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European Patent OfficeOffice européen des brevets
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EP0 907 913B1
Description
FIELD OF THE INVENTION:
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[0001]Thepresentinventionrelatestoapparatusandmethodsfordetectinganddiagnosingmalfunctionsinprocesscontrol systems for large, complex and continuous manufacturing systems such as a pulp and paper mill.BACKGROUND TO THE INVENTION:
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[0002]Inamodernlargeandcomplexcontinuousmanufacturingsystemtherearetypicallymanyhundredsofphys-icalquantitiesbeingautomaticallycontrolledbyacomputerizedsystememployingon-linedataacquisition,decisionmaking,andphysicaladjustmentofactuators.Themainpurposeofsuchacontrolsystem,apartfromperformingthebasicsequentialtasksnecessarytoruntheprocess,istomaintainoptimaloperatingconditionsbyminimizingtheeffectofnaturalfluctuations(suchasrawmaterialvariations)onthequantitiesundercontrol.Severalcommonsourcesofcontrolsystemmalfunctioncandisruptthisbasicobjectiveofthecontrolsystem,withoutnecessarilytriggeringprocessalarmsorotherindicationsoffailure.Causesofmalfunctionscaninclude:poorchoiceofcontrolalgorithmortuningconstants,valvestiction,deteriorationofsensors,orapoorinitialchoiceofcontrolstrategy.Thesetypesofincipientproblemscanpersistundetected,oftenwithseverenegativeeconomicconsequenceswhichstemfromlossofproductuniformityorsub-optimaloperatingconditions.Theextentofthistypeofmalfunctioncanbeverygreatwhentherearemanyvariablesareundercontrolandmaintenanceresourcesarelimited.Forinstance,inatypicalintegratedpulpandpapermill20-60%ofthe1000-5000variablesunderautomaticcontrolmaybecontributingsomeadditionalvariationduetovarioustypesofcontrolmalfunctionasnotedin\"DreamsvsReality:AViewfromBothSidesoftheGap\byW.L.Bialkowski,and\"ControlSystems92,Whistler,B.C.,AMillPrototypeforAutomaticMonitoringofControlLoop Performance\[0003]Inmostindustrialplantsthevastmajorityofvariablesundercontrolareregulatedindividuallybymanipulationofasingleprocessinput.Assuch,theprocesscontrolsystemcanbethoughtofasbeingdividedintoseparateunitsor\"controlloops\eachresponsibleforthecontrolofaseparatequantity.Consequently,tracingthesourceofacontrolsystemmalfunctionrequireslocalizationoftheeffectedloopfromamongthemanyhundredsofcontrolloopsintheplant.[0004]Theprimarysymptomofprocesscontrolmalfunctionsisincreasedvariabilityinthequantityundercontrol.Consequently,muchofthepriorarthasusedvariousmanifestationsofelevatedlevelsofvariancetolocatemalfunc-tioningcontrolloops,e.g.,U.S.Patent4,885,676andU.S.Patent5,249,119.Thedrawbackoftheapproachisthatchangesinthelevelofvariabilitycontributedbymalfunctionsoftheprocesscontrolsystemcannotbedistinguishedfromtheeffectsofchangesproducedbyotherexternalperturbationssuchasthosearisingfromrawmaterialvariationsor turbulent flows.
[0005]Anotherapproachtakeninthepriorartisthedirectdetectionofasubclassofcontrolmalfunctionscausedbyvalveoractuatorfailure,e.g.,U.S.Patent5,329,465andU.S.Patent3,829,848.Thescopeofthesetechniques,however,islimitedtoaparticulartypeofmalfunction,andspecialinstrumentationmustbeinstalledandconnectedtoeach actuator or valve to be monitored.
