外文翻译-基于油液分析的机械磨损状态识别模式

AnIdentificationModelofHealthStatesofMachineWearBasedonOiLAnalysisFUjun-qing,lihan-xiong,suanxin-hua1.SchoolofAutomobile&MechanicalEngineringChangshaUnivcrsityofSciene&TechnologyChangsha410076,P.R.China2AbstractThispaperpresentsisamodelingprocedureforderivingasing1evaluemeasurebasedonaresgressionandamethodfordeterminingastatisticalthrehoIdvalueasidentificationcriterionofnomalorabnomalstatesofmachinewearArea1。numerica1exampleisexamfinedbythemethodandidentificationcriterionpresented.TheresultindicatethatthejudgmentsbythepresentedmethodsareBasicallyconsistentwiththerea1facts,andthereforethemethodandidentificationcriterionarecaluableforjudgingtheno;malstateofmachinewearbasedonoilanalysis.Keywords:oilanalysisrcgrcssionmodel,singlevalue,measure,andthresholdvalueIntroductionOilanalysishasbeenusedworldwideasamethodforreducingmaintenancecost,improvingrcliabilityandproductivityinvariousindustries1.Currently,mostoilanalyzersusethemethodsofatomicemfissionspectrometryopticalorelectronicmicroscopyandferrogmph\yetctoconducttheoilanalysis.Theaimofoilanalysisistoevaluatetheconditionofthelubricationortheequipmentfromthe1ubricantoilsamplceofamachine.,andrecommendmaintenanceactionstotheequipmentopemtingactivity.Withoutdisassemblingthemachinetheoilsamplesofamachinecanbeacquiredaccordingtocertaregulations,andthroughanalysisoftheoilsampletheoilandmachineconditioncanbeevaluatedOriginalequipmentmanufacturers(OEM),lubricantsuppliersandoilanalysislabomtoriesprovidespecificguidelinesforvicarmetalconcentrationsintheoil.Theselimitsprovidegoodgencralguide1inesforinterpretingoilanalysisdata.Buttherearemanyelementsinoilanalysisdate,itisverydifficulttodirectlyjudgethewearstateaccordingtotheoilanalysisdata.Forengineeringapplication,asinglevalueindexormeasureisneededforidentifyingthestatesofthemonitoredoilsamplesV.Macianetal(8)derived。generalexpressionoftherateofvicarfromengineoilanalysisdateanddefinedtheenginewearrate(Zer)asanindexZ.Theindexvalue(Z)wasusedtoevaluatethewearrateofanenginebeingnormalorabnormalbyreferencetoanormalwearrate(EMwr).Infactindexandreferenceindexshouldberandomvariablesofoilsamplesandnotexactvalues,thereforeastatisticalmodeloftheindexesisneededChunhuaZhaoetaldevelopedamodelbymeansofastepwisepluralisticregressionwhichdeletessomeinsignificantelementsorlinearlyrelateelementsinoilanalysisoriginaldate,andtransferstheoilanalysisdataintoasinglevalue.Thesinglevaluewasusedasajudgmentofthewearstate,buttherewasnothresholdorcriticalvalueusedasanidentificationcriterion..Thusforthevaluesofthesamplesfarfromthenormalstatevalue1orabnormalstatevalue2,itwasnotclearwhethertheybelongedtothenormalorabnormalstate.ThispaperfirstimprovesthemodelingprocedureinReference(9).fordorivingasinglevaluemeasure，basedonaregressionmodeandthenpresentsamethodtodetermineastatisticalthresholdvalueasanidentificationcriterionofanormalorabnormalstate,Arealnumericalexampleisexaminedbythemethodandanidentificationcriterionarepresented.Theresultsindicatethatthejudgmentsbythepresentedmethodsarebasicallyconsistentwiththetruefacts,andthereforethemethodandidentificationcritcrionisvaluableforjudgingthenormalora5normalstateofmachinewearfromoilsamples.2Modelingprocedure2.1ExperimentdesignandsampleRegularlyorirregularlycollectandanalyzeoilsamplestoobtaintheconcentrationofvariouselementsinoilsamples.Inmeantime,thoroughlyinspectanddeterminethehealthstatesofmachineweatbymeansofothermethodssuchasdissemblingmachine,measuringdebrisshapesandetcInthispaper，thehealthstateissimplyofbinary-value,ie.normalandabnormalOncesufficientdataarecollected,theexperimentisstoppedandsinglevaluemodelwillbebuilt2.2ModelingTheobserbvedhealthstatesaredefinedasfollowsOntheotherhand,they-valueeventuatedbyamodelwillbearealnumbercolseto1to2。Whereyisafunctionofconditionvatiablessuchasconcentrationsofweardebris,ie.y=g(x1,x2,…xn)Initiallyconsiderthefollowingregressionmodelsy=a0+(1)Whereaistheregressioncoefficient,xtheconcentrationofelements,atheinterruption,andnthenumberofelementsintheoilanalysis.TheabovemodelregressioncanbecompletedinExcel,whichisapartofMicrosoftOfficeAccordingtotheregressionmodel(1),somecoefficientsareinsignificantintheregressionmodel.Inordertostressthesignificantelementsofthemodelasmuchaspossible,someinsignificantelementsshouldbedeletedfromthemodel.Theinsignificantelementsareindicatedbyp-valuesinExcelIfthep-valuesarelarge,itislikelythatthepossibilityoftherelatedelementregressioncoefficientsiszero,andwherethep-valuesaresmallerthepossibilityislessInthepaperthep-value0.1istakenasasignificantcriterionofelements,whichmeansthatthepossibilityofregressioncoefficientofasignigicantelementbeingzerowillbelessthan10%.Theproceduretodeletealloftheinsignificantelementsisasfollows.Step1Regressallofelementsofoilanalysis,andoutputthep-valuesofallelementsCheckthep-valuesandselectanelementrelatedtothemaximump-value.Step2Deletetheelementsrelatedtothemaximump-value.Againregresstheleftelementandoutputthep-valuesoftheelementsCheckthep-valuesandselectanelementrelatedtothemaximump-value.Repeatstep2untilthep-valuesoftheremsiningelementsarealllessthan0.1.Atthistime,themodelingprocedureisendedandtheresultmodelisy=a0+(2)Althoughthestatevariavleyofthemodel(1)isonlybinarystates1and2,thevaluesoftheoutputyoftheresultmodel(2)willgenerallynotbeexactly1and2.Iftheoutputvaluesarelessthan1,thestateywillbelongtonormalandiftheoutputvaluesaremorethan2,thestateywillabnomal.Butifthevaluesarebetween1and2,itisvaguewhetherthestatesarenormalorabnormal.Thereforeathresholdvalueisneededtojudgethestatesoftheoutputvalues.DeterminationofthethresholdvalueOncethemodelisbuilt,accordingtotheknownnormalandabnormalstateofvariabley,allsamplescanbedividedintothetwosub-samples(normalandabnormal),whichcanbetransferredintotwosingle-valuesamplesofyintermsoftheresultingmodel(2).Consideringthatthetwosingle-valuesamplesarefromtheresultingmodel,soitisreasonablethatbothofthesingle-valuesamplesobeyanormaldistribution.FitthemintotwodistributionfunctionsfA(y)andfN(y),anddeterninethemeans)andstandarddeviations()ofthesefunctionsasinFigure1.Figure1Thepossibledistributionfunctions(PDF)ofnormalandabnormalgroupsandthethresholdvalueForanyofyvaluesfromtheresultingmodel(2),itsiaproblemtobesolvedthatitbelongstonormalorabnormal.Forthisreasonathresholdvalueneedstobedeterminedwhichisacriticalvalueofyanddenotedas.Foranyvalue,therearetwotypesofjudgmenterrors.Normalstatesiwronglyjudgedasanabnormalstatewiththeprobabilitu.1-FN(yc)Abnormalstateiswronglyjudgedasanormalstatewiththeprobability.FA(yc)ThesumoftheerrorsisgivenbyS(yc)=1-FN(yc)+FA(yc)(3)WhereFA(yc)andFN(yc)are,respectively,theprobabilityfunctionofanormalstateandtheprobabilityfunctionofanabnormalstate.Forminimizingjudgmenterrors,itisobviousthatthevalueyisoptimallydeterminedbyminimizing.TheexistenceoftheminimalvalueyhasSeenprovedintheAppendix.AccordingtotheAppendixthethresholdvalueycanbeeasilydetermined.Nowgivenanobservation,wecancalculateayvalueusingthedevelopedmodel(2)andcompareitwiththethresholdvalue.Inthiswaythemonitoredmachine`sstatecanbedeterminedNumericalexampleDataoftheexamplefromReference{9}isshowninTable1,whichcontains8elements(A1,Cu,Si,Pb,Cr,Mn,Ni,Fe).and1statevariable(State).FortheobserveddataofTable1themodelingprocedureisdescribedasfollowsand0.016472andtheyarefarlessthan0.1.Thuswehavetheregressedmodely=0.05166+0.549707Al–(4)Second,nowwecanusetheregressedmodel(4)tocomputethestatevaluesofsamplesanddividethesevaluesintotwogroupsbythemeansoftheknownnormalandabnormalstatesofsamples.Assumethatyvaluesforanygroupfollowthenormaldistribution.WehaveOncewehavetwodistributionsandthoseparameters,wecanoptimallyfindthethresholdvaluereferringtotheAppendix.Theresultis=14354withthewrongjudgmentprobability=397%.Thecurveofthetotalwrong-judgmentpossibilityviathresholdvalueyisshowninFigure2Now,wecanchedkthepredicitonpowerofthemodel.Forthemodelingsamples,thevaluesofstatevariableycomputedbymodel(4)arelistedintheycolumnofTable1.ThejudgedresultsofcomparingyvalueswiththethresholdvaluearelistedinthejudgmentcolumnofTable1,thereisnowrongjudgmentforallsamples.Thisindicatesthatthethresholdvalue1.4354withthewrongjudgmentprobability=3.97%isreasonableandthattheabovemodelingprocedureisalsoreliable.Inordertoverifyfurtherthecorrectionofthemodel(4)anditsthresholdvalue,wecanchecktheother5testingsamples,thecheckedresultsofthe5samplesareshowninTable2.FromTable2,wecanseethattherestillarenowrongjudgmentsforallsamples.Therefore,wecantakeadvantageofthemodel(4)andthethresholdvaluetojudgewhetheranynewoilsamplesarenormalorabnormalBasedonthejudgments,somesuggestionsoractionsofmaintenancecanbeobtained,whichwillsavemorecostsofmaintenance.ConclusionsanddiscussionsTheabovemodelingprocedureisanimprovedversionofReference[9],whichcaneffectivelydeletetheinsignificantelementsofoilanalysisdata.TheregressionmoduleofExcelcanverysimplyfinishthemodelingprocedure.Theregressedmodelcantransfertheoilsamplesintosingle-valuestateindexes.Consideringbinary-stateoutcomefortheobservations,amethodforoptimallydeterminingthethresholdvaluehasbeenproved.Anumericalexamplehasverifiedthatthejudgedresultsofthemodelingandtestingsamplesareconsistentwiththeoutcomeofobservations.Theaboveapproachhasafeatureofcondition-basedmaintenance.Forexample,itcanbeusdetopredictwhenamonitoreditemwillreachthethresholdvalueandtakenecessaryactions.Incaseofnotenoughsamples,thejudgmentcorrectioncanbeimprovedbymodelingthecombinationofoldsamplesandnewsamples,asmorenewsamplesareobtained.Thustheapproachcanbeconsummatedbyreplenishingmorenewsamples.Itisnotedthatthejudgmentmaybewrongwhenthey-valueisclosetothethresholdvalue.Toavoidthis,anintervalincludingyshouldbefurtherdetermined,withinwhichthejudgmentneedstobeconfirmedbyafurthercheckorothermethods.Itisthenextworktomaketheapproachpergect.References[1]V.M.MartinezandB.T.Martinez,etalResultsandbenefitsofanoilanalysisprogrammerformilwaylocomotivedieselengines.InsightVol45,No6,pp.402~406,2003[2]GNolletandD.Prince,Rotatingequipmentreliabilityforsurfaceoperation,PartOilanalysisinamineCIMBulletinVol96,No1067,pp.82~86,2003[3]R.W.ChapmanD.JHodgesandT,JNowell,Microtomacro-weardebrisanalysisasaconditionmonitoringtoolInsightVol44.No,8,pp.498~502,2002[4]S.Berg,AstudyofsamplewithdrawalforlubricatedsystemsPart2:practicalsamplewithdrawalandselectionofpropersamplingmethods,IndustrialLubricationandTribology,Vol53,No.3,pp.97~107,2001[5]R,Ong,J.H.DymondR.D.FindlayandB.Szabados,Systematicpracticalapproachtothestudyofbearingdamageinalargeoil-ring-lubricatedinductionmachine.IEEETransactionsonIndustryApplications,Vol36,No6,pp.1715~1724,2000[6[W.WangP.A.ScarfandM.A.J.Smith,Ontheapplicationofamodelofcondition-basedmaintenanceJournaloftheOperationalResearchSooiety,Vol51,No.11,pp.1218~1227,2000[7]G.Fisher,DonalueAFilterdebrisanalysisasafirst-lineconditionmonitoringtoolLubricationEngineerng,Vol56,No2,pp.18~22，2000[8]V.Macia’n,B.Tormos,P.OlmedaandLMontoro,Analyticalapproachtowearratedeterminationforinternalcombustionengineconditionmonitoringbasedonoilanalysis.TribologyInternational,Vol36,NO10,pp.771~776,2003[9]C.H.Zhao,X.P.Yanetal.Thepredictionofwaremodelbasedonstepwisepluralisticregression。