Gas turbine performance prognostic for condition-based maintenance

AppliedEnergyjournalhomepage:www.elsevier.com/locate/apenergyGasturbineperformanceprognosticforcondition-basedmaintenance

Y.G.Lia,*,P.NilkitsaranontbabSchoolofEngineering,CranfieldUniversity,Cranfield,BedfordMK430AL,England,UKChevronThailandExplorationandProduction,SCBParkPlaza,Chatuchak,Bangkok10900,Thailandarticleinfoabstract

Gasturbineenginesexperiencedegradationsovertimethatcausegreatconcerntogasturbineusersonenginereliability,availabilityandoperatingcosts.Gasturbinediagnosticsandprognosticsisoneofthekeytechnologiestoenablethemovefromtime-scheduledmaintenancetocondition-basedmaintenanceinordertoimproveenginereliabilityandavailabilityandreducelifecyclecosts.Thispaperdescribesaprognosticapproachtoestimatetheremainingusefullifeofgasturbineenginesbeforetheirnextmajoroverhaulbasedonhistoricalhealthinformation.Acombinedregressiontechniques,includingbothlinearandquadraticmodels,isproposedtopredicttheremainingusefullifeofgasturbineengines.Astatistic‘‘compatibilitycheck”isusedtodeterminethetransitionpointfromalinearregressiontoaquadraticregression.ThedevelopedprognosticapproachhasbeenappliedtoamodelgasturbineenginesimilartoRolls-RoyceindustrialgasturbineAVON1535implementedwithcompressordegradationovertime.Theanalysisshowsthatthedevelopedprognosticapproachhasagreatpotentialtoprovideanestimationofengineremainingusefullifebeforenextmajoroverhaulforgasturbineenginesexperiencingatypicalsoftdegradation.Ó2009ElsevierLtd.Allrightsreserved.Articlehistory:Received2May2008Receivedinrevisedform9February2009Accepted10February2009Availableonline18March2009Keywords:GasturbineEnginesPerformanceprognosticsRemainingusefullifeRegression1.IntroductionIngasturbineapplications,maintenancecosts,availabilityandreliabilityaresomeofthemainconcernsofgasturbineusers.Withconventionalmaintenancestrategyengineoverhaulsarenormallycarriedoutinapre-scheduledmannerregardlessofthedifferenceinthehealthofindividualengines.Asaconsequenceofsuchmain-tenancestrategy,gasturbineenginesmaybeoverhauledwhentheyarestillinaverygoodhealthconditionormayfailbeforeascheduledoverhaul.Therefore,engineavailabilitymaydropandcorrespondingmaintenancecostsmayarisesignificantly.Forgasturbineengines,oneoftheeffectivewaystoimproveengineavail-abilityandreducemaintenancecostsistomovefrompre-sched-uledmaintenancetocondition-basedmaintenancebyusinggasturbinehealthinformationprovidedbyenginediagnosticandprognosticanalysis.Theperformanceofmostphysicalassetsdegradesovertimeandfollowscertainfailurepatterns.Researchrevealsthatthereareatleastsixfailurepatternsactuallyoccurinpractice[1].Agasturbineengine,asaphysicalasset,hasitsownfeaturesinper-formancedegradations.Observationsofgasturbinefoulinginoperations[2–4]showthatperformancedegradationovertimeduetofoulingisnearlylinearwithslightaccelerateddegradationrate.Observationsofgasturbinenon-recoverabledegradationover*Correspondingauthor.Tel.:+441234754723;fax:+441234751566.E-mailaddress:i.y.li@cranfield.ac.uk(Y.G.Li).0306-2619/$-seefrontmatterÓ2009ElsevierLtd.Allrightsreserved.doi:10.1016/j.apenergy.2009.02.011timeshowthatperformancemaydegradewithnearlyconstantrateinsomecases[5,6],slightlyincreasingrate[6]ordecreasingrate[7]inothers.SaravaramuttooandMaclsaac[8]referredthreetypesoffailure,i.e.instantaneous,delayedtime-dependentandpurelytime-dependent,todescribegasturbinefailure/degradationandconcludedthattheratesofdegradationforgasturbinesareseldomknownandnotlikelytobelinear.Brothertometal.[9]de-scribedthegasturbinedegradationmodeasbathtubtype.Differentprognostictechniquesandrelevantissueswerere-viewedandinvestigatedbymanyresearcherssuchasBrothertonetal.[9],Bytingtonetal.[10],Roemeretal.[11],DePoldandGass[12],RoemerandKacprzynski[13],Brothertonetal.[14]andHessetal.[15]andthesetechniquesaresummarizedasexperi-ence-basedprognostics,model-basedprognostics,evolutionaryprognostics,neuralnetworks,stateestimatorprognostics,rule-basedexpertsystems,fuzzylogicbasedmethods,etc.Lineartrendingofgasturbinedegradationisoneoftheprognosticmethodsandhasbeeneffectivelyusedforshorttermpredictionofenginehealth;examplesofwhicharethosegivenin[16,17].Suchtrendingmethodsbaseonlinearregressionsovertimeandhavethelimitationthattheymayonlybeacceptableforshorttermhealthprediction.Initialinvestigationofgasturbinediag-nosticandprognosticanalysistakingintoaccountcombinedlin-earandnon-lineardegradationovertimeisshownin[18].Theobjectiveoftheresearchinthispaperistofurtherinvestigatethelinearand/oranon-linearprognosticapproachforthepredic-tionofpotentialengineperformancedegradationintothefutureY.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–21612153NomenclatureSymbolseE()GPAHLmfnNP

skew()t

ta/2,n-2tptutoTV()~x

~zgaspathmeasurementparametervector

b0,b1,b2regressioncoefficientsaaccumulatedtailprobabilityoft-distributionemeasureofdifferencebetweenactualandpredicted

measurements;randomerror

gisentropicefficiencykGPAIndexlmeanvaluerstandarddeviationwpredictionerrororprognosticuncertaintyDdeviationSubscript1–9enginegaspathstationnumbers(showninFig.7)Superscripts^estimatedTtransposeÀ1inverse

residual

meanvalue

GasPathAnalysis

InfluenceCoefficientMatrix(ICM)summationofsquaresofdeviationsfuelflowrate(kg/s)numberofdatapoints

gasgeneratorrotationalspeedtotalpressure(kPa)Skewnesstime

upper(a/2)percentagepointofthet-distributionwith(nÀ2)degreeoffreedom

predictedpessimisticusefullife

predictedusefullifewitharegressionmodelpredictedoptimisticusefullifetotaltemperature(K)variance

