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-weardebrisanal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2之間，狀態是正常還是異常將要是模糊的。因此,需要一個臨界值來判斷該狀態的輸出值.2.3臨界值的測定一旦模型被建立，按照的正常和異常狀態下的變量y，所有樣品可分為兩個小組樣品(正常與異常)，它根據計算模型2可以轉換成兩個單樣本的Y值。考慮到兩個單樣品值來自計算模型，所以兩個單值樣本服從正態分布是合理的。把它們代入兩個分布函數fA(y)和fN(y)，并確定如1圖中這些函數的系數和偏差。并確定如圖1中這些函數的系數)和偏差()圖1正常或異常組的可能分布函數(PDF)和臨界值〔閾值〕對于從計算模式2中得出的任何一個y值都是用于解決是屬于正常還是異常這個問題的。為此需要有一個臨界值來決定關鍵值y并記作。對于任何值，都有兩種判斷錯誤的類型，正常的狀態可能被錯誤的判斷為異常的狀態1-FN(yc)或異常的狀態可能被錯誤的判斷為正常的狀態FA(yc)錯誤的總和被給出如下S(yc)=1-FN(yc)+FA(yc)(3)這里FA(yc)和FN(yc)分別是正常狀態下的可能函數和異常狀態下的可能函數。為減少判斷失誤,顯然y值最好通過減少的s值來決定。最小y值的存在被看作在附錄中的證明。按照附錄臨界值能很容易的被確定。現在按照觀察，我們能用模型2來計算出y值并把它和臨界值相比擬。用這種方法來確定檢測機械的狀態。2.4數值例子在參考[9]中的數據出示在表1中，它包含了8個元素(鋁、銅、硅、鉛、鉻、錳、鎳、鐵)和1狀態變量〔狀態〕。對表1中的數據建模過程描述如下。表1鐵元素樣本的磨損條件模型首先，使用〔1〕，我們可以發現,錳、鎳、鉻、鐵是無關緊要的元素，而銅、鋁、硅,都是重要的元素.和0.016472他們都遠遠小于0.1。因此，我們得到了回歸模型y=0.05166+0.549707Al-0.19089Cu-0.15495Si(4)其次，我們能夠使用回歸模型〔4〕來計算出樣品的狀態值，并把其通過的樣本的正常和異常狀態分成兩組。假設y值符合以下任何一組的正態分布，我們將要有系數=1.026557偏差=0.198596用于正常組系數=1.84667偏差=0.200158用于異常值圖2由臨界值得出的錯誤可能性曲線圖一旦我們有了兩個分布和參數,我們可以參考附錄找出最正確臨界值.結果為=1.4354的錯誤判斷可能性為3.97%由臨界值得出的錯誤可能性曲線圖如圖2所示。現在，我們可以檢查這個模型的建模能力。為樣本建模，由模型〔4〕計算出的狀態變量y的值被列在表1的y欄中。Y值與臨界值比擬相比擬的判斷結果被放在表1中的判斷欄，對于所有的樣本沒有錯誤的判斷結果。這說明臨界值1.4354被錯誤判斷的可能性是3.97%，是合理的。以上所有的建模過程也都是合理的。為了進一步核實模型〔4〕以及它的臨界值的正確性，我們可以檢查其他5個測試樣本，5個樣本的檢測結果被出示在表2中。從表2我們可以看出，在所有的樣本中仍然沒有錯誤的判斷結果。因此,我們可以利用該模型(4)和臨界值的判斷結果來判斷在任何一份新的石油樣本是正常的還是異常的，一些維修的建議或方法將被獲得，這將節省更多的維修費用.表25個測試樣本的預計狀態變量值y結論與討論上述建模過程是對參考[9]的改良版本，它可以有效地刪除在石油分析數據中的無關緊要的元素.Excel的回歸模塊能非常簡單的完成建模過程。回歸模型可以將石油樣本轉換成單值狀態指標。考慮二進制狀態的觀測結果,確定最正確臨界值已被證明.實例證實,建模和測試樣本的判斷結果與觀測結果是一致的。上述方法的一個特點是基于條件的維修。例如，它可以用于當一個監測工程將要到達臨界值時的預測,并采取必要的行動.如果沒有足夠的樣本,可以通過改善新老結合建模過程來得到正確的判斷結果，直到更多的新的樣品被提供。因此，通過補充更多的新的樣本來使這個方法更加完善。我們注意到,當y值接近臨界值時判斷可能是錯的。為了防止這一點，包含y值在內的間隔應進一步確實定，通過進一步的檢查或其他的方法進一步查證判斷間隔。這是完善方法的下一步工作。參考資料[1]V.M.MartinezandB.TMartinez,鐵路上機車柴油機