A Method of Remaining Capacity Estimation for LithiumIon Battery鋰離子電池剩余壽

HindawiPublishingCorporationAdvancesinMechanicalEngineeringVolume2013,ArticleID154831,7pageshttp://dx.doi.org/10.1155/2013/154831

ResearchArticle

AMethodofRemainingCapacityEstimationforLithium-IonBattery

JunfuLi,LixinWang,ChaoLyu,WeilinLuo,KehuaMa,andLiqiangZhang

SchoolofElectricalEngineeringandAutomation,HarbinInstituteofTechnology,Harbin150001,ChinaCorrespondenceshouldbeaddressedtoLixinWang;wlx@hit.edu.cn

Received8September2013;Revised22October2013;Accepted22October2013AcademicEditor:XiaosongHu

Copyright?2013JunfuLietal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.

Combiningparticlefilter(PF)withsampleentropyfeatureofdischargevoltage,amethodofremainingcapacityestimationforlithium-ionbatteryisproposed.Thesampleentropycalculatedfromdischargevoltagecurvecanserveasanindicatorforassessingtheconditionofbattery.Underacertainworkingcondition,afunctionalrelationshipbetweensampleentropyanddischargecapacityiscreatedandestimationscomputedfromthefunctionaretakenasobservationstopropagateparticlesinPF.Theresultsindicatethatthealgorithmenhancestheaccuracy.Duetotheestablishmentoffunctionsatdifferentdischargeratesandtemperaturemodification,prognosticaccuracyofdischargecapacityhasbeenimprovedundermulti-operatingworkingconditions.

1.Introduction

Withtherapiddevelopmentofindustrialtechnology,theexplorationandutilizationofnewenergyhavebeeninurgentneed.Electricvehicleoccupiesapivotalpositioninnewenergyautomobile.Batterymanagementsystem(BMS)isspeciallydesignedtoimproveefficientutilization,topreventoverchargeoroverdischarge,toprolongtheservicelife,andtomonitorthestateofthebattery.Amoresophisticatedprognosticofbatteryhealthstateismuchneededforhighrequirementsofreliability,stability,andsecurityofbatteries.Consequently,thepredictionofremainingbatterylifeisconsideredasoneofthepromisingresearchfields.Numerouspapershavereportedthestudiesonstateofcharge(SOC)andstateofhealth(SOH)whicharethefocusofbatteryPrognosticandHealthManagement(PHM).

Batterydischargecapacityreachingitscriteriawithoutanyomenleadstoadisastrousfailureinsomecases.Theaccuratepredictionofremainingusefullife(RUL)ofbatteryisessentialforlong-timeefficientuse.ThecausesofcapacityfadingareinternalfactorssuchasanodicandcathodicactivematerialchangesandSEImembraneincrassation[1,2].AccuratebatterySOCestimationisofgreatsigni-ficancetobatteryelectricvehiclesandhybridelectricvehi-cles.SOCestimationaimsatthemanagementofenergyflowsofelectricvehiclesandavoidingbatteryoverchargeor

undercharge.Leeetal.[3]proposedanExtendedKalmanFilter(EKF)methodalongwithameasurementnoisemodelanddatarejectionoflithium-ionbatterySOCestimation.Theproposedalgorithmandmodelapproachwereverifiedthroughseveralexperiments.AnadaptiveunscentedKalmanfilteringmethodtoestimateSOCoflithium-ionbatterywaspresented[4].TheproposedSOCestimationmethodhadabetteraccuracycomparedwithpreviousworks.Leeetal.[5]estimatedtheSOCandthecapacityofalithium-ionbatterywithamodifiedOCV-SOCmodel.ThemethodovercamethevariationinconventionalOCV-SOC.

Methodsofbatterycapacityestimationareproposedbasedonthefollowingtwoideas.Onemethodisfeature-based.Inonesense,asvariationsofvoltage,current,andtem-peraturecharacteristiccurvescouldreflectthebatteryagingprocessesorinternalresistancevariations,somecharactersareoftenextractedfromthem.Salkindetal.[6]proposedapracticalmethodthatresistancesobtainedbyelectrochemicalimpedancespectroscopy(EIS)measurementandcoulombcountingtechniqueswereemployedinpredictingSOCandSOH.Theadvantageoftheworkwasthattherewasnoneedtoknowpreviousdischargeorcyclinghistory.Gomezetal.[7]madeadetailedanalysisonEISandpointedoutthataginginformationcouldbeextractedfromtheparametersofEISequivalentcircuitmodel.Pincus[8]firstlyintroducedtheconceptofapproximateentropymainlytocomputethe

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complexityoftimeseries.Widodoetal.[9]tooksampleentropyfeaturesobtainedfromdischargevoltagecurvesasinputsofsupportvectormachine(SVM)andrelevancevectormachine(RVM)forSOHprediction.Theresultsshowedthatthemethodproposedwasplausible.

Theotherismodel-based.Generally,faultfeatureiscloselyrelatedtotheparametersofthemodel.Correctionandadjustmentofmodelparameterscanenhancethepre-dictionaccuracy.Themodel-basedtechniquescontributetoanin-depthunderstandingofthemechanismandhavetheadvantageofreal-timefaultprediction.Amodelofbatterysystemstateisestablishedtodescribethedischargebehaviororbatteryhealthstate.Abbasetal.[10]introducedanintegratedmethodologybasedonbothphysicsoffailuremodelsandBayesianestimationmethodsforprognosisofelectricalcomponents.Anempiricalformulawasproposedtodepictdischargingbehavioroflithium-ionbatteries[11–13].SimulationresultsindicatedthatPFalgorithmwasappropriateforthepredictionofbatteryhealthstate.Sahaetal.[14]presentedseveralalgorithmsincludingARIMA,RVM,EKF,andPF.ARVM-PFframeworkhadsignificantadvantagesovertheconventionalmethodsofRULestimationlikeARIMAandEKF.

Someresearchershavealsoestablishedelectrochemicalnumericalmodelandthermalmodelforthestudyonbatteryinternalcharacteristics.PorouselectrodemodelwithliquidelectrolytewasproposedbyWestetal.[15].Thatelectrolytedepletionwastheprimarylimitingfactorofcapacitywasdemonstrated.Parketal.[16]presentedanelectrochemicalheatconductionphenomenalmodel.Abetterunderstandingofconductionphenomenaoflithium-ionbatterieswaspre-sented.Kimetal.[17]extendedone-dimensionalmodelingapproachtothreedimensionstocapturegeometricalfeaturessuchasshapesanddimensionsofcellcomponents,tosimulateoventestsandtodeterminehowalocalhotspotcanpropagatethroughthecell.Thoughsomekeybehaviorsofbatterycellscanbecapturedinthesemodels,itiscomplextodeployalargenumberofunknownparametersduetothememoryandcomputation.Lumpedbatterymodelsarelikelytobethepreferredchoicewitharelativelyfewerparameters.Asystematiccomparativestudyoftwelvelumpedbatterymodelswasconducted[18].ThedevelopedcellvoltagemodelscouldbeusedinSOCestimationinBMS.

Thisworkisconductedbythecombinationofthetwoideasmentionedabove.Inthefollowingsection,wefirstlyintroducethetheoryaboutsampleentropyandbasicuti-lizationofparticlefilterintermsofprognosticsoflithium-ionbatteryRUL.Then,wepresentthedetailedpredictionprocedure.

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sampleentropyisasfollows.Foragivenseries{????},weform?????+1vectorsas

??(??)=[??(??),??(??+1),...,??(??+???1)],

for??=1to?????+1.

(1)

Thedistancebetweenvectors??(??)and??(??)isdefinedas

??????,??[??(??),??(??)]=max??????????(??+??)???(??+??)??

for??,??=1to?????+1,

??=0to???1.

Foragiven??,calculatethenumberwhen??[??(??),??(??)]<

??,for??=??,anddefinethefunction

??????(??)=

1

num{??[??(??),??(??)]<??}.(3)(2)

Then,taketheaverageof??????(??).Theresultisexpressedas

?????+1

1

??(??)=∑??????(??).

??=1??

(4)

Similarly,replace??with??+1andrepeatthestepsfromthebeginning.Afterwards,wecandeterminethetwovalues????(??)and????+1(??).Asthesamplelengthisalwayslimited,thesampleentropyisestimatedby

????+1(??)

].SampEn(??,??,??)=?ln[(5)

ThevalueofSampEn(??,??,??)iscloselycorrelatedwith??,??,and??.Thus,theproperselectedparameterscouldresultinmorereasonablestatisticalproperties.

