锂离子电池循环寿命的融合预测方法

36720157ChineseJournalofScientificInstrumentVol.36No.7Jul．20152014-12ＲeceivedDate2014-12*61301205、51317040302*12111．1500802．014010、。。。3。。TP206+．3TH165+．3A510．40Afusionpredictionmethodoflithium-ionbatterycycle-lifeLiuYuefeng12ZhaoGuangquan1PengXiyuan11．DepartmentofAutomaticTestandControlHarbinInstituteofTechnologyHarbin150080China2．SchoolofInformationEngineeringInnerMongoliaUniversityofScience＆TechnologyBaotou014010ChinaAbstractAccordingtotheproblemsoftraditionallithium-ionbatteryremainingusefullifeＲULpredictionmethodbasedonparticlefiltersuchasexcessiverelianceonbatteryexperiencedegradationmodelandthesingleinputvariableofthemodelafusionＲULestimationap-proachforlithium-ionbatteryisproposedbasedonrelevancevectormachineＲVMparticlefilterPFandtheautoregressiveAＲmod-el．ThedegradationtrendofbatteryhistoricaldataisextractedbyＲVMandthetrendequationisbuilttoreplacethebatteryexperiencedegra-dationmodelwhichisadoptedasthestatetransitionequationofthePFalgorithm．Long-termtrendpredictionvaluesoftheAＲmodelareusedtoreplacetherealvaluesandthentheobservationequationofthePFalgorithmisconstructed．ThreemethodsareintegratedtoestimatethebatteryＲUL．Experimentalresultsshowthatthepredictionprecisionoffusionmethodishighandtheproposeddatadrivenapproachismorecommonbecauseitcanavoidbuildingthecomplexexperiencedegradationmodelbasedonbatteryfailuremechanism．Keywordslithiumionbatteryrelevancevectormachineparticlefilterautoregressivemodelfusionmethod1、。。。1。、、、batterymanagementsys-temBMSBMS2-3。GPSunmannedaerialvehiclesUAVs4-5。714636。LiuD．T．78FPGAＲVMremainingusefullifeＲUL9-1011。。ＲUL。MiaoQ12PFOlivaresB．E．13PFSahaB14-16PFＲUL。ＲUL17-1819、720ＲUL。ZhouJ．B．21ＲULLiuD．T．22AＲＲPFＲULLiuD．T．23ＲUL。ＲULrel-evancevectormachineＲVM、particlefilterPFAＲＲUL。PFＲVMSahaB24HuY25ＲVMPF。ＲVMtt。tＲVMPF。ＲVMPFPFtＲUL。AＲPF。2ＲVM、PFAＲＲVMPF2。AＲ。3。2．1ＲVMＲVMTipping2001supportvectormachineSVMＲVM26。ＲVMMercer。ＲVMSVM。xiyiMi=1xiyiMＲVMyxw=∑Nn=1wnkxxn+w0ui=yxiw+εii=12…M1w=w0w1…wNNＲVkxxnεi～N0σ2uiyi。wεi。αi。wα－1ipwi|αi～Nwi|0α－1i2pw|α=∏Ni=0Nwi|0α－1i3α=α0α1．．．αNΦ。ασαnewi=γi/μ2i4σ2new=u－Φμ2N－Σiγi5Σ=σ－2ΦTΦ+A－1μ=σ－2ΣΦTuγi=1－αiΣii。αi。αiwi。ＲVM26。2．2PFPF。PF27。2。。146436。PF。51xt=fxt－1vt6zt=hxtωt7txtztxtvtωt。2pxt|xt－16。3wit=wit－1pzt|xit84。。effectivesamplesizeESSESSt=∑ni=1wit2－19nwi=1/ni=12…nESStn。ESSt。PFTESSTESS=n/2ESSt＜TESS。27。5xtpxt|z0t≈∑ni=1witδxt－xit10n10。2．3AＲ、PHMAＲ。AＲxtxt=1xt－1+2xt－2+…+pxt－p+atp≠{011Φii=12…patt=0±1…σ2a。pAＲAＲp。AＲxtAＲpp+2p、Φ1Φ2…Φpσ2a11AＲ。AＲ。ΦpppΦp。AkaikeinformationcriterionAIC12AICp=Nσ2a+2p12pNσ2ap。2．43PF6。。PF。ＲVM。ＲVMPFPF。