[0006]Extensivematerialhasbeenpublishedintheacademicliterature,describingvariousmethodsforcontrolloopmonitoringanddiagnostics.Muchofthisliteraturehasfocusedonwaystoovercomethelimitationoftechniquesbasedonmeasuringtheabsolutelevelofvariabilitypreviouslymentioned.Forinstance,in\"AutomaticMonitoringofControlLoopPerformance\byT.Hagglund,Controlsystems'94aproceduretodetectprocessvariableoscillationsresultingfromcontrolloopmalfunctionsispresented.However,boththistechniqueandclassicaltechniquesbasedondetectionofpowerspectrumresonances,arelimitedtodetectionofcontrolmalfunctionswhichinduceoscillationandwherethereisanabsenceofinter-loopinteraction(seebelow).Amajorsteptowardsamoregeneralandrobustmethodofquantificationofcontrolloopperformancewasmadeinthepaper\"AssessmentofControlLoopPerformance\byT.J.Harris,Can.J.Chem.Eng.,67,pp.856-861,19.Harrisproposedassessingcontrolperformanceusingacomparativemeasureofvariance.Thisperformanceindexwasdefinedastheratiooftheobservedlevelofvarianceofacontrolledvariabletotheminimumvarianceachievablebyaminimumvariancecontroller.Harrisfurtherdevisedameansofcomputingtheindexfromobservationoftheclosed-loopoperatingdata(i.e.withoutrequiringanyinvasiveprocessperturbation)andanestimateofthedelaybetweentheprocessinputandoutput.Asasinglenumber,thisindexprovidedaveryeasilyinterpretedquantificationofloopperformance,idealforuseinacomputermethodfordetectingcontrolmalfunctions.Furthermore,thetechniqueforevaluatingtheindexhastheadvantageofbeingunaffectedbyfluctuationsintheintensityofexternaldisturbance,sincesuchchangeseffectboththeobservedvarianceandtheminimumvarianceestimate by the same factor.
[0007]Theseadvantagespromptedotherresearcherstogeneralizethetechniques.Forinstancein\"PerformanceAssessmentMeasuresforUnivariateFeedbackControl\byL.D.DesboroughandT.J.Harris,Can,J.Chem.Eng,70,pp.1186-1197,1992,amethodofestimatinganormalizedformofHarris'indexispresented,togetherwiththestatistical
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propertiesoftheestimator.In\"PerformanceAssessmentMeasuresforUnivariateFeedforward/FeedbackControl\byL.D.DesboroughandT.J.Harris,Can,J.Chem.Eng,71,pp.605-616,1993,theseresultsareextendedtoincludeperformanceassessmentofsingleloopfeedbackincombinationwithfeedforwardcontrol.Industrialapplicationofthesetechniquesisdescribedin\"TowardsMill-WideEvaluationofControlLoopPerformance\byM.PerrierandA.Roche,ControlSystems'92,and\"AnExpertSystemforControlLoopAnalysis\byP.Jofriet,C.Seppala,M.Harvey,B.Surgenor,T.Harris,PreprintsoftheCPPAAnnualMeeting,1995.In\"MonitoringandDiagnosingProcessControlPerformance:TheSingleLoopCase\"byN.Stanfelj,T.MarlinandJ.MacGregor,Proc.oftheAmericanControlCon-ference,pp.2886-22,1991,thesetechniquesarefurtherinvestigated,andamethodfordistinguishingexcessvar-iabilityduetopoorcontroldesignfromthatduetopoormodelestimationispresentedforcaseswherethereiscon-tinuous set point variation.