2.2.ParticleFilter.PFisaBayesianlearningtechniqueusingMonteCarlosimulations.Theideaistodescribethesystemstateasaprobabilitydensityfunction(PDF)approximatedbyparticlesthataregeneratedfromaprioridistributionandupdatedfromobservationsthroughameasurementmodel.Modelparametersareincludedasapartofthestatevectortobetracked[11].PFframeworkcanbeappliedtoRULpredictionofbatteryduetoitsgoodstatetrackingperformance.

Actualdischargecapacityisassociatedwithmanyfactors.Itisobviousthatchargingdirectlydeterminesthedischargecapacityinonecycle.Besides,reactionproductsforminguparoundtheelectrodeswilldecomposeduringrestorrelaxationperiod,whichleadtotheincreaseofavailablecapacityinnextcycle.Primarily,consideringthemaininflu-encefactorsofbatterycapacity,thefollowingstateequationsarecasttodescribethemodelasfollows:

????+1=??1????+??2exp(????(??+1)=????(??)+V??(??),

??3

),??

??=1,2,3,

(6)(7)

2.TheoryandIntelligentPrognosticMethod

2.1.SampleEntropy.SampleentropyisdefinedasgenerationrateofnewinformationbyRichmanandMoorman[19]forthecalculationofcomplexityoftimeseries.ItcanbeexpressedasSampEn(??,??,??),where??isagiventotalnumberofdata,??isthetoleranceforacceptingmatrices,and??isthedimensionofvectors.Thespecificalgorithmof

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where??iscycleindex,????denotesthechargecapacity,Δ????istherelaxationperiodbetweenthetwoadjacentcycles,????+1isthedischargecapacity,??1,??2,and??3areparametersofthestateequation,andV1,V2,andV3areindependentzero-meanGaussiannoiseterms.

SahaandGoebel[11]establishedameasurementmodelandregardedchargingcapacityastheobservationtoprop-agateparticles.Areasonableobservationformeasuringtheweightsofparticlesandselectivelypropagatingthemplaysanimportantroleinpredictionaccuracy.Inthecaseofourapplication,viathefittingmethod,afunctionalrelationshipofsampleentropyanddischargecapacityisestablishedtoobtainanappropriateobservation.Particularly,sampleentropyiscalculatedfromthedischargevoltagecurveofthecyclenumber??.Thecorrespondingoutputofthefunctionisusedastheobservationincycle??+1.Itisworthmentioningthatthereisnoneedtotakeotherexperimentstoobtainsuchfeatures,forthedischargevoltagecurvescanbeeasilyobtainedduringthemonitoringineachcycle.

2.3.IntelligentPrognosticMethod.Theprocedurecomprisesthefollowing.

(1)Datacollectionisasfollows.

(a)Extractbatterydischargevoltagecurvesfromtrainingdataandtheselectedparameters??and??are2and0.1,respectively.Thefunctionalrelationshipofdischargecapacityandsampleentropyiscreatedunderthecurrentoperatingcondition.

(b)Gaindischargecurrentcurves,chargingcapac-ity,andrelaxationtimeofadjacentdischargecyclesfromvalidationtestdata.Inaddition,somehistoricalcapacitydataarealsoneeded.(2)Particlefilterinitializationisasfollows.

(a)Setthestartingpredictionpoint??inproportiontothenumberofhistoricalcapacitydata.

(b)Obtaininitialparameters????(??=1,2,3)viafitting.

(c)500initialparticlesaregeneratedwithvaluesobtainedin(2)-(b)andthevariancesofnoisetermV??(??=1,2,3)areabout10,000timessmallerthan??.(3)Predictionisasfollows.

????

(a)Particles{????}??=1areupdatedby(7)andtheprioridischargecapacityvaluesincycle??+1arecalculatedthroughthoseupdatedparticles??

}??{????+1??=1.

(b)Takesampleentropyfeatureastheinputofthefunctionandcomputetheweightofeachparti-cleperdeviationbetweenthecalculatedobser-vationandpreviousdischargevoltagevalue.

3

Normalizetheveryparticlesusingthefollowingformula:

??????+1

??(????+1)

=

??

????+1(????+1)

∑??=1

??????+1(????+1)

.(8)

(c)Throughthemethodofrandomsampling,each

??

particle{????+1}????=1iscopiedorabandonedselec-tivelyaccordingtoitsweightandthennew

??

}??sample{?????+1??=1isobtained.

??