ProceedingsofInternationalConferenceonIntelligentMaintenanceSystem,Xi’an,China,pp.66~72,Oct2003BriefbiographiesFujun-qingisnowanassociateprofessorofchangshauniversityofscienceandtechnology,hisresearchfieldisinmechanicalvibration,faultdiagnosis,signalanalysisandsoon.Lihan-xiongisnowaprofessorofcentralsouthuniversity,hisresearchfieldsisinfuzzycontrol,processesandintelligentcontrol,processidentification,andsoon.Xiaoxin-huaisnowanassociateprofessorofchangshauniversityofscienceandtechnology.Hisresearchfieldsisincombustionengineengineering,reliabilityandmechanicaldesign.AppencixLettheprobabilityfunctionofnormalstatesamplegroupbeandtheprobabilityfunctionofabnormalstatesamplegroupFN(yc)=(A-1)FA(yc)=(A-2)ThenthefunctionofwrongjudgmentprobabilityisS(yc)=1-FN(yc)+FA(yc)S(yc)=1-+(A-3)Inodertominimizethewrongjudgmentprobability,differentiatetheprobability(a-3)respecttoy,thus=+(A-4)=(A-5)Simplifyingtheaboveequation,wehave(A-6)Thetwosidesofequation(a-6)areactedonwithain(*)functionandletin，thentheequation(a-6)becomes〔A-7〕Simplifyingandcollectingtheaboveequation(a-7),wehave(A-8)Generally,themeansofnormalandabnormalsamplegroupsaredifferentandthemeanismorethan,thatisand<(A-9)Undertheconditions(a-9),accordingtowhetherthevariance(standarddeviation)isequaltoornot,theequation(a-8)canbeclassifiedintothetwocasesasfollowsCase1:=Theequation(a-8)cansimplifiedas=0(A-10)Theequation(a-10)hasasolesolutionofthethresholdvalueofminimumwrongjudgmentprobability=(A-11)(A-12)形式2Inthiscase,equation(a-8)canbesimplyrewrittenas(A-13)WhereTheequation(a-13)isgeneralsecondorderequationwithonevariable,thesolutionofrootsis(A-14)Forthesolution(a-14),thejudgmentconditionofexistingtherealrootsisf=>0(A-15)Infact,theconditionfromequation(a-13)canbesimplifiedasf==22(A-16)Forthejudgmcntcquation,if>，R=ln.Itisobvious(A-17)Andif<,R=R=ln,thejudgmentformula(A一16)canbewrittencanas(A一18)anditisalsoobviousthatf>0(A-18)Untiltonow,wehavetheproofthatthereareonlyrealrootsinthesolution(a-14).Thereforebothandarerealroots.Theyarethetwoextremepointsofthefunctionofwrongjudgmentprobability(a-3).Accordingtothefigure1ofdistributions,wecandirectlyobservethatoneoftherootscorrespondstoamaximumvalueofprobabiity(a-3),anothertoaminimumvalue,andtheroottotheminimumvalueshouldusuallybelessthanandmorethenthusbasedonthetheseroots,wecandeterminetheminimumthresholdvalueofwrongjudgmentprobabilityasfollowsIf，thenIf，then(A-20)基于油液分析的机械磨损状态识别模式付俊庆李汉雄肖新华长沙科技大学，汽车与机械工程学院摘要，本文提供了一个建模过程，这个过程源于回归模型根底上的单值测量方法和用以确定临界值为正常或异常的标准机械磨损状态的统计方法。用这种算法和标准验算了一个实数例子。结果说明,基于油液分析机械磨损状态正常与否的判断方法和算法根本符合客观事实。关键词，油液分析退回模型单值测量和临界值1引言石油分析方法已成为各行各业在世界范围内用于降低维修本钱、提高生产率和可靠性的方法。目前，大局部石油分析仪使用发射光谱、电子显微镜、光学或铁等方法进行石油分析。石油分析的目的是探讨从机械中提取润滑油样本所起的滑润作用或设备的条件和设备推荐维修经营活动的行动未拆机器,按照一定的关系能够获得机械的油样样本，并且通过分析油液的油液样本和机械状态来评估原设备厂商。润滑油供给者和油样分析实验室提供具体的具有指导性的在油样中磨损金属的含量。这些限制提供了良好的解读石油分析数据的一般准那么。但在石油数据分析中还有许多因素，按照石油分析数据很难直接判断出机械的磨损状态。在工程应用中，在塞米松或测量中的单值对于检测油样状态是必要的。从设备油液分析数据中导出机械的磨损率，用以确定引擎的磨损率〔zwr〕记作Z.