componenthealthparametervector

bytakingintoaccountpossiblechangeofdegradationpatternsovertime.Gasturbinegaspathdiagnosticsisanessentialsteptowardseffectiveprognosticanalysis.Differentgaspathdiagnostictech-niqueshavebeendevelopedinthepast.TypicalonesareGasPathAnalysis(GPA)anditsderivatives[19–26],neuralnetworks[27–29],BayesianBeliefNetworks[30],GeneticAlgorithm[31–33],FuzzyLogic[34–36],diagnosticsusingtransientmeasurements[37,38],etc.ThisresearchfieldhasbeensummarizedbyLi[39]andSingh[40].Theforecastingofenginedegradationorengineprognosticsisverychallengingduetogreatuncertaintyassociatedwithgastur-binedesign,manufacturing,ambientandenvironmentalcondition,operatingcondition,dutymissions,maintenanceactions,etc.Thisstudyexplorestheincorporationofprognosticandstatisticalknowledgeanddevelopsatechnicalapproachtopredicttheremainingusefullifeofgasturbineengines.Theapproachisthenappliedtoamodeloffshoregasturbineapplicationimplantedwithsoftcompressordegradationovertimetoshowtheeffectivenessoftheapproach.2.Gaspathprognosticapproach2.1.BasicassumptionsGasturbinedegradationphenomenonissocomplicatedthatnoanysinglediagnosticandprognosticapproachcancoverallscenar-ios.Therefore,tomakethediagnosticandprognosticapproachde-scribedinthisstudyapplicableitisassumedthat(1)Onlyenginesoftdegradationassociatedwithperformancechange(suchasfoulinganderosion)thatdevelopsgraduallyovertimeisdiscussedinthisstudy.(2)EngineoperatesatthestandardISOambientconditionandatmaximumpowerthroughoutitslife.(3)Engineperformancedegradationfollowsafailureratepat-ternshowninFig.1whereaconstantfailureratelastforaperiodoftimefollowedbyanincreasingfailurerate.Thisassumptionalsocoversthescenariowhereonlyconstantfailurerateorincreasingfailureratehappens.Regularmain-tenanceactions,suchasonlineandoff-linecompressorwashing,donotchangeenginedegradationpatterns.(4)Theuncertaintyassociatedwiththeprognosticanalysisisnormallydistributedarounditstruehealthandbecomeslar-gerintothefuture.(5)Onlymajorenginecomponentdegradations,suchascom-pressorandturbinedegradations,areincludedintheanaly-sisandthedegradationisdescribedbythedeviationofisentropicefficiencyandflowcapacityfromtheirclean(un-degraded)value.(6)Enginehealthanalysisiscarriedoutcontinuouslyfromthebeginningofitsoperation.However,thefrequencyofsuchanalysisisdependentonthefrequencyofmeasurementdatasampling.(7)Frequent/recurrentmaintenanceactionssuchason-lineandoff-linecompressorwashingareregularlycarriedoutanddonotchangethefaultpatterns.2.2.GaspathdiagnosticsDegradationcanberecognizedasthedeviationinperformancefromthatwhentheenginewasnew.Anon-linearGPAdiagnosticapproachusedinthisstudyistheonedevelopedbyEscherandSingh[25]andLiandSingh[26].Toassisttheunderstandingofsuchdiagnosticapproachabriefdescriptionofthemethodispro-videdasfollows.xFailure rate pattern Degradation patternAllowed Degradation Pessimistic Useful Life (tp)Predicted Useful Life (tu)Optimistic Useful Life (to)Current timeFig.1.Degradationandprognosticmodel.t 2154Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–2161Atagivenoperatingpointandatcertaintimeduringoperation,alinearrelationshipbetweengaspathmeasurementdeviationvectorD~zandenginecomponenthealthparameterdeviationvec-torD~x,Eq.(1),canbeobtainedfromengineperformancemodel~z¼fð~xÞbyusingaTaylorseriesexpansion.D~z¼HÁD~xð1ÞwhereHiscalledthe‘‘InfluenceCoefficientMatrix”(ICM).Therefore,engineperformancedegradationrepresentedwithD~xcanbeob-tainedwithEq.(2)ifthenumberofmeasurementsequalsthenum-berofhealthparameters,orEq.(3)ifthenumberofmeasurementsismorethanthenumberofhealthparameters.D~x¼HÀ1ÁD~zð2ÞD~x¼ðHTHÞÀ1ÁHTÁD~zð3ÞTheabovemethodiscalledlinearGasPathAnalysis(GPA).Duetothatengineperformancerarelydeviateslinearlywithdegradationandthelinearapproachmayresultinsignificantpredictionerrorsindiagnosticanalysis.Thisleadstothedevelopmentofanon-linearGPAwherethelinearGPAisusediterativelyuntilaconvergedsolu-tionisobtained(Newtom–Raphsonmethod).AccuratepredictionofenginedegradationwiththeGPAap-proachdependsonaprioriinformationofdegradedcomponentsandthereforeconfusingsolutionsmaybeobtainedifdifferentde-gradedcomponentsarepre-assumedduetolackofsuchinforma-tion.Inordertoisolateactuallydegradedcomponent(s),aGPAIndexkdefinedinEq.(4)isusedtoassesstheaccuracyofthepre-dictionsolutions.k¼11þeð4Þwhereeisameasureofthedifferencebetweenthemeasuredandpredicteddeviationsofenginegaspathmeasurements.Allenginegaspathcomponentsmaydegradeduringoperation.Toisolatethemostseverelydegradedcomponent(s)effectively,componentfaultcases(CFC)representingpossiblecombinationofdegradedcomponentsthatcoverallthecombinationsofpoten-tialdegradedcomponentsareassumedandtheGPAdiagnosticsearchisthenappliedtoeachofthefaultcases.ThecaseswithhighGPAIndicesindicatethemostlikelyenginedegradations.Thedetailsoftheapproacharedescribedin[26].2.3.LinearregressionforprognosticanalysisOncetheenginehealthisanalyzedwiththenon-linearGPAatallindividualmomentsinthepast,enginefuturehealthcouldbepredictedwiththeobtainedhistoricalenginehealthdata.Inthecontextofthisstudy,theforecastingmethodstobeusedarethesimpleregressionmethods,suchaslinearandquadraticregressions.Regressionanalysisisastatisticaltoolthatcanpro-ducepredictionsandprovideexplanationofdata.Basedontheassumptionthatgasturbineengineswouldexpe-riencealongperiodofsoftdegradationfromthebeginningofitsoperationwithaconstantfailurerate,Fig.1,alinearregressionisappliedfirsttothehistoricaldatatoproducearegressionlineforthepurposeofprognosticanalysis.Supposethatthetruerelationshipbetweenenginehealthparameterxiandtimetisastraightlineandthatxi,kateachtkisarandomvariable.TheexpectedvalueofxiforeachvalueoftispresentedbyEq.