(d)Theaverageofthesample{?????+1}????=1represents

theprobabilitydensitydistributionexpectationofeachparameterin(6).Then,thefinalestima-tion????+1canbeeasilyfiguredupby(6).

(e)Repeatthestepfrom(3)-(a)to(3)-(d)untilthecapacityreachesitscriterionwhichisa30%fadingofratedcapacity.

3.ExperimentData

Thefullsetofagingdatacollectedfromcommerciallyavailable18650-sizelithium-ioncellsprovidedbyNASAAmesPrognosticsCenterofExcellencewastakenasobjectofstudy.BatteryanodeandcathodematerialsaremostlyLiNi0.8Co0.15Al0.05O2andMAG-10graphite,respectively.Theelectrolyteis1.2MLiPF6inEC:EMC(3:7wt%)andtheseparatoris25??mthickPE.

Alltestingbatterieswererunthroughdifferentworkingprofiles(charge,discharge,andimpedance).BatteriesNo.6andNo.18weretestedbythefollowingsteps:(1)chargingwascarriedoutinaconstantcurrentmodeat1.5Auntilthebatteryvoltagereached4.2V,(2)aconstantvoltagemodewastheninoperationuntilthechargecurrentdroppedto20mA,(3)batterieswereputasideforaperiodoftime,(4)impedancemeasurementwasimplementedwithanelectrochemicalimpedancespectroscopyfrequencysweepfrom0.1Hzto5kHz,(5)at24°C,dischargingwascarriedoutataconstantcurrentlevelof2Auntilthebatteryvoltagefellto2.5V,(6)thesamestepas(3),and(7)thesamestepas(4).Repeatedcharginganddischargingresultedinanacceleratedagingprocess.Theexperimentswerestoppedwhenthebatteriesreachedtheend-of-lifecriteriawhichwasa30%fadinginratedcapacity(from2Ahrto1.4Ahr).

4.ResultsandDiscussion

4.1.SingleWorkingCondition.Figure1depictsthedischargevoltagecurvesindifferentcycles.Ataconstantcurrentof2A,thevoltagedropsfrom4.2Vto2.6V.Obviously,thecurvesvaryfromcycletocycleintheagingprocesses.ItcanbeseenfromFigure1thatthelowestvoltagepointbouncesbackinstantlyattheendofdischargeandsubsequentlyrisesslowlyuntilitcomestoastop.Thetwoarrowspointouttheprocessesmentionedabove.Observingthedefinitionofsampleentropy,wecanfindthatwhenthemaximumdistancecomputedfromtheadjacentvectorsconstitutedbythesequentialsamplesisgreaterthan??,thecomplexitynumberofthecorrespondingvectorin(3)willnotchange

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4.2

Voltage (V)

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instatisticalcalculations.Otherwise,ifthenoisesignalisaddedtothesampleswithlargeramplitude,itwillbeignoredbydetection,forthedistancebetweenthedisturbedvectorsislongerthanothers.Inthatsense,sampleentropycouldcapturethefeaturesofvoltagevarianceinaconstantcurrentmode.

Asbatteryisaginggraduallyduringtheusageperiod,wefindaninterestingconnectionbetweenthesampleentropyfeatureandthedischargecapacity.Inconsequence,sampleentropycouldserveasanindicatorforassessingtheconditionofbattery.WithtrainingdataofbatteryNo.18,acubicpolynomialfittingisintroducedtofindoutthefunctionalrelationshipbetweenthem.Whentheparameter??and??aredeployedto2and0.1,respectively,abetterfittingeffectisobtainedwithareasonablestatisticalresult.

Thestartingpoint??andpredictinglengthare25and115.Figures2and3showthepredictionresultofbatteryNo.6anditserrors.Fromtheactualdischargecapacitycurve,itisevidentthatbatteryNo.6hasfadedtoitslimit1.405Ahrwhenitcyclesatcyclenumber108.ObservingFigure3,apartfromseveralpoints,mostrelativeerrorsarewithin5%.Theearlypredictionhashigherprecisionanderrorsofsomereboundpointsarelessthan2%.

ToillustratethesuperiorityofthisworkcomparedwithSahaandGoebel[11],Figure4showsthecomparativepre-dictionresult.

AsisshowedinFigure4,somekeypointsofpredictionarepointedoutbysevenarrowsonthegraphandthecontrastivepredictionapparentlyengendersagreatererror.Predictionaccuracyismeasuredbytheroot-mean-squared(RMS)errorandpeakerror.ThestatisticalfiguresrevealthatRMSerrorsofbothpredictionsare8.64%and4.30%,respectively,andthepeakerrorsare37.86%and8.28%.

