOBERESOLVEDTHEFOLLOWINGOPERATIONSHAVETOBECONSIDEREDISELECTIONOFADATAGENERATOR,IIDEFINITIONOFTHERANGESANDDISTRIBUTIONOFINPUTDATA,IIIDATAGENERATION,IVDATAPREPROCESSING,VSELECTIONOFTHENEURALNETWORK’SARCHITECTURES,VISELECTIONOFTHETRAININGALGORITHMS,VIITRAININGOFTHENEURALNETWORKS,VIIIVALIDATIONANDACCURACYEVALUATION,ANDIXTESTINGOFTHEARTIFICIALNEURALNETWORKSTHEPRELIMINARYSTEPINDEVELOPMENTOFTHENEURALMODELOFADISCBRAKEOPERATIONISTHEIDENTIFICATIONOFTHEMODELINPUTSANDOUTPUTSINPUT/OUTPUTIDENTIFICATIONDEPENDSONTHEMODELOBJECTIVESANDCHOICEOFTHEDATAGENERATORFORTHEPURPOSESOFTHISPAPER,THEINPUTPARAMETERSAREDEFINEDBYTHEFRICTIONMATERIALCOMPOSITION,ITSMANUFACTURINGPROCESSCONDITIONS,ANDTHEDISCBRAKEOPERATINGCONDITIONSTHEBRAKEFACTORCHASBEENTAKENASTHEOUTPUTPARAMETERANDUSEDFORREPRESENTINGTHEDISCBRAKEPERFORMANCETHEBRAKEFACTORCCORRESPONDSTOCHANGESOFTHEFRICTIONCOEFFICIENTINTHECONTACTOFFRICTIONPAIRDURINGBRAKINGC2MTHEBRAKEFACTORCISCALCULATEDFROMTHEMEASUREDVARIATIONOFTHEBRAKINGTORQUEANDAPPLICATIONPRESSUREDURINGTHEBRAKINGCYCLE,ANDKNOWNVALUESOFTHEPISTONDIAMETERANDEFFECTIVEBRAKEDISCRADIUSACCORDINGTOEXPRESSION1C4TPD2CPRE1THETYPEOFDATAGENERATORDEPENDSONTHEAPPLICATIONANDTHEAVAILABILITYINTHISCASE,THEDATAGENERATORHASBEENASINGLEENDFULLSCALEINERTIALDYNAMOMETER,DEVELOPEDATTHELABORATORYFORFRICTIONMECHANISMANDBRAKINGSYSTEMSFRIMEKSAUTOMOTIVEDEPARTMENT,FACULTYOFMECHANICALENGINEERING,UNIVERSITYOFBELGRADEOBVIOUSLY,THETESTINGMETHODOLOGYNEEDSTOBECHOSENACCORDINGTOTHERANGEANDDISTRIBUTIONOFDATATHATAREGOINGTOBECOLLECTEDTABLE1PRESENTSTHETESTINGMETHODOLOGYUSEDFORTHEOUTPUTDATAGENERATIONTHEBRAKETESTINGCONDITIONS,AFTERTHEBURNISHINGPROCEDURE,HAVEBEENCHOSENINORDERTOIDENTIFYTHEINFLUENCESOFAPPLIEDHYDRAULICPRESSUREANDINITIALEQUIVALENTOMINMINIMUMOUTPUTVALUEBRBAYESIANREGULATIONLEARNINGALGORITHMBRABCDNEURALMODELBRBAYESIANREGULATIONLEARNINGALGORITHM;ATHENUMBEROFINPUTS;BTHENUMBEROFNEURONSINTHEFIRSTHIDDENLAYER;CTHENUMBEROFNEURONSINTHESECONDHIDDENLAYER;DTHENUMBEROFOUTPUTSVEHICLESPEEDONTHEFINALCOLDPERFORMANCEOFTHEDISCBRAKEFORTHEDIFFERENTTYPESOFFRICTIONMATERIAL18THESEDATAHAVEBEENUSEDFORTRAINING,VALIDATION,ANDTESTINGOFTHENEURALNETWORKSINORDERTOESTABLISHTHEFUNCTIONALRELATIONSHIPBETWEENTHEDISCBRAKEOPERATINGCONDITIONS,THETYPEOFTHEFRICTIONMATERIAL,ANDTHEBRAKEFACTORCVARIATIONASTHEOUTPUTITISOBVIOUSTHATTHERANGESANDDISTRIBUTIONOFTHEINPUTSDATAFORTRAINING,VALIDATION,ANDTESTINGHAVETOBEPREDEFINEDTHENEURALMODELOFDISCBRAKEOPERATIONTAKESINTOCONSIDERATIONTHETABLE1TESTINGMETHODOLOGYTESTCONDITIONSAPPLIEDPRESSUREBARINITIALSPEEDKM/HTEMPERATURE1CNUMBEROFBRAKINGEVENTSINITIALBURNISHING4090O100150BRAKINGREGIMES20,40,60,80,10020,40,60,80,100O10025ARTICLEINPRESSDALEKSENDRIC,DCBARTON/TRIBOLOGYINTERNATIONAL4220091074–10801076TABLE2THESELECTIONANDRANGESOFRAWMATERIALSFORTHEFRICTIONMATERIALCOMPOSITIONSVOLRAWMATERIALSF1–F9TRAININGANDVALIDATIONDATASETFT1TESTDATASETFT2TESTDATASETPHENOLICRESIN17–252517IRONOXIDE3–553BARITES26–151526CALCIUMCARBONATE1–331BRASSCHIPS1–331A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