[0008]Theabilityofthesetechniquestodistinguishelevatedvariabilityarisingfromchangesinexternaldisturbancesfromthatduetocontrolmalfunctionsislimitedhowevertocaseswhereonlytheintensityratherthanthefundamentalcharacteroftheexternaldisturbanceschanges.Theassessmentofperformanceisinfactbiasedwhenthecharacterofthosedisturbanceischanged,forexampleduetoamalfunctioninthecontrolofanotherquantitywhichisdynamicallyrelatedtothecontrolledvariable.ThisphenomenonisillustratedinExamples1and2.ThiseffectcouldconceivablybeovercomebytheuseofadirectmultivariableextensionoftheHarrisindexanditsmethodofcomputation.Thepracticaldifficultywithsuchageneralizationisthatitwouldrequirepracticalextensiveprocessmodellingandexper-imentationinordertofindthemultivariableextensionoftheprocessdelay,i.e.,theprocessinteractortransferfunctionmatrix.Thecomplexityandcostofthistypeofextensivemodellingwouldmakethisapproachunsuitableforlargescaleindustrialimplementation.Anothersourceofbiasincontrolloopperformanceassessmentusingthesetechniquesistheeffectoftemporaryupsetsintheprocesswhichinducenonstationarydisturbancestotheloopunderconsideration,inviolationofthepriorassumptionsmadebyHarrisandotherpriorcontributorstothepriorart.Yetanotherbiasintheevaluationofperformancecanoccurformalfunctionswhichareinducedbyanon-linearityintheloopunderassess-ment,suchasthatcausedbyhighlevelsoffrictioninavalveoractuator.Thisbiashasitsrootsintheviolationoftheassumptionofapproximateprocesslinearitymadeinthepriorart,whichfailstoholdforthisclassofcontrolmalfunc-tions.Thesecommonlyoccurringnon-idealconditionswillcauseanymethodbasedonthetechniquesdescribedinthe above papers to yield false positive and false negative indications of control loop malfunction.
[0009]Thereareanumberoftechniquesavailableinthecommercialdomainfortestingofvalvesandactuatorsforfunctionaldefectssuchasstiction.Someofthesetechniqueshavebeenmentionedinvariousformsintheopenliter-ature,e.g.,\"IntelligentActuators-WaystoAutonomousActuatingSystems\byR.IsermannandU.Raab,Automatica,29, #5, pp. 1315-1331, 1993 and U.S. Patent 3,829,848. All employ some variant of the following procedure:
a) the controller output is moved according to some preset sequence;
b)theresponse,eitherorthevalveitselforsomeothermeasurementoftheprocesscondition,istestedforde-partures from a \"normal\" characteristic;
c) any detected departures provide a diagnostic.
[0010]Thistypeoftechniquecanbeautomatedsothattheprocedureisperformedon-line.Thedrawbackisthattheinvasiveprobingofthevalvecarriesariskofcausingupsetsandgeneratingadditionalprocessvariability.Ontheotherhand,ifroutinecontrolleroutputsignalstothevalveoractuatoraretobeusedinsteadofaprobingsignal,thenacontinuousmeasurementrelatedtotheactuator/valvepositionmustbeavailableinadditiontothequantitybeingcontrolled.Thisrestrictionisaconsequenceofthefactthattherelationshipbetweenthecalculatedcontrolleroutputordesiredprocessinputandthemeasuredcontrolledvariableiscompletelyexplainedbythecontrolmethoditselfwhentheprocessisoperatinginclosed-loop;assuchitcanrevealnoinformationabouttheprocessintheabsenceofanyset-pointadjustments.Hence,variantsoftheabovetechniqueswhichuseroutinedatatomonitorvalvesoractuatorsrequireasecondmeasurementpointwhichisstronglyrelatedtotheactuatorvalvepositionandnotcom-pletely dependent on the computed centralization.