Thedischargecapacityisnotonlydirectlyrelatedtochargecapacityandresttimeofadjacentcyclesbutisalsoaffectedbyactualworkingconditions.Whentheforecastingandtrainingconditions,suchthatambienttemperatureanddischargerateareinconsistent,itcanbeeasilyexpectedthattheestimationpointswilldeviatefromtheactualonesineachcycle.

4.2.MultioperatingWorkingCondition.Withoutknowingofagingmechanism,itishardtomakeaspecificillustrationthathowtheagingprocessinsidethebatteryisinfluencedbyenvironmentalfactors.But,itiscertainthatasbatteryagingprocesses,differentoperationalconditionsaccountsforthedischargecapacityfadingbehaviors.Itisrequiredtoupdateorrevisetheaforementionedfunctionproperlytosatisfytherequirementofhighaccuracywhenfacingamultioperatingworkingcondition.ThedatasetsprovidedbyNASAonlyincludeseveraldischargerates.Thus,thepaperbuildsthreefunctionstakingdifferent??-ratesundereachambienttemperatureintoaccountsummarizedinTable1,where??issampleentropyand??istheestimationcapacityusedasobservationinalgorithmPFinourmethod.

Supposethattheoperatingambienttemperatureis24°C.Itisinterestingtofindthattherelativemeandeviationsbetweenestimationvaluesanddischargecapacitiesatactual

3.83.432.6Time

First cycleSecond cycleThird cycleFourth cycle

Figure1:Batteryvoltagecurvesindifferentcyclesandthetwovoltagevariationprocesseswerepointedoutbythe

arrows.

2.1

Capacity (Ahr)

1.91.71.51.3Cycle (—)

Actual discharge capacity

Estimated value with observationobtained from sample entropy

Figure2:PredictionofbatteryNo.6.

0.08

Error (%)

0.060.040.02020

40

60

80Cycle (—)

100

120

140

Figure3:Relative

errors.

2.1

Capacity (Ahr)

1.91.71.51.3

1.1

Cycle (—)

Actual discharge capacity

Estimated value with observationobtained from sample entropyEstimated value with observationobtained from charging capacity

Figure4:Comparativesimulationresultsthroughdifferentmeth-ods.

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Table1:Capacityestimationfunctionsunderdifferentoptionalconditions.

Dischargerate0.5C1C2C

0.20.10?0.1?0.2?0.3?0.4?0.5

5

Ambienttemperature

4C24°C24°CCapacityestimationfunction

??=(9.6169???0.4326??+0.0035??+0.0001)×10??=(?1.1240??3+0.0154??2?0.0166??+0.0018)×103??=(?7.2590??3+0.3225??2?0.0044??+0.00003)×105

Table2:RMSerrorsandpeakerrorsofbatteryNo.55.Startingpoint??10152025

RMSerror(%)

3.262.642.302.24

Peakerror(%)

13.227.076.755.63

Offset (Ahr)

0510

15202530Temperature (deg)

354045

Figure5:Offsetsatdifferenttemperature.

1.41.31.21.110.90.80.7

Table3:RMSerrorsandpeakerrorsofbatteryNo.31.Startingpoint??101215

RMSerror(%)

2.171.641.37

Peakerror(%)

5.274.223.12

Capacity (Ahr)

0102030

4050Cycle (—)

607080

ActualEstimated

Figure6:PredictionofbatteryNo.55.

1.821.781.741.71.66

5

10

15

2025Cycle (—)

30

35

40

ActualEstimated

Figure7:PredictionofbatteryNo.31.

1.61.2

0.8

0.400

5

10

15

2025Cycle (—)

303540

ActualEstimated

Figure8:PredictionofbatteryNo.39.

temperature4°Cand43°Carearound?0.38and0.02.Asamatteroffact,higherorlowertemperatureaffectstheactualdischargecapacity.Onaccountofthehigherambi-enttemperature,theinternalsubstancesaremoreactiveresultinginalargerdischargecapacity.Onthecontrary,thelowertemperaturesslowdownthephysicochemicalreactionsinsidethebatteryleadingtothefactthattheactualcapacitycannotreachthemaximum.Inaconstantdischargecurrentmode,itisreasonableandessentialtomodifythecapacityobservationsinPFalgorithm.Thus,accordingtothepreviouscalculations,afunctionalrelationshipbetweenambienttemperaturesandestimationoffsetsisestablishedthroughquadraticcurvefitting.ThefittingresultisgiveninFigure5.