(5).EðxijtÞ¼bi;0þbi;1tð5Þwherebi,0andbi,1areunknownregressioncoefficients.Itisas-sumedthateachxi,kcanbedescribedbyEq.(6).xi;k¼bi;0þbi;1tkþei;k;k¼1;2;...;nð6Þwhereei,karerandomerrorswithzeromeanandvariancer2i.Therandomerrorsei,kcorrespondingtodifferentxi,karealsoassumedtobeuncorrelatedandnormallydistributed.Fig.2showsatypicalscatterplotofhistoricalenginehealthdataovertimeandanestimatedlinearregressionline.Thevalueofbi,0andbi,1canbeestimatedbyaleastsquaresmethodtoobtainabestfittothedataxi,k(k=1,2,...,n)wherethesumLofthesquaresofthedeviationsofxi,k,Eq.(7),fromthetrueregressionlineisminimized.XnL¼e2i;¼Xnkðxi;kÀbi;0Àbi;1tkÞ2ð7Þt¼1k¼1Moredetailsofthemethodcanbefoundinmanybooks,suchas[41].ThesolutiontoEq.(7)resultsinleastsquaresestimators^bi;0and^bi;1.Therefore,theestimatedregressionlineisrepresentedbyEq.(8).^xi¼^bi;0þb^i;1tð8ÞNotethateachpairof(xi,k,tk)satisfiestherelationshipshowninEq.(9).xi;k¼^bi;0þb^i;1tkþei;k;k¼1;2;...;nð9Þwhereei;k¼xi;kÀ^xi;kiscalledtheresidualdescribingtheerrorinthefitofthemodeltoxi,k.2.4.QuadraticregressionmodelInasituationwhereanincreasingfailurerateoccurslinearregressionisnolongerapplicable.Therefore,aquadraticregressioncouldbeabettersolutionforprognosticprediction.Fig.3showsatypicalscatterplotofenginehealthdataovertimeandaquadraticregressionlinetofitthedata.Similartothelinearregression,supposethatthetruerelation-shipbetweenenginehealthparameterxiandtimetisaquadraticlineandthatxi,kateachtkisarandomvariable.TheexpectedvalueofxiforeachvalueoftisrepresentedbyEq.(10).EðxijtÞ¼bi;0þbi;1tþbi;2t2ð10Þwherebi,0,bi,1andbi,2areunknownregressioncoefficientsthatwouldhavetobeestimated.Itisassumedthateachxi,kcanbede-scribedbyEq.(11).xi;k¼bi;0þbi;1tkþbi;2t2kþei;k;k¼1;2;...;nð11Þwhereei,karerandomerrorswithzeromeanandvariancer2i.Therandomerrorsei,kcorrespondingtodifferentxi,karealsoassumedtobeuncorrelatedandnormallydistributed.Tofindthecoefficients(bi,0,bi,1andbi,2)oftheregressionlinefornpairdata(xi,k,tk),k=1,...,n,theleastsquareestimatorbi,0,bi,1andbi,2arethosevaluesthatminimizeL,Eq.(12).xi Regression lineHistoric data (xi,k, tk)t Fig.2.Linearregressionmodel.Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–21612155xi Regression lineHistoric data(xi,k,tk)t Fig.3.Quadraticregressionmodel.L¼Xne2i;k¼Xnðx2i;kÀbi;0Àbi;1tkÀbi;2t2kÞð12Þt¼1k¼1Therefore,theestimatedregressionlinebecomesEq.(13)^xi¼^bi;0þb^i;1tþb^i;2t2ð13ÞNotethateachpairof(xi,k,tk)satisfytherelationshipshowninEq.(14).Moredetailsofthemethodcanbefoundinmanybookssuchas[42].xi;k¼^bi;0þb^i;1tkþb^i;2t2kþei;k;k¼1;2;...;nð14ÞForbothlinearandquadraticregressions,theregressioncoefficientsdeterminethequalityoftheregressionlines,Eqs.(8)and(13).Thereliabilityoftheregressionlinesrepresentingthetruevaluesofthehealthparametersdependsontheaccuracyofthemeasurementsamples,thenumberofthemeasurementsamplesandtheaccuracyoftheGPAdiagnosticanalysis.2.5.TransitionofregressionmethodsIngasturbineapplications,thedegradationpatternofagastur-bineengineovertimeisunknown.Itcouldbelinear,non-linearorthecombinationofboth.Basedonpublishedinformation[2–9],itcanbeseenthatthecombinedfailureratepatternshowninFig.1isoneofthetypicaldegradationpatternsofgasturbineengines.Forsuchadegradationprocess,theenginedegradationdevelopslinearlywithaconstantfailurerateduringthefirstperiodofoper-ationwhenenginesexperiencesoftandgradualdegradationandisthenfollowedbyanincreasingfailurerateduringthesecondper-iodofoperation.Therefore,theprognosticpredictionisstartedwiththelinearregressionmode.Acompatibilitycheckofmoni-toredpointsaroundtheregressionlinesiscontinuouslyconductedtodetermineifthequadraticregressionmodelshouldbeusedtoreplacethelinearregressionmodel,Fig.4.Itisimportanttoaccu-ratelydetermineatransitionpointwheretheprognosticmodelisswitchedfromthelinearregressionmodeltothequadraticregres-sionmodelinordertohaveanaccurateprognosticassessment.Whenonlylineardegradationhappensthelinearregressionmodelwillbecontinuouslyused.Whenonlynon-lineardegradationhap-penstheprognosticanalysiswillturntoquadraticregressionmod-elsoonafterthebeginningoftheoperationbasedonthecompatibilitycheck.Todeterminethetransitionpointforthetransitionfromthelin-earregressiontothequadraticregression,acompatibilitycheckisproposedinthisstudyandcarriedoutcontinuouslyintheprog-nosticanalysistoassessifcurrentregressionmodelfitsactualfail-ureratepattern.Ifcurrentregressionmodelisvalid,thevarianceofnewobservationsofthehealthparametersshouldcontinuetobenormallydistributedaroundcurrentregressionline.Otherwise,adifferentfailureratepatternandcorrespondingregressionmodelshouldbeapplied.xiModel tTransition