[0011]Ithasbeennotedintheacademicliteraturethatnonlinearelementsinacontrolloopwillinducelimitcyclesinprocessvariableswhichhaveanon-normaldistribution.ThepioneeringworkinthisareawasdonebyFullerin\"AnalysisofNonlinearStochasticSystemsbyMeansoftheFokker-PlanckEquation\byA.T.Fuller,Int.J.Control,9,6,pp.603-655,1969whoderivedpartialdifferentialequationsdescribingthedependenceofthecontrolledvariableprobabilitydensityfunctionontheprocessdynamicsandthenonlinearity.Theseequationsweresimplifiedin\"Approx-imateAnalysisofNonlinearSystemsDrivenbyGaussianWhiteNoise\byD.XueandD.Atherton,Proc.OftheAmer-icanControlConference,pp.1075-1079,1992forsomecommonprocessmodelsandmemorylessnonlinearitieswithdisturbancesrepresentedbywhitenoise.Inbothcasesthisworkisofatheoreticalnature,andwasconfinedtoderi-vationoftheprobabilitydensityfunctionforknownprocessmodels.Testsfornon-normalityoftheprobabilitydensityfunctionofatime-seriesusingestimationofthe4thmomentshavealsobeepproposedintheopenliteratureforotherpurposes,forexample\"ThetheoryofStatistics\byG.U.YuleandM.G.Kendall,Griffin,1953.However,thistypeof
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testislimitedbytherequirementthattheobservationsofthetime-seriesbeindependent,aconditionwhichisneversatisfiedforthetimeseriesgeneratedbythemeasuredvalueofalimitcyclingcontrolloop.Anon-normalitytestusingthistechniquewasalsoproposedinU.S.Patent5,239,456\"MethodandApparatusforProcessControlwithOptimumSetpointDetermination\".Thepurposeofthetestasitwasproposedinthispatentwastoprovideanalarmifthekeytechnicalassumptionofthepatentedtechniquefailedtohold;itwasnotusedtoprovideacontrolsystemdiagnostic.[0012]ThereisdisclosedinWO93/06537(documentD1)(UKAtomicEnergyAuthority)amonitoringsystemforaplantorapparatusinwhichstatussignalsareusedtoindicateifrespectiveparametersoftheplantorapparatusrep-resentanacceptablestate.Thesystemdetectsfaultconditions.Adesiredsequenceofoutputsignalsisprovidedaslongastheparametersremaininacceptablestates.Thesystemdoesnotdiscloseanymeansforprovidingadiagnosticfunction in relation to a detected fault condition.
[0013]ThereisdisclosedinEP-B-0481971(documentD2)(JohnsonServiceCompany)acontrolsystemforastampingpresswhichdisablesthepressintheeventofunacceptableforcevariations.Thedisclosedmethodcomprisesdatacomparisonandgeneratingcontrolsignalstocontrolthepressinaccordancewiththecomparison.Upondetectionofoutoftoleranceconditionsanalarmisgenerated.Thereisnotdisclosedasystemfordiagnosticanalysisofunac-ceptable conditions in the press.SUMMARY OF THE INVENTION:
[0014]Thepresentinventionrelatestoamethodofdiagnosticdifferentiationasdefinedintheaccompanyingclaims.Inanembodiment,suchamethodisprovidedwhichpermitsautomaticassessmentofcontrolloopperformanceinthemulti-loopinteractiveandnonlineardynamicenvironmenttypicalofindustrialsettings.Theembodimentlocalizesmal-functionsintheprocesscontrolsystembyanalyzingoperatingdataroutinelyrecordedbytheplantdataacquisitionsystem.Theembodimentcanalsoderiveadiagnosticformalfunctionswhichhavebeenlocalized,andcanquantifytheseverityofanydetectedmalfunctionintermsoftheamountofvariabilityitcontributestothequantityundercontrol.[0015]Prior process data required for the analysis may include:
i.) an estimate of which groups of controlled variables may exhibit significant mutual dynamic interaction;
ii.)thedelaybetweenmakingachangeateachcontrolleroutputandobservingthefirstsignofitseffectonthecontrolled variable;
iii.) the \"order or magnitude\" of the open-loop time constant.
[0016]Thelattertwoestimatesarerequiredforeachcontrollooptobemonitored.Theymaybeobtainedfromroutinedata if frequent set-point changes are made; otherwise a \"one-time-only\" bump test may be required.
