A data-driven approach for predicting long-term degradation of a fleet of micro gas turbines

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ContentslistsavailableatScienceDirect

Energy

and

AI

journalhomepage:www.elsevier.com/locate/egyai

A

data-driven

approach

for

predicting

long-term

degradation

of

a

ﬂeet

of

micro

gas

turbines

Tomas

Olsson

a,∗

_,

_Enislay

_Ramentol

b

_,

_Moksadur

_Rahman

c

_,

_Mark

_Oostveen

d

_,

Konstantinos

Kyprianidis

c

a Division Digital Systems, Industrial Systems, RISE Research Institutes of Sweden, Stora Gatan 36, Västerås 722 12, Sweden

b Department of Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, Kaiserslautern 67663, Germany c School of Business, Society and Engineering, Mälardalen University, Västerås 721 23, Sweden

d Micro Turbine Technology B.V., Esp 310, Eindhoven 5633 AE, The Netherlands

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•Long-termdegradationofaﬂeetofmicro gasturbineswaspredictedusinganovel data-drivenmethod;

•Degradationisestimatedandpredicted withouttheneedofareferencesystem;

• Degradationof output poweris mea-suredrelativetotheidealoutputpower unaﬀectedbywear;

•Degradationwasvalidatedagainstthe referencemodelwithr>0.9forfour sys-temsandr>0.8foronesystem;

•Forecastsusingonlyrunninghoursas inputwereequallygoodorbetterfor4 of5systemscomparedtoanestimation model.

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Article history:

Received 8 December 2020

Received in revised form 27 February 2021 Accepted 1 March 2021

Available online 5 March 2021 Keywords:

Fleet monitoring Micro gas turbine Machine learning Health monitoring Predictive maintenance Power generation

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Predictivehealthmonitoringofmicrogasturbinescansignificantlyincreasetheavailabilityandreducethe operatingandmaintenancecosts.Methodsforpredictivehealthmonitoringaretypicallydevelopedfor large-scalegasturbinesandhaveoftenfocusedonsinglesystems.Inanefforttoenablefleet-levelhealthmonitoring ofmicrogasturbines,thisworkpresentsanoveldata-drivenapproachforpredictingsystemdegradationover time.Theapproachutilisesoperationaldatafromrealinstallationsandisnotdependentondatafromareference system.Theproblemwassolvedintwostepsby:1)estimatingthedegradationfromtime-dependentvariables and2)forecastingintothefutureusingonlyrunninghours.Linearregressiontechniqueisemployedbothforthe estimationandforecastingofdegradation.Themethodwasevaluatedonfivedifferentsystemsanditisshown thattheresultisconsistent(𝑟>0.8)withanexistingmethodthatcomputescorrectedvaluesbasedondatafrom areferencesystem,andtheforecastinghadasimilarperformanceastheestimationmodelusingonlyrunning hoursasaninput.

1. Introduction

Estimatingandpredictingperformancedegradationofgasturbines isanimportantcomponentforcondition-basedmaintenancetoallow

∗ _{Corresponding}_author.

E-mailaddress:tomas.olsson@ri.se(T.Olsson).

dynamicplanningthatonlytakesactionwhenneeded[1].By know-inginadvancewhenaresourceneedstobemaintained,both unneces-sarymaintenanceactionsandunplannedstopscanbeavoidedthatin turnsavebothtimeandmoney.Twomainreasonsfortheperformance degradationofgasturbinesoverthelong-termarefoulinganderosion. Incontrast,suddenorfastfailuremechanisms,suchasbearingfailure orforeignobjectdamage,cannotbeeasilypredictedinadvanceforlong periods.Unaddressedperformancedegradationmightleadtoincreased https://doi.org/10.1016/j.egyai.2021.100064

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fuelconsumption,uneconomicaloperationandincreaseingreenhouse gasemissions[2].Theexperiencefromthecurrentusecaseisthatthe long-termdeterioration(countedover1000ormorerunninghours)is moreimportantformaintenanceplanningthantheshort-term immedi-atefailures.

Untilrecently,technologydevelopmenthaslargelybeenfocusingon thehealthmonitoringofsingleandlarge-scalegasturbines.Incontrast, weenvisionafuturewheredistributedfleetsofmicrogasturbineswill gainimportancewhenconnectedandmanagedtogetherinagrid[3]. Themicrogasturbinesaremeanttobeinstalledin,forinstance,large housesmulti-familyhomes,offices,schools,andhistoricbuildings.The targetistoreplaceothermeansofproducingenergylocally,suchas, us-ingcoalorotherfossilfuels.Inthescenarioofthispaper,theturbines aretypicallysituatedindifferentgeographicallocationswithvarying workingconditionsforparameterssuchastheambientpressure, hu-midity,andoutdoortemperature.Atypicalmicrogasturbine would generatelessthan100kWandinordertokeepthecostdown, prefer-ablybebuiltoutofoff-the-shelfcomponents(COTS)fromthe automo-tiveindustry[3,4].However,usingoff-the-shelfpartscanalsoleadto greaterperformancevariationbetweenindividualgasturbines,which inturnmakesithardertodetecthealth-relatedproblems.Inaddition tothat,thesmallsizeandlowcostalsomeanthatthenumberof avail-ablesensorsisalsolimitedandaddingnewsensorsmustbemotivated byverylargeperformanceoreconomicgains.Therefore,eachgas tur-binemustbeindividuallymonitoredusingalimitednumberofsensor signals.

Thispaperpresentsanoveldata-drivenpredictivemaintenance ap-proachthat estimatesandforecastslong-termindividualunit perfor-mancedegradationforaﬂeetofmicrogasturbinesusingonlythe avail-ablesensors.Thepaperisorganisedasfollows.First,wepresentrelated workwithincondition-basedmaintenanceformicrogasturbines.Next, wedescribethestudiedmicroturbinein detailincludingother back-groundknowledgeneededtounderstandthiswork.Followingthat,we deﬁnetheproblemthatwesolve,andthedatausedinthiswork. There-after,wepresentthedata-drivendegradationmodelanddescribethe developedforecastmodel.Finally,weevaluatethemethodsanddraw someconclusionsinthelastsections.