PointFig.4.Compatibilitycheckformodeltransition.Intheproposedcompatibilitycheck,twostatisticalparametersareusedinthisstudyandtheyareSignificanceLevelandSkew-ness.TounderstandtheconceptoftheSignificanceLevel,anullhypothesisisassumed,wheretheobservationsofthevarianceofthehealthparametersarenormallydistributed.TheprobabilityofrejectingthenullhypothesiswhenitistrueiscalledtheSignif-icanceLevel[41].TheSignificanceLevelmayvaryfrom0to1;alowervalueoftheSignificanceLevelwouldindicatethatthenullhypothesisshouldberejectedandviceversa.AcriticalvalueoftheSignificanceLevelisapplicationdependentandshouldbedeterminedbasedonapplicationstatisticsandpastexperience;atoosmallvaluewouldallowanenginetodegradetoomuchwhileatoobigvaluewouldoverhaulanenginewhenitisstillhealthy.Inthisresearch,acriticalvalueof0.2ischosenfortheSignificanceLevelinordertodetermineifthenullhypothesisshouldbere-jected.TheapproachandthesoftwareusedtocalculatetheSignif-icanceLevelistheShapio–Wilk(S–W)statistictest[43]andtheSPSSforWindows[44],respectively.Inacasewherenewobserva-tiondatashiftawayfromthecurrentregressionlinewiththeSig-nificanceLevelbecomingsmallerandsmaller,itindicatesthatthecurrentregressionmodelisnolongervalidandadifferentregres-sionmodelshouldbeappliedtofitthedata.TheSkewnessisthemeasureofsymmetryofdatainastatisticsense.SymmetricdatashouldhaveaSkewnessvaluenearzero.AnegativeSkewnessvalue(skewedtotheleft)indicatesthatdataarebunchedtogetherabovethemeanbutwithalongtailbelowthemean,whileapositiveone(skewedtotheright)indicatesthatdataarebunchedtogetherbelowthemeanbutwithalongtailabovethemean.Fig.5illustratesthenotionofSkewnesswherebothprobabilitydensityfunctions(PDFs)ofthedatahavethesameexpectationandvariance;theoneontheleftispositivelyskewedandtheoneontherightisnegativelyskewed.TheSkewnessofrandomvariablexiisdenotedasskew(xi)andisdefinedinEq.(15).Skew to the left Skew to the right Fig.5.Schematicdemonstrationofskeweddatadistribution.2156Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–2161skewðxÀiÞ¼E½ðxiliÞ3󰀄r3ð15Þiwhereliandriarethemeanvalueandstandarddeviationofdataxi,respectively.MoredetailsoftheSkewnesscanbefoundin[45]andthesoftwareusedtocalculatetheSkewnessistheSPSSforWin-dows[44].Inacasewherearegressionlinedoesnotmatchtheactualfail-urepattern,thedifferencebetweenthedataandtheregressionline,(xi,kÀbi,0Àbi,1tk)or(xi;kÀbi;0Àbi;1tkÀbi;2t2k),shouldbeeithernegativewiththedatashowingontheuppersideoftheregressionlineorpositivewiththedatashowingonthelowersideoftheregressionline.Therefore,acontinuousdecreaseorincreaseintheSkewnessvalueindicatesthatadifferentregressionmodelshouldbeusedtofitthedata.CriticalvaluefortheSignificanceLevelandtheSkewnessshouldbedefinedinordertodeterminethetransitionpoint.How-ever,suchcompatibilitycheckisbasedonstatisticinformation.ThereforethefrequencyofsamplingovertimeandthenumberoftotalavailabledatasampleshavesignificantinfluenceonthecalculatedvaluesoftheSignificanceLevelandtheSkewness.Cer-taincrispcriterionforthetransitiononlybecomesmeaningfulwhenthefrequencyofsamplingovertimeandtheamountofdatasamplesaredetermined.2.6.PrognosticuncertaintyOncearegressionline,Eq.(8)or(13),hasbeenestablished,itcanbeusedtopredictneworfuturehealthparameters.However,thepredictionerrororprognosticuncertaintyrepresentedbyEq.(16).wi¼xiÀ^xið16Þisstronglyassociatedwithtimeintothefutureandcanberegardedasanormallydistributedrandomvariablewithazeromeanandavariancearoundthepredictedhealthatafuturetimeofinterest.Suchprognosticuncertaintyisverydifficulttoestimateasitcouldbeaffectedbymanyfactors,suchasenginedesignsafetymargins,manufacturetolerance,ambientandenvironmentalconditions,operatingconditions,missionduties,maintenancescheduleetc.Forexample,anenginehastoworkwithhigherfiringtemperatureinhotdaysthanincolddayswhenthesamepoweroutputisre-quired.Thereforetheengineperformancemaydegradefasterinhotdays.Themanufacturingqualityofgasturbineenginesofthesamefleetmayalsobedifferentduetomanufacturingtoleranceandtherefore‘‘good”enginesmaydegradeslowerthan‘‘bad”en-ginesbecauseofdifferentfiringtemperaturerequiredtoprovidethesamepoweroutput.Duetothecomplexityofthedegradationuncertainty,engineoperatingfielddataandexperiencemaypro-videgoodinformationfortheestimationofprognosticuncertainty.Toassistcurrentprognosticstudyanddemonstratetheideaofthewholeprognosticsystem,aprognosticuncertaintymodel[41]basedonthevarianceofhistoricaldataofanengineisadoptedasfollows.Letxi,kbethefutureobservationofanenginehealthparameterattimetand^xi;kbegivenbythefittedmodelofeitherEq.(8)or(13).Thevarianceofpredictionerrorwi¼ðxi;kÀx^i;kÞisassumedtohavemeanzeroandvarianceestimatedbyEq.(17).\"2#VðwiÞ¼r^1i1þnþðtÀtoÞSð17Þttwherer^iistheestimateofthestandarddeviationof^xi;kandS1 tt¼Xnt2Xn!2kÀntkð18Þk¼1k¼1a100(1Àa)%predictionerroronafutureobservationxi,kattimetisdefinedbyEq.(19).vu^xi;kÆta=2;nÀ2Áuffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit\"r^21ðtÀt2#i1þnþ0ÞSð19Þttwherenisthenumberofmeasurementsamplesusedintheestima-tion,ta/2,nÀ2theupper(a/2)percentagepointofthet-distributionwith(nÀ2)degreesoffreedomandathecumulatedtailprobabil-ityofthet-distribution.Suchapredictionerrorisusedastheesti-mateoftheprognosticuncertaintyintothefuture.Theprognosticuncertaintyisofminimumwidthattime(t=t0)andincreasesasthetvalue(timeorrunninghours)movesawayfromcurrenttimeintothefuture.Theestimateoftheprognosticuncertaintydescribedaboveisbasedonhistoricaluncertaintyofenginehealthdatainclusionofdifferentexistinginfluentialfactorssuchasdesignandmanufacturingqualityofanengine,ambientandenvironmentalconditions,missionprofiles,maintenanceac-tions,etc.Iftheseinfluentialfactorschangeinthefuturetheprog-nosticuncertaintymayalsochangeaccordinglyandsuchchangesarenotconsideredinthisstudy.2.7.DeterminationofremainingusefullifeBasedongasturbinehistoricaldatauptothecurrenttimeofoperation,gasturbinedegradationintothefuturecanbepredictedwithlinearorquadraticregressionwithanupperandlowerboundofprognosticuncertaintydeterminedbyEq.