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30520169JOUＲNALOFUNIVEＲSITYOFJINANSci．＆Tech.Vol．30No．5Sep．20161671－3559201605－0347－06DOI10．13349/j．cnki．jdxbn．20160606．009121121．1026002．100044PHMPHM、3。PHM45．730．9。TP206TH115AＲesiduallifepredictionofrollingbearingsonrailvehiclesbasedonproportionalhazardmodelZHANGYuan1QINYong2DUYanping1GAOZhenqing1WEIXiukun21．SchoolofMechanicalEngineeringBeijingInstituteofGraphicCommunicationBeijing102600China2．StateKeyLaboratoryofＲailTrafficControlandSafetyBeijingJiaotongUniversityBeijing100044ChinaAbstractForaccuratelypredictingtheresiduallifeofrollingbearingsofrailvehicleswithcomprehensiveutilizationofmonitoringdataandreliabilitydatatheresiduallifepredictionmethodwasproposedbasedonproportionalhazardmodelPHM．Threespecificstepsoftheproposedlifepredictionmethodweredescribedindetailincludingsampledatacollectionparameterestimationandlifepre-diction．Theexperimentwascarriedoutbyusingofvibrationdataandfailureeventdataofrollingbearings’fulllifecycle．Theexperi-mentalresultsshowthattherootmeansquareerrorofPHMoutputsis45．73andthecorrelationcoefficientbetweenPHMoutputsandtargetsisgreaterthan0．9whichverifiestheeffectivenessandfeasibilityoftheproposedresiduallifepredictionapproachbasedonPHM．Keywordsrollingbearingsofrailvehiclesremaininglifepredictionproportionalhazardmodel1。10%～20%23。、2016－03－262016－06－061204ＲCS2016K0050608091500127170115005/001。1985—。1978—。http//．cnki．net/kcms/detail/37．1378．N．20160606．1204．018．html、、。。proportionalhazardmodelPHMCox4。PHM5。PHM36－10PHM11－12。PHM。1。、、。。、、。1。、、、4。。。。。1—2—3—4—5—6—。12PHM2．1PHMλtX=λ0t·gX=λ0t·eXβ1λtXtXλ0ttgXXXt=x1tx2t…xmttmβ=β1β2…βmT。X。Xλtλ0t。Weibull、。Weibull13Weibullλ0tWeibull。λ0t=γη·t()μγ－12γWeibullγ＞0ηWeibullη＞0。2843301λtX=γη·t()μγ[]－1·expXβ33PHM。2．2PHMPHM3、14。2．2．13γ、η、β3。1。2。3δδ=0δ=1。Di=tiXiδii=12…N4DiitiiXiiiδiiN。2．2．2。NlγηβD12…N=ΠNi=1λitiXiδi·ＲitiXi5λitiXi=γη·ti()μγ－[]1·expXiβ6ＲitiXi=exp－∫ti0λivXivd{}v7λitiXii6ＲitiXii7。5lnlγηβD12…N=∑Ni=1δilnλitiXi－∑Ni=1∫ti0λivXivdv。868lnlγηβD12…N=∑Ni=1δilnγ+γ+1lnti－γlnη+Xiβ－∑Ni=1∫ti0γ·vγ－1ηγ·expXiβdv9N93)γ、)η、)β。9、、Netwon－Ｒaphson。。2．2．3)γ、)ηtXttλtXt=)γ·t)γ－1)η)()γ·expXt)β。10tＲtXt=exp－∫t0λvXvdv=exp－∫t0)γ·v)γ－1)()η·expXt)βd{}v。1111tLＲLＲtXt=ET－tT＞t=∫+∞0ＲtXtdt=∫+∞0exp－∫t+τtλvXvd{}vdτ=∫+∞0exp－∫t+τt)γ·t)γ－1)η)()γ·expXt)βd{}vdτ。12t't'Xt'12。943533．1PHMcenterforintelligentmaintenancesystemsIMS152。2ＲexnordZA－21152000r/min。PCB353B33。NI6062E20kHz。10min110s。360h215621010s。162PHM。32T2SPE。3aT2250h250～300haT2bSPE3300h。3bSPE200h200h。2PHM。3．2PHMPHM6216。MatlabOptimizationToolbox1200、、、、20。4PHM。1000PHM12。13β112。3．33250533041PHMγηβ11β1214．01211．05－9．54－5．95PHM6PHM。5PHM6PHM5PHM。PHM。PHMEＲMS=45．73。7PHM。Ｒ=0．94380．81PHM。7PHM4PHM。PHM45．73PHM0．9438PHM。、PHM。1BＲUNISGOODALLＲMEITXetal．ControlandmonitoringforrailwayvehicledynamicsJ．VehicleSystemDynamicsInterna-tionalJournalofVehicleMechanicsandMobility2007457/81535743－779．2．IMFJ．．2008283229－232．3．J．20133266－12．4COXDＲ．Ｒegressionmodelsandlife-tableswithdiscussionJ．JournalofＲoyalStatisticalSocietySeriesBMethodologi-cal1972342187－220．5ZHOUQSONJZHOUSetal．ＲemainingusefullifepredictionofindividualunitssubjecttohardfailureJ．IIETransactions201446101017－1030．6．PHMJ．201111369113－9115．7．J．2011303124－128．8．J．2010102132－2135．9．J．201234112－117．10．J．2006214716－721．11JAＲDINEAKSLINDBANJEVICD．Areviewonmachinerydiagnosticsandprognosticsimplementingcondition-basedmainte-nanceJ．MechanicalSystemsandSignalProcessing20062071483－1510．12LIAOHZHAOWGUOH．Predictingremainingusefullifeofanindividualunitusingproportionalhazardsmodelandlogisticre-gressionmodelC//AnnualＲeliabilityandMaintainabilitySym-posium2006．s．l．IEEE2006127－132．13．J．2013443963－969．14．D．2012．15QIUHLEEJLINJ．Waveletfilter-basedweaksignaturedetec-tionmethodanditsapplicationonrollerbearingprognosticsJ．JournalofSoundandVibration20062891066－1090．16ZHANGYQINYXINGZYetal．ＲollerbearingsafetyregionestimationandstateidentificationbasedonLMD－PCA－LSSVMJ．Measurement20134631315－1324．25330