2. Literaturereview

TheriseofIndustry4.0– thefourthindustrialrevolution– andthe well-knownIoT(InternetofThings)haveallowedtheevolutionof data-drivenmodelsforpredictingmaintenanceanddegradationinindustry. TheheartofIndustry4.0isintelligentmachinesthatshareinformation

witheach other,organizeandworktogethertocoordinate processes anddeadlines[5].

Intheconsultedliterature[6–8],wehavefoundthatmanyauthors agreethattocarryoutpredictivemaintenanceinIndustry4.0,ﬁve com-ponentsarerequired:

1. Sensors:fordatacollection,sensorsmustbe installedinphysical machines;

2. Data communication: allowsdata toﬂow securely betweenthe monitoredassetandthecentraldatastore;

3. Centraldatastore:iswherethedataisstored(canbeon-premises orinthecloud),processed,andanalysed;

4. Predictiveanalytics:predictiveanalyticalgorithmsareappliedin ordertoﬁndpatternsandgenerateusefulinformationfordecision support;

5. Rootcauseanalysis:toolsfordataanalysisareusedbyspecialists andengineerswiththeaimtodeterminecorrectiveactiontotake. Consideringthatinourcasestudycomponents1,2and3arealready available,wewillfocusonsolutionsforcomponents4and5.Thus,in this section,wewillstudythemost signiﬁcantmodelsforpredicting degradation andmaintenancewithin thecurrent state-of-the-art.We willfocusonthoseapplicationsrelatedtomGT(MicroGasTurbine), butwewillalsostudyotherdegradation andmaintenancemodelsto betterunderstandtheproblem.

Inrecentyearstherehasbeenanincreaseinapplicationsand pub-licationsforthediagnosisofmGT.ThereasonisthemGThasemerged as”energyconversiontechnology,whichofferspromisingfeatureslike highfuelflexibility,lowemissionslevel,andefficientco-generationof heatandpower”[9].

Theavailableapproachescanbedividedinthreegroups[10]: • Data-drivenapproaches

• Model-basedapproaches • Hybridapproaches.

Fig.1 showsthethreecategoriesoftheapproachesforPDD (Prog-nostics,Diagnostics,Degradation).

A goodexampleof amodel-basedscheme wasproposed in[11], wheretheauthorsmodeledacombinedheatandpowersystembasedon anmGT,focusingonlyonthefaultidentiﬁcationlevel.Theyproposeda four-stepschemewhereintheﬁrsttwosteps,called”Adaptation”,they simulatedthepreliminaryindicationaboutfaultlocationandmagnitude usingasinputtheactualconditionmeasuredandtheexpected perfor-manceattheISA(InternationalStandardAtmosphere).Inthethirdstep, theycomputed”Exchangerates” havingasinputsthesimulatedoutput

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fromthepreviousstepandtheISAreferencecondition.Finally,instep 4,themaximumcorrelationbetweenengineexchangeratesandthe sig-naturesfromthedatabase1_is_computed_and_the_possible_fault_location

anditsmagnitudeareestimated.

Areviewofthemainreliabilityestimationmodelsbasedon degra-dationwaspublishedrecentlyin[12].Theauthorsreviewedthemost commonly applied deterministic and stochastic degradation models in thestate-of-art andexplainin detail aroadmap for adoptingthe degradation-basedreliabilityestimationmodelsbasedontheconcept oftheIIoT(IndustrialInternetofThings).

Anotherreviewwaspresentedin[2].Theauthorspresentedadeep studyaboutthemostrepresentativetechniquesinthestate-of-the-artfor conditionmonitoring,diagnostic,andprognostic.Theyreviewedmostly thosediagnostic/prognostictechniquesthatuseperformance parame-tersobtainedfromtheoperatingsystemsofgasturbines.Allthelisted techniquesweredividedintothefollowingcategories:

• Onlinemonitoring

• Performanceparameters • Non-performancesymptoms • Oﬄinemonitoring.

Theauthorsalsolistedthemostcommonlyusedperformance param-etersdividedintomeasurableonesandcalculableones,providinguseful explanationsabouteachone.Thepaper[2]presentedthemostrelevant andrecentresearchinthearea;itcanbeconsideredasacomprehensive handbookofmonitoring,diagnostics,andprognosticsforGT.Fentaye etal.[13] thoroughlyreviewedtheavailablegasturbinefault diagnos-ticmethods,summarisedtheirstrengthsandweaknesses,andnotedthe challengesandfutureresearchdirectionsinacomprehensiveway. Par-ticularlytheauthorshighlightedtherecenteﬀortsonAI(Artiﬁcial In-telligence)methodsduetotheirremarkablecapabilityofhandlingthe currentchallengesandmeetthemajorityofthedesirableattributes.

MachinelearninghasproventobeaneffectivetoolforPDD[14,15]. Adeeplearningapproachforanomalydetectioningasturbine combus-torswasproposedin[16].Thisapproachisnotexactlyamaintenance predictionapproach,ratherananomalydetectionapproachthatearly detectsabnormalbehavioursandincipientfault.Theauthorsintroduced adeeplearningapproachforthecombustoranomalydetection.Inafirst step,theylearnedfeaturesfromthesensormeasurementsofexhaustgas temperaturesandthentheyusedthelearnedfeaturesastheinputtoa neuralnetworkclassifierforperforminganomalydetectioninthe com-bustor.

Amethodologyforgasturbinepathanalysiswaspresentedin[17], wheretheauthorusedartiﬁcialneuralnetworkstodetect,isolate,and evaluatefailures duringthe operatingconditions. Thepresented ap-proachusedasinputseveralmeasurementsovertheenginegivingas outputthevariationsofcomponentcharacteristicsandtheﬂowrate.