(z)的指数值用来评价引擎正常或异常工作的磨损率以参考一个正常的磨损率(EM)。事实上,指数和参考指数应该是石油样本的随机变量而不是确定的数值，因此,该指数的统计模型需要开展一个依靠多元逐步回归的模式，这个模式删去了一些在油液分析的原始数据中无关紧要的元素和线性相关的元素，使石油分析数据转换成了单值。这个单值作为磨损状态的判断依据，但没有门槛或临界值,作为这个值的鉴定标准。因此,样本的这个值远偏离于正常状态的值1或异常状态的值2，还不清楚他们是属于正常状态还是异常状态。本文首先完善了这样一个建模函数，它是参考了基于回归模型的单值测量。然后提出了一种确定阈值的统计标准作为辨识正常或异常状态的方法。一个实数例子被所提供的方法和坚决标准所检验。结果说明有所提供的方法演算出的值根本符合客观事实，因此这个方法和判别标准对于从油样中判断在正常或异常状态下机械的磨损状态是有价值的。2模拟过程通过定期或不定期的收集和分析石油样本来获得油样中的各种元素浓度。在此期间,通过例如拆卸机械，测量碎片形状等其他方法来检查和确定机械的磨损状态。在这篇文章中，健康状态用二进制数值来表示，也就是说，正常状态和异常状态。一旦足够的数据被采集到,这个实验就会中止，单值模型将被建立。被观察的健康状态定义如下1，正常状态状态=2，异常状态在另一方面,y值经过一个模型的验算将要得到一个接近于1或2的实数。这里y值是各种状态的函数，例如磨粒浓度，即y=g(x1,x2,…xn)初步考虑以下回归模型y=a0+(1)这里是回归系数，是元素的浓度，是中断，是石油分析中的元素数量。以上的回归模型可以在Excel上完成,这是一个微软办公软件的一个局部。根据回归模型(1),Excel中由p值决定。如果p值很大，很可能是因为相关元素的回归系数等于零，并且p值越小这种可能性越小。在这篇文章中，p值等于0.1被作为元素的一个重要基准，0.1意味着一个有意义的元素的回归系数为零的可能性缺乏10%。删除所有的无关紧要的元素的步骤如下。第一步退回石油分析中的所有元素，输出所有元素的p值。检查p值并选出涉及最大p值的元素。第二步删除涉及最大p值的元素。再一次退回到最左边的元素并且输出所有元素的p值。检查p值并选出涉及最大p值的元素。重复第二步直到剩余元素的p值全都小于0.1。这时，建模过程被完成，建模结果是y=a0+(2)虽然模型1中的状态变量y只是状态1和2，但结果模型2的输出y值一般不是准确的1和2。如果输出值小于1，状态值y将属于正常状态。如果输出值大于2，状态值y将是异常的。但如果值介于1和2之间，状态是正常还是异常将要是模糊的。因此,需要一个临界值来判断该状态的输出值.2.3临界值的测定一旦模型被建立，按照的正常和异常状态下的变量y，所有样品可分为两个小组样品(正常与异常)，它根据计算模型2可以转换成两个单样本的Y值。考虑到两个单样品值来自计算模型，所以两个单值样本服从正态分布是合理的。把它们代入两个分布函数fA(y)和fN(y)，并确定如1图中这些函数的系数和偏差。并确定如图1中这些函数的系数)和偏差()图1正常或异常组的可能分布函数(PDF)和临界值〔阈值〕对于从计算模式2中得出的任何一个y值都是用于解决是属于正常还是异常这个问题的。为此需要有一个临界值来决定关键值y并记作。对于任何值，都有两种判断错误的类型，正常的状态可能被错误的判断为异常的状态1-FN(yc)或异常的状态可能被错误的判断为正常的状态FA(yc)错误的总和被给出如下S(yc)=1-FN(yc)+FA(yc)(3)这里FA(yc)和FN(yc)分别是正常状态下的可能函数和异常状态下的可能函数。为减少判断失误,显然y值最好通过减少的s值来决定。最小y值的存在被看作在附录中的证明。按照附录临界值能很容易的被确定。现在按照观察，我们能用模型2来计算出y值并把它和临界值相比拟。用这种方法来确定检测机械的状态。2.4数值例子在参考[9]中的数据出示在表1中，它包含了8个元素(铝、铜、硅、铅、铬、锰、镍、铁)和1状态变量〔状态〕。对表1中的数据建模过程描述如下。表1铁元素样本的磨损条件模型首先，使用〔1〕，我们可以发现,锰、镍、铬、铁是无关紧要的元素，而铜、铝、硅,都是重要的元素.和0.016472他们都远远小于0.1。因此，我们得到了回归模型y=0.05166+0.549707Al-0.19089Cu-0.15495Si(4)其次，我们能够使用回归模型〔4〕来计算出样品的状态值，并把其通过的样本的正常和异常状态分成两组。假设y值符合以下任何一组的正态分布，我们将要有系数=1.026557偏差=0.198596用于正常组系数=1.84667偏差=0.200158用于异常值图2由临界值得出的错误可能性曲线图一旦我们有了两个分布和参数,我们可以参考附录找出最正确临界值.结果为=1.4354的错误判断可能性为3.97%由临界值得出的错误可能性曲线图如图2所示。现在，我们可以检查这个模型的建模能力。为样本建模，由模型〔4〕计算出的状态变量y的值被列在表1的y栏中。Y值与临界值比拟相比拟的判断结果被放在表1中的判断栏，对于所有的样本没有错误的判断结果。这说明临界值1.4354被错误判断的可能性是3.97%，是合理的。以上所有的建模过程也都是合理的。为了进一步核实模型〔4〕以及它的临界值的正确性，我们可以检查其他5个测试样本，5个样本的检测结果被出示在表2中。从表2我们可以看出，在所有的样本中仍然没有错误的判断结果。因此,我们可以利用该模型(4)和临界值的判断结果来判断在任何一份新的石油样本是正常的还是异常的，一些维修的建议或方法将被获得，这将节省更多的维修费用.表25个测试样本的预计状态变量值y结论与讨论上述建模过程是对参考[9]的改良版本，它可以有效地删除在石油分析数据中的无关紧要的元素.Excel的回归模块能非常简单的完成建模过程。回归模型可以将石油样本转换成单值状态指标。考虑二进制状态的观测结果,确定最正确临界值已被证明.实例证实,建模和测试样本的判断结果与观测结果是一致的。上述方法的一个特点是基于条件的维修。例如，它可以用于当一个监测工程将要到达临界值时的预测,并采取必要的行动.如果没有足够的样本,可以通过改善新老结合建模过程来得到正确的判断结果，直到更多的新的样品被提供。因此，通过补充更多的新的样本来使这个方法更加完善。我们注意到,当y值接近临界值时判断可能是错的。为了防止这一点，包含y值在内的间隔应进一步确实定，通过进一步的检查或其他的方法进一步查证判断间隔。这是完善方法的下一步工作。参考资料[1]V.M.MartinezandB.TMartinez,铁路上机车柴油机