(19),Fig.1.Forthesakeofsafetyofgasturbineengines,gasturbineoperatorsmayonlyuseeitherlowerboundorupperboundtodeterminetheremainingusefullifedependingonthedirectionofthevariationofhealthparametersovertime–forthosehealthparametersdecreasingovertime,lowerboundofprognosticuncertaintypro-videspessimisticpredictionandisusedtodeterminetheremain-ingusefullife,andviceversa.Therefore,thepredictionprocedureofremainingengineusefullifeisasfollows:󰀆Alloweddegradationforhealthparameters(thresholds)shouldbedetermined.󰀆Thetimeperiodfromcurrenttimetotheintersectionpointbetweenthepredictedenginedegradationlineandalloweddeg-radationlineistheestimateofthepredictedremainingusefullife(tu).󰀆Thetimeperiodfromcurrenttimetotheintersectionpointbetweenthelowerprognosticuncertaintyboundofthepre-dictedenginedegradationline(incaseofhealthparametersdecreasingovertime)andalloweddegradationlineistheesti-mateofthepredictedpessimisticremainingusefullife(tp).󰀆Similarly,apredictedoptimisticremainingusefullife(to)canbeobtainedbutcausecomparativelylittleworrytogasturbineusers.󰀆Theactualremainingusefullifeshouldbebetweenthepessi-misticandpredictedengineremainingusefullives(tpandtu)ifthepredictionissatisfactory.2.8.IntegrateddiagnosticandprognosticapproachToapplytheabovediagnosticandprognostictechniquestogasturbineapplications,adiagnosticandprognosticapproach,Fig.6,isproposedandexplainedasfollows:Step1:ApplytheGPAdiagnosticapproachtodetectenginedeg-radationuptocurrenttimeusingavailablegaspathmeasure-ments.SuchGPAdiagnosticapproachisabletodiagnosemajorenginegaspathcomponents,suchascompressorsandturbines.Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–216121573)Conduct Compatibility check 2) Apply Linear Regression to historical data 1) Apply GPA to detect historical degradation No Compatible? Yes 4a) Continue using Linear Regression. 4b) Apply Quadratic Regression.5) Predict upper & lower uncertainty bounds Fig.6.Diagnosticandprognosticssystemforgasturbines.6) Predict remaining useful life Theselectedmeasurementsshouldbeuncorrelatedgaspathmea-surementsthataresensitivetothedegradationofthesegaspathcomponentdegradations.Duetothestatisticnatureoftheap-proach,themoretheamountofmeasurementsamplesthebetterprognosticresultsmaybeachieved.Step2:Applythelinearregressionmodeltofithistoricalperfor-mancehealthdataandpredictfutureenginehealthparameters.Step3:ConductCompatibilityCheckstodeterminewhethertheregressionmodeliscompatiblewiththeactualpatternofenginefailurerate.Step4:(a)Ifgoodcompatibilityisdemonstrated,thelinearregressionmodelwillcontinuetobeused.(b)Otherwise,thequa-draticregressionshouldbeusedinstead.Step5:Prognosticuncertaintyovertimeintothefutureisesti-matedinordertodeterminetheupperandlowerboundsofprog-nosticuncertaintyofthepredictionline.Step6:Allowableenginedegradationspecifiedwithathresholdforeachenginehealthparametershouldbedeterminedandtheestimatedengineremainingusefullife,includingthepessimisticusefullife,canbeobtained.Itisassumedthat:󰀆ThepatternofenginefailureratefollowstheoneshowninFig.1.󰀆Thedegradationinthisgasturbineoccursduetosignificantcompressordegradationrepresentedbythedeviationofcom-pressorflowcapacityandisentropicefficiency.Duetothatthesetwocompressorhealthparametersareindependentfromoneanotheraparticularcaseofdegradationwherethedegradationinflowcapacityisdoublethedegradationincompressoreffi-ciencyissimulatedinthisstudy.󰀆Theenginedegradesataconstantfailureratefromthebegin-ningofoperationto20,000hofoperationandthenanincreas-ingfailurerateoccurs.TheenginereachesÀ3%degradationinefficiencyandÀ6%degradationinflowcapacityat30,000hofoperation.󰀆ThemeasurementnoisehasanormaldistributionaroundtruemeasurementvaluesandthemaximumlevelofmeasurementnoisefordifferentgaspathparametersisshowninTable1[46].󰀆Diagnosticassessmentsarecarriedoutforevery500hofoper-ation.However,duetothestatisticnatureoftheanalysisincon-cernmorefrequentdatasamplingwillimprovethepredictionaccuracy.Thisisduetothefactthatthemeasurementnoisecanbeassessedmoreeasilyandaccuratelyandtheobtainedregressionlineswillprovidebetterpredictionoftruevaluesofhealthparameters.󰀆Theengineistoberemovedforanoverhaulwhenthedegrada-tioninefficiencyreachesÀ3%,orthedegradationinflowcapac-ityreachesÀ6%.Theavailablegaspathmeasurementsfordiagnosticandprog-nosticanalysisarechosentobethoseshowninTable2.Todemonstratetheproposedprognosticmethod,atypicalcom-pressordegradationdevelopedovertimeisimplantedintothemodelgasturbineengine(solidlineinFigs.8and9)andthecor-respondingdegradedengineperformanceandgaspathmeasure-3.ApplicationandanalysisTheintegrateddiagnosticandprognosticapproachdescribedintheprevioussectionisappliedtoamodelindustrialgasturbineen-ginesimulatedwithgasturbineperformancesimulationsoftwareinordertodemonstratetheeffectivenessoftheapproach.3.1.PerformancesimulationanddiagnosticsofamodelengineThemodelgasturbineengineusedinthisstudyisatwo-shaftindustrialgasturbine,similartoRolls-RoyceindustrialAVONMk1535,thathasonecompressor,oneburner,onecompressortur-bineandonepowerturbine.Thebasicperformanceparametersareasfollows:TotalpressureratioTurbineentrytemperatureExhaustmassflowratePoweroutputHeatrate3.33869(°C)77.3(kg/s)15(MW)12,258(kJ/kWh)Power turbine Nozzle Intake Compressor Compressor turbine 7Burner Generator CranfieldUniversitygasturbineperformanceanddiagnosticsoft-ware[26]isusedtocreateanengineperformancemodelandsim-ulatethecleananddegradedperformanceovertime.ThemodelengineconfigurationisshowninFig.7.1 2 3 45 6 7 8 9 Fig.7.Modelengineconfiguration.2158Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–2161Table1