Asetofmachinelearningtechniquesforgasturbinediagnosticswas evaluatedin[18].Inthepaper,theyevaluatedtheuseofSVM(Support VectorMachine)andthreetypesofANN(ArtificialNeuralNetworks) forgaspathdiagnosticsinaclassificationtask.Thepaperproposedan algorithmforvariablesclassificationallowingavery flexiblewayto changeelementslikeforexampletypeofclassused,patternnumbers, faultseverity,classquantity,etc.Thisalgorithmcreated12fault classifi-cations,thattheauthorsthenusedtostudytheinfluenceofclassification structureonthefinaldiagnosticaccuracy.

Fentaye et al. [19] combined adaptive gas path analysis and a Bayesiannetworktoassessthehealthstatusofgasturbines.Zaccaria etal.[20] studiedahybridapproachforreal-timefaultdiagnosticsof gasturbinesbycombiningaBayesiannetworkwithcorrelationanalysis. Thehybridmethoddemonstratedsuperiorperformancewith94%and 96%correctisolationratesinpresenceofengine-to-enginevariations andoperationalvariationsrespectively.

1 _Inventory_of_faults_obtained_by_simulating_diﬀerent_component_faults.

Fig.2. TypicallayoutofmicrogasturbineinCHPconﬁguration[11].

Fig.3. MTT’smicrogasturbineassembly[25].

3. Preliminaries

Inthissection,weprovidethepreliminariesthatmaketherestofour paperself-contained.First,weprovideabriefintroductiontothe stud-iedmGTanditsmainfeaturesandfunctionalities.Next,weprovidean introductiontolineardegradationanditsrelevancetoourresearch. Fi-nally,wetakealookatregularisedregression,whichisanintroduction tothebasisforunderstandingthedata-drivenmethodwewilldescribe laterinthepaper.

3.1. Themicrogasturbine

Microgasturbinesaresmallscalegasturbineswithpoweroutput rangingfromafewkWetoover500kWe[21].Thedownsizing nega-tivelyaffectsthepoweroutput,electricalefficiency,andthecapitalcost [22].However,italsoleadstonumerousbenefitssuchascompactsize, lowweightperunitpower,simpleoperability,highfuelflexibility,low maintenanceandlowerlevelofemission[23].Similartothelarge-scale gasturbine,mGTalsooperatesontheverywell-knownBraytoncycle. InasimpleBraytoncycle,theairiscompressedinacompressor.Theair isthenmixedwithfuelandburnedinacombustorunderapproximately constantpressure.Theresultinghotgasesareexpandedinaturbinethat

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Fig.4. PeismeasuredandPe_coriscorrectedpower,andenginereplacementindicatesstartofcurrentlyinstalledenginelife.

drivesthecompressorandthehigh-speedgenerator.InmGTs,a recuper-atorisgenerallyfittedaftertheturbinetopre-heatcompressedairprior tocombustion,inordertoreducefuelconsumptionandthusimprove cycleefficiency.Moreover,oftenexhaustheatisrecoveredbyusinga boilerthatresultsinhighthermalefficiency[24].Atypicallayoutof anmGTinCHP(CombinedHeatandPower)configurationisshownin Fig.2.

TheEnerTwinis acommercialmGTbasedmicro-CHPthatis the focusofthestudypresentedinthispaper.ThemGTunithasbeen de-velopedtodeliver3.2kWelectrical powerand15kWthermalpower. Thethermalpowerisintendedtobeusedforheatingandhottap wa-terusage.TheuniquefeatureofmGTunitisthatitisbasedonCOTS (CommercialOﬀ-The-Shelf)automotiveturbochargertechnology.The turbomachineryassemblyofanEnerTwinsystemispresentedinFig.3. AppendixAcontainsmoredetailsfortheEnerTwinsystemandthe sup-plierprovidedmaintenanceintervals.

3.2. Lineardegradation

Likeanyotherphysicalassets,theperformanceofgasturbines de-grades overtimeandshows adistinct degradationpattern andrate. Typically,degradationoftheentireengineisjustasummationofits individualcomponentdegradation.Eachcomponentdegradesata dif-ferentrateandfollowsacertaindegradationpattern.Thisdegradation canbeclassiﬁedasrecoverableandnonrecoverabledegradation.

Recoverabledegradationis performancedropsthat canbe recov-eredbyoperationalprocedures withouttheneedformajorrepairor hardwarereplacement.Contrarily,nonrecoverabledegradationis per-formancedropsthatcannotberecoveredwithoutmajorrepairor re-placementofaﬀectedcomponents[26].Typically,thisdegradation re-sultsinincreasedtipclearance,changeinbladegeometryandsurface roughness,whichinturnleadstoareductioninpoweroutputandarise inthermalenergylosses[27].

Accordingto Zagorowskaet al. [28], thenonrecoverable perfor-mancedegradationofgasturbinesisevidentlylinearinnature.Among recoverabledegradation,foulingalsoshowsnearlylinearperformance deteriorationofengineovertime[29].Still,thediagnosticsresearch communityhasyettoreachaconsensusregardingthelinearityof degra-dationsingasturbines.InBrothertonetal.[30],thegasturbine degra-dationmodeisclaimedtohavearecedings-shape.Saravaramuttooand Maclsaac[31]arguedtheratesofdegradationforgasturbinesarerarely knownandnotlikelytobelinear.Additionally,everygasturbine de-signwillshowadiﬀerentbehaviour,whichwillalsobeaﬀected fur-therbywherethegasturbineisoperated(i.e.,dust,environment,etc.) andhowharshlyitisoperated (i.e.,start-stop cycle,loadchange be-haviour,controlstrategies,etc.).EscherandSingh[32]andLiandSingh [33] claimedthedegradationsingasturbinesarenonlinearinnature anddevelopedanon-linearGPAbaseddiagnosticapproach.However, manyresearchersconsideredlineardegradationofgasturbinestobe

areasonableassumptionwhiledevelopingdiagnosticsandprognostics methods.PugginaandVenturini[34] consideredgasturbine degrada-tionasalinearfunctionoftime.TsoutsanisandMeskin[35] assumed degradationwasmonotonicallyincreasingandemployedamoving win-dowapproachforgasturbineperformanceprognosticsby approximat-ing degradation tobe locally linearwithin each window.Mahmood etal.[36]simulatedtheleakagefromtherecuperatoroutlettothe am-bientandittobe linearinnature.Later,Kimetal.[37] studiedthe inﬂuenceofinternalleakageonamicrogasturbineperformanceand foundthattheeﬀectisalmostlinearataconstantspeed.