Theselectedoffsetbenchmarkiszeroat24°C.Figures6and7showthepredictionresultsofbatteryNo.55(4°C,1??)andNo.31(43°C,2??).Bothtwooffsetsareseparately?0.38and0.02.Asisexpected,thepredictioncurvesarebasicallyconsistentwiththeactualones.

Tables2and3showtheRMSerrorsandpeakerrorsatdifferentpredictionstartingpoints.Theresultsindicatethatasthenumberofhistoricalcapacitydataisincreasing,errorshavethedownwardtrends.

BatteryNo.39istestedunderamultioperatingworkingcondition.Thefirstseveraldischargecyclesaretestedat24°C,2??andtheothersat44°C,0.5??.Thecorrespondingcapacityestimationfunctionshouldbeselectedinaccordancewiththeoperatingcondition.Asoneoftherelevantfunctionsisbuiltat4°C,0.5??,theactualoffsetat44°Cshouldbeincreasedto0.398ratherthan0.018inFigure5.ThepredictionresultofbatteryNo.39ispresentedinFigure8andtheRMSerroris5.78%.

Figure9showsthecontrastivepredictionresult.Withouttheconsiderationof??-rateandambienttemperature,theestimationperformsmuchworsewith27.56%RMSerror.

Capacity (Ahr)

Capacity (Ahr)

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A Method of Remaining Capacity Estimation for LithiumIon Battery鋰離子電池剩余壽命估計方法.doc下載

6

1.61.2

0.8

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Capacity (Ahr)

Acknowledgments

ThisresearchisfinanciallysupportedbytheNationalNat-uralScienceFoundationofChina(no.51107021)andtheFundamentalResearchFundsfortheCentralUniversities(Grantno.HIT.NSRIF.2014021).WesincerelyappreciatethesignificanthelpontranslationbyMiss.HanWang.

0.400

5

10

15

2025Cycle (—)

303540

ActualEstimated

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Figure9:Comparativeprediction.

Alargeamountofdischargedatasetswillberequiredmainlyforestablishmentofasetofcapacityestimationfunctions.Thechoiceofaproperfunctioninaccordancewiththeworkingconditionisnecessaryfortheimplementofalgorithm.Otherwise,ittakesaboutaperiodof200msproportionaltothenumberofestimationpointstocompletepredictionforeachcycle.

5.Conclusions

Thispaperfocusesondevelopinganintelligentpredictionmethodofbatterycapacitythroughparticlefilterandsampleentropy.Underacertainoptionalcondition,afunctionalrelationshipofsampleentropyanddischargecapacityiscre-ated.TheestimationscomputedfromthefunctionaretakenasobservationstopropagateparticlesinPF.Whenfacingamultioperatingworkingcondition,thispaperbuildsthreefunctionsconsideringdifferent??-ratesunderdifferentambi-enttemperatures.Itisakeypointtoselectacorrespondingcapacityestimationfunctionandtomodifytheobservationbytemperature.Onaccountofgoodtrackingcapabilities,PFalgorithmisappliedtodeterminetheunknownparametersandfulfillthepredictionwithbetterstatisticalcalculations.Thepredictionresultcanreflectthecapacityfadingbehaviorsandhasahigheraccuracywithnotmorethan5%RMSerrorofbatteryNo.6.Comparedwithothermethods,prognosticaccuracyhasbeengreatlyimprovedunderalargerangeofcyclingconditionswithlessthan6%RMSerror.

Inaddition,thoughthepredictionresultshavebeensatisfactory,therestillleavesconsiderableroomforimprove-ments.Ourmethodisnotfitforpracticalapplicationnow,fortheambienttemperatureand??-ratesareconstantsinonecycleinourwork.Whenfacingadynamiccycle,suchasacomplexcurrent,itsimpactoncapacitycouldbeequivalentlyseenasaconstantone,whichseemstobeaconsiderablesolution.Withanimprovingunderstandingoftheseimpactsonbatterycapacity,theprognosticperformancecanbefurtherrefined.

ConflictofInterests

Theauthorsdeclarethatthereisnoconflictofinterestsregardingthepublicationofthispaper.

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