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1、ApplicationofBayesianInferencetoMillingForceModelingJaydeepM.Karandikar,TonyL.SchmitzandAliE.AbbasAbstractThispaperdescribestheapplicationofBayesianinferencetotheidentificationofforcecoefficientsinmilling.Mechanisticcuttingforcecoefficientshavebeentraditionallydetermi

2、nedbyperformingalinearregressiontothemeanforcevaluesmeasuredoverarangeoffeedpertoothvalues.Thislinearregressionmethod,however,yieldsadeterministicresultforeachcoefficientandrequirestestingatseveralfeedpertoothvaluestoobtainahighlevelofconfidenceintheregressionanalysis

3、.Bayesianinference,ontheotherhand,providesasystematicandformalwayofupdatingbeliefswhennewinformationisavailablewhileincorporatinguncertainty.Inthiswork,meanforcedataisusedtoupdatethepriorprobabilitydistributions(initialbeliefs)offorcecoefficientsusingtheMetropolis-Has

4、tings(MH)algorithmMarkovchainMonteCarlo(MCMC)approach.Experimentsareperformedatdifferentradialdepthsofcuttodeterminethecorrespondingforcecoefficientsusingbothmethodsandtheresultsarecompared.IntroductionInmetalcuttingoperations,thecuttingforcecanbemodeledusingthechipar

5、eaandempiricalconstantsthatdependonthetool-workpiececombination.Themechanisticcuttingforcecoefficientsaredeterminedusingalinearregressiontothemeanforcevaluesmeasuredoverarangeoffeedpertoothvalues[1].However,theleastsquaresmethodhastwolimitations.First,themethodrequire

6、dtestingatseveralfeedpertoothvaluestoachieveahighlevelofconfidenceintheregression.Second,formicromillingapplicationsormachiningparameters(radialandaxialdepth)resultinginameanforcevalueclosetozero,thesignaltonoiseratioisverysmallwhichcanresultinapoorleastsquaresfit.Toa

7、ddresstheselimitations,thepaperdemonstratesmillingforcemodelingusingtheMCMCmethodforBayesianinference.TheadvantageofusingBayesianinferenceisthatexperimentsovermultiplefeedpertoothvalues,whichcanbetimeconsumingandcostly,arenotnecessaryfordeterminingthecuttingforcecoeff

8、icientvalues.Inaddition,theuncertaintyintheforcecoefficientscanbeevaluatedbycombiningpriorknowledgeandexperimentaldata.Thema