3.3. Regularisedregression

Supervisedmachinelearningistheproblemoffindingafunction 𝑓(⃗𝑥)sothatforobservations⃗𝑥,𝑦wehave𝑦=𝑓(⃗𝑥)+𝑒where𝑒isasmall error.Wewilluse ̂𝑦todenotethepredicted𝑦sothat ̂𝑦=𝑓(⃗𝑥).Inmost cases,acertainfamilyoffunctionsisselectedwhere𝑓 isparameterised withparameters𝑤⃗sothat ̂𝑦=𝑓(⃗𝑥;𝑤⃗).Thefunction𝑓 canbeboth non-linearandlinear,wherenon-linearfunctionscanbeanarbitrary func-tionforinstanceanartificialneuralnetwork[38].Thentheproblemis tofind𝑤⃗inordertohaveasmallerrorbetween𝑦and𝑓(⃗𝑥;𝑤⃗).

Inthisworkwewillonlyconsiderlinearfunctions.Ifthefunctionis linearsothat𝑓(⃗𝑥;𝑤⃗)=⃗𝑥𝑇 𝑤⃗(withcolumnvectors),andtheerroristhe 𝑙2-norm,then– givenindependentandidenticallydistributed observa-tions– wegetlinearregression,whichminimisesthebelowerror[39]: ∑

𝑖

(𝑦_𝑖−⃗𝑥𝑇 _𝑖𝑤⃗)2 (1)

wheresumover𝑖isforallobservationof⃗𝑥_𝑖,𝑦_𝑖.

Inordertoimprovethegeneralisingpoweroftheabovemodel,and toavoidoverfittingthetrainingdata,itisalsopossibletoguidethefitby puttingmoreorlessweighttothedifferentvariablesin⃗𝑥byconstraining thecorrespondingcoefficientsin𝑤⃗tobeclosertozero.Thiscanbedone withregularisation,thatis,alossisaddedtoEq.(1)byforinstanceusing the𝑙2-norm: ∑ 𝑖 (𝑦_𝑖−⃗𝑥𝑇 _𝑖𝑤⃗)2+𝐶×∑ 𝑗 | ⃗𝑤𝑖 | 2 ₍₂₎

where𝐶 isaweighthatisusuallyselectedusingcross-validation.By usingcross-validation,itisensuredthattheresultingmodelgeneralises tootherdatathanthetrainingdataandthus,overﬁttingcanbeavoided. Theabovetypeofregularisedlinearregressioniscalledridgeregression whileincaseofusing𝑙1-norm,itiscalledlassoregression[40]: ∑

𝑖

(𝑦_𝑖−⃗𝑥𝑇 _𝑖𝑤⃗)2+𝐶×∑ 𝑗 | ⃗𝑤𝑖 |

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Table1

Thedatausedinthisworkincludingmeasuredvariablesandsetpoints(emphasised).

Variables Parameters Unit/type

Predicted variable ( 𝑦 ) - (Net electric) output power Watts

Ambient variables ( ⃗𝑥 )

- Measured return water temperature Kelvin

- Inlet air temperature Kelvin

- Ambient pressure bar

- Ambient pressure at stand still a _bar

- Measured turbine speed rpm

- Turbine rotational speed set point rpm - The internal set point for desired code speed and turbine exit temperature

- Ambient pressure is missing b _dummy

Time dependent variables - Total number of running hours hours affecting the degradation trend ( ⃗𝑡 ) - Total number of starts and stops frequency count Maintenance actions ( 𝑀) - Total number of running hours _{when action was taken} hours The ideal output power - Net electric output power during c _Watts

per system ( 𝑘 ) installation

a _The_pressure_is_only_measured_at_standstill,_so_it_is_not_measured_{continuously.}_It_was_originally_used_as_a

replacementinthereferencemodelwhentheambientpressureismissing.

b _In_order_to_handle_missing_values_of_the_ambient_pressure_variable,_we_add_a_dummy_variable_that_is₁_when

thevariableismissingand0whenitispresent.Thus,weestimateareplacementvalueforthemissingvalue.

c _The_ideal_output_power_is_measured_at_installation_and_corresponds_to_the_output_power_generated_without

degradation.However,theambientconditionscouldnotbecontrolledsothereisasourceoferrorinthisestimate.

as,gradientdescent.Manydeeplearningframeworkssupportgradient descentformanypossibletypesofconstraintsandregularisations.In thiswork,weusetwodeeplearninglibrariesKeras[41] togetherwith Tensorflow[42]. Thetwolibrariesformagenericapproachtousing gradientdescenttofitanyartificialneuralnetwork,includingsimple linearregression.

4. Problemdeﬁnitionanddata

Inthissectionweﬁrstdeﬁneourproblemandourgoal.Secondly, wedescribethedatausedinthiswork.

4.1. Problemdeﬁnition

Thegoalofthisworkwastomeasureandpredictthedegradationof aﬂeetofmGTsbeforeactionneedstobetaken.Theproblemisthatthere isnoexplicitmeasurementofthedegradation,whichtherefore some-howmustbeestimated.Thecurrentapproachtoestimatingdegradation usesalinearmodelforcomputingcorrectedvalues,whichwascreated usingdatafromareferencesystem.Therelationusedtocomputethe correctedpoweris:

𝑃𝑒 _𝑐𝑜𝑟 =𝑃𝑒 −𝑎∗(𝑇𝑟𝑒𝑓 −𝑇𝑟𝑒𝑡 )−𝑏∗(𝑇𝑖𝑠𝑎 −𝑇0)+𝑐∗(𝑝𝑖𝑠𝑎 −𝑝0)+𝑑∗(𝑁𝑟𝑒𝑓 −𝑁1)

where𝑃_𝑒istheoutputpower,𝑇_𝑟𝑒𝑡and𝑇_𝑟𝑒𝑓arethereturntemperature anditsreferencevaluerespectively,𝑇0and𝑇𝑖𝑠𝑎 aretheinlet

tempera-tureanditsISAreferencevaluerespectively,𝑝0and𝑝𝑖𝑠𝑎 aretheambient

pressureanditsISAreferencevaluerespectively,𝑁1and𝑁𝑟𝑒𝑓 arethe

turbinerotationalspeedanditsreferencevaluerespectively,whilethe constantsa,b,canddareeitherempiricallydeterminedordeﬁnedby modelling.Fig.4showsanexampleofthecurrentapproachwhere yel-lowcurveshowsthecorrectedpower,whichisnotverysmooth.The downwardtrendoftheyellowcurvedisusedasanindicationof degra-dation.