Maximummeasurementnoise[46].MeasurementRangeTypicalerrorPressure3–45psia0.5%8–460psia±0.5%or0.125psiawhicheverisgreaterTemperatureÀ65–290°C±3.3290–1000°CÆqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi°C2:52þð0:0075ÁTÞ21000–1300°CÆqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3:52þð0:0075ÁTÞ2FuelflowUpto250kg/h41.5kg/hUpto450kg/h34.3kg/hUpto900kg/h29.4kg/hUpto1360kg/h23.7kg/hUpto1815kg/h20.8kg/hUpto2270kg/h23.0kg/hUpto2725kg/h25.9kg/hUpto3630kg/h36.2kg/hUpto5450kg/h63.4kg/hUpto12,260kg/h142.7kg/hTable2

Instrumentationset.MeasurementMeaningP3Compressorexittotalpressure(kPa)P7Compressorturbineexittotalpressure(kPa)T7Compressorturbineexittotaltemperature(K)P8Powerturbineexittotalpressure(kPa)T8Powerturbineexittotaltemperature(K)mfFuelflowrate(kg/s)NGasgeneratorrotationalspeed(%)mentsaresimulated.Thenitisassumedthattheimplanteddegra-dationisunknowntothediagnosticsystemandtheGPAdiagnosticsystemdescribedin[26]isusedtoisolateandquantifyenginecomponentdegradationovertime.Thepredicteddegradationplot-tedovertime(dottedlineinFigs.8and9)representingtheenginedegradationhistoryisusedintheprognosticanalysistoestimatepotentialengineremainingusefullife.3.2.ComponentdiagnosticanalysisusingGPAapproachIndiagnosticandprognosticanalysis,thenon-linearGPAisap-pliedtoalltheenginehistoricaldatauptothecurrenttimetoana-lyzetheenginehealthdegradationhistory.Thisincludesisolatingthedegradedenginecomponent(s)usingtheconceptoffaultcasesandGPAIndexandquantifyingthecomponentdegradation[26].Duetothatthediagnosticanalysisisnotthefocusofthispaper,1.0 0.0)%0 5000 10000 15000 20000 25000 30000 35000( p-1.0ord -2.0ycne-3.0iciffE-4.0-5.0Predicted with GPAImplanted-6.0Operating time (hrs)Fig.8.ImplantedcompressorefficiencydegradationandpredicteddegradationwithGPA.0.0 )%0 5000 10000 15000 20000 25000 30000 35000( -1.0pord -2.0yticap-3.0ac w-4.0olF-5.0Predicted with GPAImplanted-6.0Operating time (hrs)Fig.9.ImplantedcompressorflowcapacitydegradationandpredicteddegradationwithGPA.thedetailedcomponentfaultisolationandquantificationisas-sumedtobedonesuccessfullywhiletheinterestedreadersmayre-ferto[26]formoreinformationoftheprocess.Oncethedegradationanalysisisdoneforallindividualpoints,thepredicteddegradationforcomponenthealthparametersovertimecanbeplotteduptothecurrenttime.Figs.8and9showthepredicteddiagnosticresultsindottedpointsintermsofthepredicteddegra-dationofcompressorefficiencyandflowcapacity,respectively.Asdiscussedin[26]thenon-linearGPAisabletoprovideaccuratediagnosticresultsifenginegaspathmeasurementsareaccurate.Thereforethescatteringofthepointsareduetotheimpactofmea-surementnoisethatcontributestothediagnosticpredictionerrorsandthequantitativelevelofsuchpredictionerrorsismoreorlesssimilartothemeasurementnoiseofthegaspathmeasurements.Duetothestatisticnatureoftheprognosticmethodtheamountandtheaccuracyofmeasurementssamplesandtheaccuracyofdiagnosticanalysishavegreatimpactontheaccuracyofprognosticanalysis.Afterthehistoricaldiagnosticinformationbecomeavail-able,theproposedprognosticapproachisthenusedasfollows.3.3.ApplyinglinearregressionmodelforprognosticanalysisAsthefirststepoftheprognosticanalysis,thelinearregressionmodelisappliedtothescattereddatafromthebeginningofoper-ationforbothcompressorefficiencyandflowcapacitydegradation.Figs.10and11provideanexampleofapplyinglinearregressiontothescattereddataofcompressorefficiencyandflowcapacitydropswhenitisassumedthatthemomentafter15,000operationhoursisthecurrenttime.1.0)%( 0.0po0 10000 20000 30000 40000r-1.0d yc-2.0nei-3.0ciff-4.0E-5.0tp = 27,000 tu = 43,000 -6.0Operating time (hrs)ImplantedPredicted healthHistorical DataLower bound of predicted healthFig.10.Linearregressiontoscattereddataofcompressorefficiencyat15,000h.Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–21612159)%0.0( p-1.00 10000 20000 30000 40000ord-2.0 yti-3.0ctu = 44,500 ap-4.0ac -5.0wtp = 40,000 hrsol-6.0F-7.0Operating time (hrs)ImplantedHistorical DataPredicted healthLower bound of predicted healthFig.11.Linearregressiontoscattereddataofcompressorflowcapacityat15,000h.Basedontheassumptionthattheacceptabledegradationis3.0%forcompressorefficiencyand/or6.0%forcompressorflowcapacitybeforeamajoroverhaul,tp(thepessimisticestimateofengineusefullife)andtu(thepredictedengineusefullifewithas-sumedregressionmodel)canbedetermined.ForexampleinFig.10wherefuturedegradationofcompressorefficiencyispre-dicted,tpisaround27,000handtuaround43,000h.Therefore,withtheprognosticpredictiontakingplaceat15,000hbasedonthecompressorefficiencydata,thepredictedremainingusefullifefortheengineisroughlybetween12,000and28,000h.SimilarlyinFig.11wherefuturedegradationofcompressorflowcapacityispredicted,tpisaround40,000handtuaround44,500h.Therefore,thepredictedremainingusefullifeoftheengineisroughlybe-tween25,000and29,500h.ItcanbeseenbythecomparisoninTa-ble3thatthepredictedremainingusefullifebasedoncompressorefficiencydataprovidesmoreconservativeresultduetogreaterscatteringofthehistoricaldata.Thesignificantdifferencebetweenthepredictedremainingusefullifebasedonefficiencydataandthatbasedonflowcapacitydataisduetothesignificantdifferenceinprognosticuncertainties.Althoughthelowerprognosticuncer-taintyboundofthelinearregressionlineforthecompressoreffi-ciencydatacoverstheimplantedremainingusefullife(Fig.10),itisverylikelythatthepredictionofremainingusefullifemaynotbereliableduetothatthelinearregressionmodeldoesnottakeintoaccountthesituationwhereactualdegradationpatternchangesinthefuture,suchasthecaseinFig.11.3.4.CompatibilitychecksOncetheprognosticanalysisstarts,compatibilitychecksofnewobservationpointsarecontinuouslyconductedtodeterminewhetherthelinearregressionmodelisstillcompatiblewithactualTable3