ＲVM。ut～N∑Ni=1wnkxtxn+w0σ213ＲVMut。utPF。piti=12…nt=12…TnT。pit～N∑Ni=1wnkxtxn+w0σ214utＲVM。14-16PFＲVMPF。PFAＲ7PF。31。714651Fig．1Theschematicdiagramofthefusionframeworkforlithium-ionbatteryＲULestimation33。NASA。3．1NASANASAPCoE2A·h11．5A4．2V22A2．5V3electrochemicalimpedancespec-troscopyEIS0．1～5Hz。endoflifeEoL70%。3Battery#05、Battery#06、Battery#07Battery#18。healthindicatorHI。EoL70%。2A·h1．38A·h。1．38A·hＲUL。CALCE。1100mA·hCS2。CS2CS2_36、CS2_37、CS2_383ＲUL。31C4．2V0．05A2．7V。70%。3．2TkNCapacityCapoutkUCapacitykPFCapoutkＲULprobabilitydensityfunctionPDFTCapacityＲVMPFPFCapoutkUＲULPDF。1Capacity2TTT3TＲVMPF4TAＲ5PFNEoLU6k=173ＲVMXik84AＲZik9珓xik=πxk|xi0k－1y1k10珘wik11Neff=1ΣNi=1珘wik2Neff≥Nthresxi0k=珓xi0kwik=珘wik珘wlkKi=lxi0k=珓xKi0kwik=1/N12Capcoutk=ΣNi=1xi0kwik13k=k+17～13Capoutk14CapoutkEoLUＲULＲUL=k15ＲULPDF。1466364NASAPCoECALCEＲULAＲ14PF7ＲVM。4．1PFNASAPCoEPF。18T=40、T=60、T=80EoLU=1．38A·hN=500Ｒ=0．0001Q=0．0001。T=80ＲUL2ＲUL1。2PFＲULT=80Fig．2ＲULestimationresultswithproposedfusionprognosticalgorithmandstandardPFalgorithmT=801PFＲULTable1ＲULestimationresultswithproposedfusionprognosticalgorithmandstandardPFalgorithmEoPＲUL_predictionＲUL_errorT=40763624PF773723T=6095355PF872713T=8098182PF899111TEoPendofpredictionＲUL_predictionＲUL_error15ＲUL_error=|ＲUL_prediction－ＲUL_true|15ＲUL_true。21T=4018EoL100ＲUL_true=100－T=60。EoP76ＲUL_prediction=76－T=36ＲUL_error=|36－60|=24。PFEoP77ＲUL_prediction=77－T=37ＲUL_er-ror=|37－60|=23。T=60ＲUL_true=100－T=40。EoP95ＲUL_prediction=95－T=35ＲUL_error=|35－40|=5。PFEoP87ＲUL_prediction=87－T=27ＲUL_error=|27－40|=13。T=80ＲUL_true=100－T=20。EoP98ＲUL_prediction=98－T=18ＲUL_error=|18－20|=2。PFEoP89ＲUL_prediction=89－T=9ＲUL_error=|9－20|=11。meanabsoluteerrorMAErootmeansquareerrorＲMSE。MAEＲMSE1617MAE=1n∑ni=1|xi－珋xi|16ＲMSE=1n∑ni=1xi－珋xi槡217nxii珋xi。PFMAEＲMSE2。2PFＲULTable2ＲULestimationresultserrorwithproposedfusionprognosticalgorithmandstandardPFalgorithmMAEＲMSE1014PF16172MAEＲMSEPFPFPFPF。714674．2ＲVMCALCEＲVM。51。37EoL142×5T=60×5、T=80×5、T=100×5、T=120×5EoLU=0．79A·hN=500Ｒ=0．0001Q=0．0001。2ＲUL33。3ＲVMＲULT=100Fig．3ＲULestimationresultswithproposedfusionprognosticalgorithmandＲVMalgorithmT=1003ＲVMＲULTable3ＲULestimationresultswithproposedfusionprognosticalgorithmandＲVMalgorithmEoPＲUL_predictionＲUL_errorT=6087×527×555×5ＲVM80×520×562×5T=80117×537×525×5ＲVM104×524×538×5T=100145×545×53×5ＲVM151×551×59×5T=120147×527×55×5ＲVM130×510×512×5ＲVMMAEＲMSE4。4ＲVMＲULTable4ＲULestimationresultserrorwithproposedfusionprognosticalgorithmandＲVMalgorithmMAEＲMSE10×514×5ＲVM16×517×533ＲVMＲVMＲVM。4MAEＲMSEＲVM。5ＲVM、PFAＲＲVMPFPFAＲPFPFＲVM。PF。ＲVMPF。1．J．20153611-16．L