Thereisalsoaverylimitednumberofsensorsavailableduetothe smallscaleofthegasturbineandtheneedtokeepthecostofthe sys-temdown.Thus,wecanonlyusethefewavailablesensors.The anal-ysedsystemsarealsotestinstallationsandthesystemdesignwasstill underdevelopmentatthetimewhenthedatawascollected.Thus,an additionalcomplicatingfactoristhatthereisalimitednumberof sys-temsandnotmanyfailures.So,itisnotpossibletouseatraditional

supervisedmachinelearningapproachtolearnwhenasystemfails.Yet anotherissueisthattheeﬀectofanexecutedmaintenanceactionisnot knownandthus,the“state” ofthedegradationisunknownaftersuch anaction.Thedesigngoalsofthedata-drivendegradationmodelare thereforeto:

1. Estimatethedegradationdue towearrelativetotheidealoutput powerwhentherearenolossesorvariationsduetoambient vari-ablessuchasweatherconditions;

2. Estimate degradation much more smoothly thanthe current ap-proach;

3. Makeiteasytosetagenericthresholdforwhenasystemshouldbe maintained;

4. Removetheneedforareferencesystemandonlyusedatafromthe realsystems;

5. Predict thedegradationin thefutureso itis possibletoplanfor maintenanceactionsinadvance.

In order to make long-term predictions, we assume approxi-matelylineardegradation,whichisalsoinlinewiththediscussionin Section3.2.

4.2. Data

ThedatausedinthisworkcomesfromﬁvediﬀerentmicroCHP sys-temswithidentities:I,II,III,IV,andV.Thedataweresampledevery minute,butwehaveusedonlyeverysecondhoursample,whichwas deemedtobeenoughforthepurposeofthiswork.Weusethe parame-terslistedinTable1 thatwereselectedfromexperience,includingthe parametersusedtocomputethecorrectedvaluesusing thereference model(seeSection4.1)andparametersthathavebeenprovenusefulin predictingtheoutputpower.

Theseparametersarechosenduetotheirimportanceinthisspecific usecasethatmightdifferfromwhatistypicalforlargergasturbines.For instance,becausethebearinghousingontheturbinesideiscooledwith wateranddependingonthereturnwatertemperature,moreorlessheat isextractedfromthegaspatharoundtheturbine.Then,sincetheturbine outlettemperatureisacontrolledtemperatureandremainsconstantfor thesameoperatingpoint,changesinthereturnwatertemperatureresult in achangeofheatextractionandthusinturbineinlettemperature. Then,thetemperaturedropovertheturbinestronglyaffectstheturbine

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Fig.5. SystemI.

outputpower,andtherefore,thereturnwatertemperatureneedstobe takenintoaccount.

5. Method:Data-drivendegradationmodel

Inordertosolvetheproblem,wedividetheproblemintotwo sub-problemsthataresolvedinsequence;oneforestimatingdegradation fromdataandanotherforforecastingfuturedegradationonlybasedon runninghours.Next,wedescribethesolutionstothetwosub-problems. 5.1. DegradationEstimation

Let ybe theoutput power, ⃗𝑥be a column vectorwith the mea-suredambientparametersliketemperature,pressure,etc.,⃗𝑡be a col-umnvectorwithtimedependentvariables,𝑛and𝑚arethenumbersof systemsandmaintenanceperiods(thatis,theperiodbetweentwo

main-tenanceactionsorsincesysteminstallation)respectively,and1≤𝑖≤𝑛 and1≤𝑗≤𝑚denoteaspecificsystemandaspecificmaintenance pe-riodrespectively.Thenwedefinethegenericmodelofdegradationas follows:

𝑦=𝑘_𝑖+𝑔(⃗𝑥)+𝑒(⃗𝑡;𝑖,𝑗) (4)

where𝑘𝑖 isaknownconstantwhichrepresentstheidealoutputpower foraspeciﬁcsystem𝑖,function𝑔 istheeﬀectof ⃗𝑥onthepowerand function𝑒isthedegradationovertimeduetowearofsystem𝑖in main-tenanceperiod𝑗.Thus,inthemodel,wesplitthesignalintotwo com-ponents:thevariationduetoambientconditionsandthedegradation trendduetotimedependentvariables.Inaddition,weassumea com-monbehaviourfortheambientvariableswhilethedegreeof degrada-tiondependsbothontheindividualsystemandthemaintenanceperiod.

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Fig.6.SystemII.

Alsolet:

𝑓(⃗𝑡;𝑖,𝑗)=−𝑒(⃗𝑡;𝑖,𝑗)

𝑘𝑖 (5)

be the normalised degradation over time 0≤𝑓(⃗𝑡;𝑖,𝑗)≤1 where 𝑓(⃗𝑡;𝑖,𝑗)=0meansthatthereisnodegradation.Thismeansthatwecan rewriteEq.4asfollows:

𝑦−𝑔(⃗𝑥)=𝑘_𝑖(1−𝑓(⃗𝑡;𝑖,𝑗)) (6)

wherethediﬀerencebetweenactualoutputpower𝑦andthepower ex-plainedbytheambientvariables𝑔(⃗𝑥)isequaltotheidealoutputpower 𝑘𝑖 multipliedbytheeﬀectofthedegradation.