Predictedremainingengineusefullifeat15,000hofoperation.

Remainingengineusefullifeat15,000hofoperationPessimisticpredictionPredictionwithconsideringprognosticquadraticregressionuncertainty(tpÀ15,000)model(tuÀ15,000)Fromcompressor12,00028,000efficiencydropdata(Fig.10)Fromcompressor25,00029,500flowcapacitydropdata(Fig.11)Basedonimplanted15,000degradationfailureratepatternoftheengine.Iftheregressionmodelisstillfit,thenewobservationpointsdistributenormallyaroundthelinearregressionline.Fig.12showstheSignificanceLevelsofcompressorefficiencyandcompressorflowcapacitydegradationderivedfromtheS–Wtestsfromthebeginningofoperationuntil25,000hofoperation,respectively.TheSignificanceLevelforcompressorflowcapacityandcompressorisentropicefficiencydegradationdecreasesovertime.After22,500h,thesignificantdecreaseintheSignificanceLe-velforboththecompressorefficiencyandflowcapacitydropsbe-lowpre-definedthreshold0.2indicatingthatthefailureratepatternhaschangedfromaconstantfailureratetoanincreasingfailurerate.Fig.13showstheSkewnessfromthebeginningofoperationun-til25,000hofoperation.ItshowsthattheabsolutevalueoftheSkewnessforcompressorflowcapacityandcompressorisentropicefficiencydegradationincreasesovertime.However,thelevelofincreaseoftheSkewnessinthecompressorefficiencydegradationdataisnotassignificantasthatofthecompressorflowcapacitydegradationdata;thismaybeduetolargescatteringofthecom-pressorefficiencydegradationdatashowninFig.8.ThecontinuousincreaseintheabsolutevalueoftheSkewnessLevelindicatesthestatusofincompatibilityofnormaldistributionofdegradationdataandsuggeststhatthelinearregressionmodeldoesnotfitthedataanymoreafter22,000–25,000hofoperationwhentheSkewnessincreasesignificantly.BasedonboththeSkewnessandtheSignificanceLevelanalysis,itcanbeconcludedthatthefailureratepatternhaschangedfrom10.90.8EfficiencyFlow Capacityleve0.7L e0.6cn0.5ac0.4ifin0.3gi0.2S0.1010000 12500 15000 17500 20000 22500 25000Operating time (hrs)Fig.12.Significancelevelofcompressorefficiencyandflowcapacitydegradationduringengineoperation.1.21EfficiencyFlow Capacity0.8s0.6sen0.4we0.2kS0-0.210000 12500 15000 17500 20000 22500 25000-0.4-0.6Operating time (hrs)Fig.13.Skewnesslevelsofcompressorefficiencyandflowcapacitydegradationduringengineoperation.2160Y.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–2161constanttoincreasingratepatternatsomepointwithintherangeof22,500–25,000hofoperation.Therefore,thequadraticregres-sionmodelshouldbeusedtoreplacethelinearregressionmodelforfurtherprognosticpredictionafteraround22,500hofoperation.3.5.ApplyingquadraticregressionforprognosticanalysisBasedonpreviousanalysis,theenginehealthprognosticanaly-sisiscarriedoutusingthequadraticregressionmodelfrom22,500hofoperationonwards.Figs.14and15showanexampleofapplyingthequadraticregressionmodeltothedataofcompres-sorefficiencyandflowcapacitydegradationwhenitisassumedthat22,500hofoperationiscurrenttimeandthatthelast30datapointsbeforethecurrenttimeareusedtoproducetheregressionlines.Similartothepracticeusinglinearregressionmodel,theremainingengineusefullifecanbeestimatedaccordingly.InFig.14wherefuturedegradationofcompressorefficiencyispre-dicted,tpisaround26,000handtuaround33,500h.Thepredictedremainingusefullifefortheenginebasedonthecompressoreffi-ciencydataisroughlybetween3500and11,000h.SimilarlyinFig.15wherefuturedegradationofcompressorflowcapacityispredicted,tpisaround29,500handtuaround35,000h.Therefore,thepredictedremainingusefullifeoftheenginebasedontheflowcapacitydataisroughlybetween7000and12,500h.Acomparison1.0)0.0%( p-1.00 10000 20000 30000 40000ord-2.0 ycn-3.0eic-4.0iffE-5.0tp = 26,000 tu = 33,500 -6.0Operating time (hrs)ImplantedPredicted healthHistorical DataLower bound of predicted healthFig.14.Quadraticregressiontoscattereddataofcompressorefficiencyat22,500h.1.0)%0.0( p-1.00 10000 20000 30000 40000ord-2.0 yt-3.0ica-4.0pac-5.0tp = 29,500 hrs wo-6.0lF-7.0tu= 35,000 hrs-8.0Operating time (hrs)ImplantedPredicted healthHistorical DataLower bound of predicted healthFig.15.Quadraticregressiontoscattereddataofcompressorflowcapacitydropat22,500h.Table4

Predictedremainingengineusefullifeat22,500hofoperation.