Now,wecanselectathresholdforwhenmaintenanceshouldbedone asforinstance:

If𝑓(⃗𝑡)>0.25thenperformacorrectivemaintenanceaction

Noticethatselectingathresholdisnotastraightforwardproblem tosolve.Itinvolvesweighinginmanyfactors,suchas,electricityprice, gasprice,subsidies,replacementcost,typeofmaintenancecontract,age ofthesystem,expectedremaininglifeandcustomerexpectations.We assumeitcanbeselectedusingexpertknowledge,buttheproblemwill notbeaddressedfurtherinthispaper.

Let’sassumealinearmodelforfunctionsgandesothatthefollowing holds:

𝑔(⃗𝑥)= ⃗𝑐𝑇 ⃗𝑥

𝑒(⃗𝑡;𝑖,𝑗)= 𝑎_𝑖+𝑏_𝑗+𝑒⃗0𝑇 ⃗𝑡+⃗𝑒𝑖 𝑇 ⃗𝑡

(7) where⃗𝑐isacolumnvectorwithweightsexplainingthevariationdueto ambientconditionswhile𝑎_𝑖and𝑏_𝑗indicatetheremainingdegradation atthemeasurementstartorafteramaintenanceactionpersystem𝑖and maintenanceperiod𝑗 respectively,and⃗𝑒0and⃗𝑒𝑖 arecolumnvectorswith

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Fig.7. SystemIII.

theindividualsystemsrespectively.Puttingitalltogether,Eq.4canbe formulatedinmatrixformasfollows:

⃗𝑦=⃗𝑘𝑇 𝑆+⃗𝑎𝑇 𝑆+⃗𝑏𝑇 𝑀+⃗𝑐𝑇 𝑋+⃗𝑒𝑇 𝑇 (8)

where:

• _⃗𝑦isacolumnvectorwithallpowermeasurements;

• _{𝑋 is}amatrixwithallambientvariablemeasurements⃗𝑥ascolumns; • ⃗𝑘isacolumnvectorwithallknown𝑘𝑖 ;

• _⃗𝑎isacolumnvectorwithall𝑎𝑖 ; • ⃗𝑏isacolumnvectorwithall𝑏𝑗 ;

• _⃗𝑐isacolumn vectorwithweightsexplainingthevariationdueto ambientvariables;

• _⃗𝑒isacolumnvectorwithacombinationof⃗𝑒0andall⃗𝑒𝑖 sothat⃗𝑒=[⃗𝑒0, ⃗

𝑒1𝑇 ,𝑒⃗2𝑇 ,…𝑒⃗𝑛 𝑇 ]𝑇 ;

• _{𝑆 is}amatrixwithdummyvariablesforallsystemssoeachcolumn correspondstoasystemandeachcolumnisﬁlledwithzerosexcept oneelementthatissettooneindicatingthesystem;

• 𝑀 isamatrixwithdummyvariablesforallmaintenanceperiods; • _𝑇 isamatrixwhereeachcolumnisoflength(1+𝑛)×lengthof⃗𝑡,

startingwith⃗𝑡(correspondingto⃗𝑒0),thenfollowedbythezero

vec-tors⃗0andanother⃗𝑡(correspondingtoaspeciﬁcsystem’s ⃗𝑒𝑖 ).For example,[⃗𝑡,⃗0,…,⃗0,⃗𝑡,⃗0,… ⃗0].Thus,therearetwo⃗𝑡and𝑛−1zero vectorspercolumn.

Noticethatwewillrunintoproblemsifwenaivelyuseanordinary leastsquaresolutiontotheEq.8,andwecanendupwithasolutionfar fromexpected.Thus,weneedtoconstrainthenumberofpossible solu-tionsusingpriorknowledgeencodedasregularisationsandconstraints. Forinstance,weneedtoconsiderthatthevarianceinthemodelshould bemostlyexplainedbytheambientvariablesandthevariables aﬀect-ingdegradation,andnottheremainingdegradationforasystemora

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Fig.8. SystemIV.

maintenanceperiod.Ifwearenotcareful,wewillendupinapiece-wise linearsolutionwithslopesclosetozerowherethevarianceismostly ex-plainedbytheremainingdegradationvariables.Therefore,weproceed byaddingan𝑙1regularisationontheremainingdegradationcoeﬃcients in ⃗𝑎and⃗𝑏tominimisetheexplainedvarianceandforcetheirweights closertozero.Also,weassumethatthedegradationismonotonicwith respecttothetimedependentvariablesunlessthereisaneﬀectofthe maintenanceactionssothatthe⃗𝑒≥⃗0.Thecodeforimplementingthe solutiontotheEq.8,with𝑙1regularisationonlyon⃗𝑎and⃗𝑏isshownin AppendixB.

5.2. Degradationforecasting

Formakingtheforecastofthedegradationweassumealinearmodel thatrelatestheestimatednormaliseddegradationtothenumberof

run-ninghours(ℎ):

𝑓(⃗𝑡;𝑖,𝑗)=𝛽_𝑖,𝑗+𝛾_𝑖ℎ (9)

where𝛽𝑖,𝑗 areweightsﬁttedtoasystemandamaintenanceperiod re-spectivelywhile𝛾𝑖 istheslopeforasystem.Thus,dependingonwhich system andwhich maintenance period, itis possible toforecast the degradationforalargenumberofrunninghoursinthefuture. How-ever,thisrequiresthatthemodelsareupdatedforeachnew main-tenanceperiod.

Furthermore,weﬁttedtheabovemodeltothedatausingtheridge regressionimplementationofscikit-learnPythonlibrary2_where_the

reg-ularisationtermwasselectedusing5-foldcross-validation.Themodel wasﬁttedtoeachindividualsystemindependentlyofeachother.In

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Fig.9.SystemV.

dition,inordertotakemorerecentdatapointsmoreimportantthan olddatapoints,weusedtherunninghoursplusthemeannumberof runninghoursassampleweights.Inthenextsection,wewillpresent theresultfromevaluatingthemodels.

6. Resultsanddiscussion

TheproposedapproachwastestedonﬁvemGTsystems.Intheﬁrst subsectionbelow,weshowtheevaluationofthedegradation estima-tionmodel.Thisexperimentshowshowwellthemodelestimatesthe degradationintermsofcorrelationtothecorrectedpowerandtothe errorofpredictingtheoutputpower.Thesecondsectionevaluatesthe approachforforecastingthedegradation.Inthisexperiment,weshow howwelltheforecastingmodelpredictstheoutputpowerforthelast 1000runninghoursincomparisontousingtheestimationmodelwhere bothrunninghoursandnumberofstartsandstopsareknown.

6.1. Estimationmodelresults

Thebelowtable(Table2)shows,foreachsystem,thePearsonr cor-relationbetweenthenormaliseddegradationcurveandthecorrected poweraswellastherootmeansquarederror(rmse)andmeanabsolute percentageerror(mapein%)forpredictingthedata.Sinceweinthis caseareinterestedinestimatingthedegradationandnotpredictingthe outputpower,thescoringfortestdataisnotveryinteresting,butthe cross-validationrmseis318,whichisquiteabithigher.

Themostimportantresultisthecorrelationtothecorrectedpower since it conﬁrms that the estimated degradation is very similar to thedegradation trendvisible in thecorrected powerasdescribed in Section4.1.Thereportederrorsonlyindicatethatthemodel reason-ablyestimatesthepower.

TheresultfromﬁttingthemodeltotheﬁvemGTsystemsarealso showninFig.5toFig.9.Thex-axisofallcurvesisthetimeintotal

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run-Table2

Theevaluationresultforﬁttingtheestimationmodeltothedata.The

𝑟scoreisthePearsoncorrelationcoeﬃcientbetweenthecorrected powerandtheestimateddegradationwhilethetwoothercolumns areerrorsbetweentheoutputpowerandthepredictedpower.

System r rmse mape

I 0.91 81.80 2.35 II 0.95 72.13 2.20 III 0.82 71.31 1.95 IV 0.92 62.85 1.83 V 0.95 52.49 1.50 All 0.92 70.59 2.01

ninghours(𝑡).Theupperﬁrstplota)ineachﬁgureshowsthepower(𝑦) asabluecurveandpredictedpower𝑔(⃗𝑥)+𝑒(⃗𝑡)astheyellowcurvewhile maintenanceactionsareexecutedattheverticalblacklines.They-axis showsthepowerinplota),b)andd),whereplotb)showsthepredicted powerwithoutdegradation𝑓(⃗𝑡).Theplotc)showstheproposed nor-malised(negative)degradationtrendcurve-𝑓(⃗𝑡)whilethelowerplot d)showsthecurrentdegradationapproachwiththecorrected power basedondatafromareferencesystem.

Fromthetableandfigures,wecanseethattheabilitytofitand pre-dictthedataisquitegoodforallsystems,whereonlysystemIIIhas rbelow0.9, whichcanalsobe seenin Fig.7. Overall,theproposed degradationtrendcurvesaresimilarbutsmootherthanthecorrected power.Yet,intheproposedapproach,despitetheregularisation,too muchweightisoftenputonsomeofthemaintenanceperiodsinstead ofthetrendvariables.Thiscouldbemanagedbyforcinglessweight ontheremainingdegradationvariables.Consequently,therecanbe mi-normisfitsfortheremainingdegradation,whicharevisibleasasudden smallincreaseordecreaseindegradationatmaintenanceactionsthat infacthavenoeffectonthedegradation.Noticealsothatthesystems wererunninginthefieldtrialphaseduringtheevaluation.Thismeans thatissuescouldbeintroducedunintentionallyduringmaintenance.It alsomeansthatmaintenanceactionsareexecutedinadifferentway, moreoften, thanitwillbe inafully developedandfunctioning sys-tem.Forinstance,therewerevariousreasonstoreplaceornotreplace anengine,notonlycausedbydegradation.Suchasnewmaterialsthat neededtestingorendurancetestswherethelowerpowerwasaccepted. Below,weexaminetheoutputforeachsystem.Wewillonlycomment onrelativelylargechangesindegradation,sincesmallchangescanbe duetotheabovedescribedreasons.

SystemI Fig.5 showstheoutputforsystemI,whereweknowthatthe enginewasreplacedatabout18,000hours.This isclearly visibleasalargeimprovementinthedegradationtrendin boththeplotc) andthecorrected powerinplotd).Other maintenanceactionscanbeonsub-components,whichmight havelittletonoeﬀectontheelectricpower,theyjustprovide boundaryconditionsforthesystemtooperateatall.

SystemII Fig.6 showsthesameforsystemII.Thereisaverylarge re-coveryofthismachineduetoareplacementoftheengine atabout4400hours.Thenthereisasmallerstepofhigher degradation atabout 5400hours,which is visible in both normaliseddegradation c)andcorrectedpowerd),butthe reasonforitisunclearfromthemaintenancelog.

SystemIII Fig.7showstheresultforsystemIIIwhereweseealargedrop inbothnormaliseddegradationc)andcorrectedpowerd)at about1800hoursduetodamagedsealingscrollengine.This wasrecoveredat2300hrsbyreplacingscrollandengine.

SystemIV Fig.8showsthecurvesforsystemIV.Also,herecanweseea largerecoverybothatabout2800hoursand11000hoursdue toreplacementoftheengineatbothinstances.Thisparticular system’slocationledtoverypollutedairinletﬁlters,which

Table3

Theerrorofforecasting1000runninghoursintothefutureforeachsystem usingthedegradationestimationmodelvs.theforecastingmodel.

System id Estimation (rmse) Forecast (rmse) #training/test examples

I 49.29 50.32 8151/423 II 146.45 121.01 2520/345 IV 93.66 77.26 1603/466 IV 89.71 121.63 9916/474 V 181.71 170.78 1972/173 All 108.25 105.57 24162/1881

resultedinpressuredropandthusperformancedegradation. Cleaningtheﬁltersresultsinapartialrestorationofthepower atabout24000hours.

SystemV Fig.9 showstheplotsforsystemV,wherewecanseethat therearemanymissingdatapoints before3000hours.We canalsoseetherecoveryfromreplacingtheengineatabout 6100hours.