Remainingengineusefullifeat22,500hofoperationPessimisticpredictionPredictionwithconsideringprognosticquadraticregressionuncertainty(tpÀ22,500)model(tuÀ22,500)Fromcompressor350011,000efficiencydropdata(Fig.14)Fromcompressor700012,500flowcapacitydropdata(Fig.15)Basedonimplanted7500degradationofthepredictedremainingusefullivestogetherwiththeim-plantedremainingusefullifeisshowninTable4.ThepredictionofremainingengineusefullivesfrombothFigs.14and15arefoundtobesatisfactory,asinbothcasestheim-plantedfailurepointiswellbetweenthepredictedfailurepointsusingthequadraticregressionmodelandthelowerboundofprog-nosticuncertainty,Table4.However,thepredictionbasedonthecompressorflowcapacitydataprovidesanarroweruncertaintyintervalthanthatbasedonthecompressorefficiencydatabecauseofdifferentlevelsofscatteringofthedataresultedfromthediag-nosticanalysisusingtheGPAanalysis.Moreconservedpredictionoftheremainingusefullifeisfromtheresultbasedonthecom-pressorefficiencydegradationdataduetoitsbiggerdatascattering.Theabovediagnosticandprognosticanalysisshouldbecarriedoutcontinuouslyduringengineoperationandthepredictedengineremainingusefullifeshouldbeupdatedwhennewgaspathmea-surementsandnewpredictedenginehealthdataareavailable.However,suchprognosticinformationcanbeusedasextrausefulinformationforgasturbineoperatorsfortheirmaintenanceplan-ninganddecisionmakingtodefinemoreaccuratetimeforplantshutdowns,schedulingofmaintenanceactivities,andorderingoflonglead-timespareparts.4.ConclusionsInthisstudy,agasturbineprognosticapproachbasedonstatis-ticanalysishasbeenproposedandappliedtoamodelindustrialgasturbinesimilartoaRolls-RoyceindustrialAVONoperatingataconstantambientandoperatingconditionwithimplantedcom-pressordegradationdevelopedovertimefollowinganassumedfailureratepattern.Inthisapproach,thevaryinglinearandnon-lineardegradationpatternsthatmayhappentogasturbineen-ginesareconsideredintheprognosticanalysis.Acombinedlinearandquadraticregressionmodelisintroducedintheprognosticanalysistofitenginedegradationdataandprovidesatisfactorypredictionofenginedegradationintothefuture.Forenginedegra-dationfollowingatypicalfailureratepatternwhereaconstantfail-urerateoccursfromthebeginningofoperationfollowedbyanincreasingfailurerate,linearregressionmodelshouldbeappliedfirstandthequadraticregressionmodelshouldbeappliedatthetimewhenthechangingfailurerateoccurs.AcompatibilitycheckusingtheSignificanceLevelandtheSkewness,acriterionforthedeterminationofatransitionpointfromlineartoquadraticregres-sionmodel,isintroducedandprovedtobeusefulinengineprog-nosticanalysis.Aprognosticuncertaintymodelbasedontheestimationofthevarianceofhistoricalenginehealthdataisintro-ducedandtheprognosticuncertaintiesareconsideredintheprog-nosticanalysisinordertodeterminetheprognosticuncertaintyY.G.Li,P.Nilkitsaranont/AppliedEnergy86(2009)2152–21612161boundsandthentheengineremainingusefullife.Theapplicationoftheproposedprognosticapproachtothemodelgasturbineen-gineshowsthatthecombinedregressionmodelisabletoprovidegoodfittingtotheenginehistoricalhealthdatawithvaryingfaultpatternsandprovidesatisfactorypredictionofenginepotentialdegradationintothefuturewiththeconsiderationofprognosticuncertainties.Thetestcaseshowsthattheproposeddiagnosticandprognosticapproachhasagreatpotentialtoprovidevaluableestimationofengineremainingusefullifeandassistgasturbineusersintheircondition-basedmaintenanceactivities.AcknowledgmentsSpecialthankstoChevronThailandExplorationandProductionthatprovidedboththewonderfuleducationalopportunityforthesecondauthorandtheimportantengineinformationrequiredtocompletethisresearch.References[1]MoubrayJ.Reliability-centredmaintenance.2nded.Oxford(UK):Butterworth-Heinemann;1997.[2]HaubGL,HauheWE.Fieldevaluationofon-linecompressorcleaninginheavydutyindustrialgasturbines.ASME90-GT-107;1990.[3]Meher-HomjiCB.Gasturbineaxialcompressorfouling–aunifiedtreatmentofitseffectsdetectionandcontrol.ASMEcogen-turboconference,vol.5;1990.p.179–90.[4]PeltierRV,SwanekampRC.LM2500recoverableandnon-recoverablepowerloss.ASMEcogen-turbopowerconference,Vienna,Austria;August1995.[5]SasaharaO.JT9Dengine/modulePerformanceDeteriorationresultsfrombacktobacktesting;1986.[6]FlashberyLS,HaubGL.Measurementofcombustionturbinenon-recoverabledegradation.ASME92-GT-2;1992.[7]CrosbyJK.FactorsrelatingtodeteriorationbasedonRolls-RoyceRB211inserviceperformance.TurbomachinPerformDeteriorat1986;37:41–7.[8]SaravaramuttooHIH,MaclsaacBD.Thermodynamicmodelsforpipelinegasturbinediagnostics.ASMEJEngPower1983(October):105.[9]BrothertonT,JahnsG,JacobsJ,WroblewskiD.Prognosisoffaultingasturbineengines.In:Aerospaceconferenceproceedings,2000IEEE,vol.6;2000.p.163–71.[10]BytingtonCS,RoemerMJ,GalieT.Prognosticenhancementstodiagnosticsystemsforimprovedcondition-basedmaintenance.In:Aerospaceconferenceproceedings,2003IEEE,vol.7;2003.p.3247–55.[11]RoemerMJ,ByingtonCS,KacprzynskiGJ,VachtsevanosG.Anoverviewofselectedprognostictechnologieswithapplicationtoenginehealthmanagement.ASMEGT2006-90677;2006.[12]DePoldHR,GassFD.Theapplicationofexpertsystemsandneural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