6.2. Forecastingmodelresults

Inthissection,wewillevaluatetheforecastingmodelsontheﬁve systems.First,weillustratehowtousethemodelbyforecasting5000 hoursintotheunknownfutureforeachsystem,wheretheresultisused todecidewhentodomaintenance.Thereafter,weevaluatethemodel performancebymakingforecastsforthelast1000hoursofknowndata andcomparetheestimationandforecastingmodels.Intheformer,we trainthemodelsusingallavailabledataandthenextrapolatethe fore-casttofuturerunninghoursnotyetseen.Inthelatter,wetrainusing alldataexceptthelast1000hrs.Then,fortheremaininglast1000hrs, weusetheknownvaluesforthetimedependentvariablestoforecast thedegradationusingtheestimationmodelandcompareittothe fore-castingmodelthatonlyusesthefuturerunninghours.

InFig.10,the5000hoursforecastsforeachsystemareshownin black,whiletheestimatednegativenormaliseddegradationisinblue. Redlinesindicatewhenthenegativedegradationisbelowthe thresh-old,wheresystemIisbelowthethresholdatabout23230hoursand systemIIIatabout5367hours.So,bothsystemsareinneedof immedi-atemaintenanceserviceinordertonotoverlydegrade.

TheresultfromevaluatingtheestimationmodelisshowninTable3 andtheforecastingmodelsonthelast1000runninghoursthatwerenot usedfortraininginthiscase.Theresultismeasuredusingrootmean squared error(rmse).Thesecond columnshows thepredictionerror fromusingtheestimationmodelforforecastingwhenassumingthatall timedependentvariablesareknown(thatis,runninghoursand num-berofstartsandstops).Thethirdcolumnisthepredictionerrorusing theridgeregressionforecastingmodel,assumingthatweonlyknowthe runninghours.Itseemsthatonlyusingthehoursisequallygoodor bet-terwithregardstofoursystems,I,II,IIIandV,andtheoverallresultis betterfortheforecastingmodel.However,thisindicatesthatthe pro-posedforecastingmodelisquitereliableincomparisontousingthefull knowledgeofalltimedependentvariables.

7. Summaryandconclusions

Inthispaper,wehavepresentedanovelmethodforpredictingthe long-termdegradationof aﬂeetofmicrogasturbines.Theproposed methodaddressedseveralissuesrelatedtothemonitoringofmicrogas turbinesdistributedovergeographicaldiﬀerentlocations.

Themaincontributionsofourpapercanbesummarizedasfollows: • Noreferencesystemisneededduetoourapproachonlyusesdata

fromtherealsystems;

• The degradation estimated is relative to the initial performance (measuredwhenasystemisinstalled);

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Fig.10. Systemforecasts:they-axisshowsthenormaliseddegradation,andthex-axisshowsrunninghours.Thebluecurveisestimateddegradationfromthedata whiletheblackcurvesshowthe5000hoursforecasts.Theredlinesshowwhentheforecastsarebelowthethreshold,whichindicateswhenmaintenanceservices areneeded.

• Thedegradationisestimatedmuchmoresmoothlythanthecurrent approach;

• Inourapproach,itiseasytosetagenericthresholdonwhenasystem shouldbemaintained;

• Ourapproachisabletoforecastthefuturedegradationoverrunning hourstoenabledynamicmaintenanceplanning.

Theproblemwassolvedintwosteps.Firstbycreatingaconstrained linearregressionmodelforestimatingthedegradationfromthedata, removingtheeﬀectoftheambientvariables.Second,aridgeregression modelwascreatedforforecastingfromtheoutputoftheﬁrststepwhere thedegradation wasprojected intothefutureusingonlytherunning

hoursasaninput.Thereby,theeﬀectofthenumberofstartandstops wasindirectlymodeledovertime.

Wesuccessfullyevaluatedthemethodonfivefieldtrialsystems.The proposedmethodwasoverallconsistentwiththecurrentdegradation approachinthattheestimateddegradationcorrelateswellwiththe cor-rectedpower(onlyonesystemwith𝑟<0.9).Wecouldalsoshowthat themethodwasabletoidentifyenginereplacementsfromthedata,and thattheforecastsareratheraccuratecomparedtorealdata.The fore-castswereequallygoodorbetterthantheestimationmodelforfourof fivesystems.

Futureimprovementstothisworkwouldbetoaddestimatesonthe uncertaintyoftheoutputfromthedegradationmodels.Forinstance, tobeabletoidentifywhenachangeindegradationatamaintenance

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actionis statisticallysigniﬁcantortoestimatetheuncertaintyofthe predicteddegradation.Initialstudies,usingresamplingofdatawith re-placements,indicatethatthevarianceofthepredictionsisquitesmall.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinﬂuence theworkreportedinthispaper.

Acknowlgedgments

ThisworkinthispaperwaspartiallyfundedbyEuropean Commis-sionunderHorizon2020program,grantnumber723523.Theresearch ofDrEnislayRamentolhasbeenfundedbytheEuropeanResearch Con-sortiumforInformaticsandMathematics(ERCIM)AlainBensoussan Fel-lowshipProgrammeandtheFraunhoferInstituteforIndustrial Mathe-matics.

AppendixA. Microgasturbinespeciﬁcation

Thisappendixcontainsadescriptionofkeyparametersofthemicro gasturbines:nominalpowers,electricaleﬃciency,thermaleﬃciencyin TableA.4,andhoursbeforemaintenanceinTableA.5.

TableA.4 mGTspeciﬁcation. Parameter Value 𝑃 𝑒_𝑛𝑜𝑚 3 kW a 𝑃 𝑡ℎ_𝑛𝑜𝑚 15.6 kW 𝐸𝑡𝑎 𝑒 16% 𝐸𝑡𝑎 𝑡ℎ 78%

a _Current_commercial_product_3.2_kW,_system_reviewed_in_paper₃_kW.

TableA.5 Maintenanceintervals. Time Action 7500 hrs Small 15000 hrs Large 22500 hrs Small

30000 hrs Likely engine replacement a

37500 Small

etc. ...

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Theregularisationweight𝑎𝑙𝑝ℎ𝑎intheabovemodelwaschosenusing 5-foldcross-validation.

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