[0017]Anembodimentofthepresentinventiondetectscontrolmalfunctionsusingthefollowingprocedure.Operatingdataiscollectedsimultaneouslyfromthepreselectedlistsofloopsjudgedlikelytoexhibitmutualinteraction.Thisoperatingdatacomprisestwotime-seriesforeachloop:thecontrolledvariablemeasurementandthecontrolloopsetpoint.Thedataiscollectedoveraperiodatleast100-500timesthelongestopen-looptimeconstantamongtheloopsinthegroup.Twotypesofperformanceindexmaythenbecomputedforeachloopunderseparateassumptionsaboutthestateofdisturbancesactingontheloop.The\"rawindex\"quantifiestheamountbywhichtheobservedvarianceofthetrackingerrorexceedsitsminimumachievablevalueafteranynonlinearelementshavebeenremovedfromtheloop.Thisindexcorrectlyquantifiesperformancewheredisturbancestotheloopconformtonormalexternalconditions.Priorestimatesoftheprocessdelayandtimeconstantareusedtoperformthiscalculation.Themethodthentestsforanyinteractionsbetweencontrolloopswhichmaybeinflatingtheestimateoftherawindexbyperturbingtheloopbeinganalyzedinanabnormalmanner.Ifsuchvariationisdetectedforaparticularloopa\"modifiedindex\"isthencomputed.Themodifiedindexisanestimateofthesamecomparativemeasureofvariability,butwiththeeffectofpotentiallyabnormaldisturbancesremovedfromthecalculation.Assuch,themodifiedindexisavalidmeasureoftheloopperformanceundertheassumptionthatthedetectedabnormaldisturbancehasexternalorigin.Henceifaloopisdeemedtobeinteractingwithothersinthegroup,therawandmodifiedindicesreflectthestatusofloopperformanceunderthecontrastingassumptionsthatanyinteractiveabnormalvariationisinternallyorexternallyproduced.Takentogether,thetwoindicesallowtheuserofthesystemtodividecontrolloopsintothreecategories:thosedefinitelymalfunctioning,thosedefinitelynotmalfunctioning,andthosewhichmaybemalfunctioningorbeingperturbedbyinteractingmalfunctioningloops.Otherinformationmayalsobeusedinthiscalculationtoassistinmakingthedistinc-tion, as described under the preferred embodiments.
[0018]Thediagnosticcomponentoftheembodimentproceedsbycomputingthehistogramofthetrackingerrorforeachloopdesignatedpotentiallymalfunctioning(i.e.,wheretherawindexexceedssomepredefinedlevel).Thekurtosisandskewnessofeachhistogramisthenquantifiedbycalculatingtheheightofthecenterbarofthehistogramrelativetoitsexpectedheightundertheassumptionthatthetrackingerrorisnormallydistributedwitheitherzeroorthesamplemeanandthesamplevariance.Theskewnessisquantifiedbycomparingthenumberofsamplesinexcessofeither
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thesamplemeanorzerowiththeexpectednumber(i.e.,halfthenumberofsamples)underthesameassumption.Underthisnullhypothesis,thestatisticalsignificanceofanydepartureofeitherstatisticfrom0iscalculated,takinginto account any inter-sample correlation of the tracking error time-series.
[0019]Inaccordancewithanembodimentoftheinvention,amethodofdetectingmalfunctionofaprocesscontrolsystemwhichincludesatleastoneclosedloopcontrolloopiscomprisedofmeasuringahistogramoftrackingerrorofthecontrolloop,determiningdistortionofthetrackingerrorrelativetoaGaussiandistribution,andindicatingamalfunctionintheprocessintheeventadeviationfromtheGaussiandistributionofthetrackingerrorexceedsprede-terminedlimits,whereinthedistortion(K)ismeasuredbysubtractingfromaheightofatrackingerrorhistogrambarofthehistogramcenteredonzero,anumberofsamplesmultipliedbyanareabetweenapairoflimitsdefininganormaldensityaboutameanofthehistogram,andthenindicatingamalfunctionintheprocessintheeventavalueofKisdifferent from O by a predetermined amount.
[0020]Inaccordancewithanotherembodiment,amethodofautomaticassessmentofcontrolloopperformanceofanindustrialmachineiscomprisedofcollectingoperatingdatacomprisingtimeseriesofcontrolledvariablemeasure-mentsandcontrolloopsetpointssimultaneouslyfrompredeterminedcontrolloops,foraperiodofatleastapproximately100timesalongesttimeconstantofthepredeterminedcontrolloops,subtractingmeasuredvariabledatafromsetpointdatatoobtaintrackingerrors,determininganamountbywhichobservedvarianceofatrackingerrorexceedsanidealminimumvalueachievableafternon-linearelementshavebeenremovedfromaloop,exploitingpriorestimatesofprocessdelayandtimeconstantinthecalculationandrepresentingtheresultasarawindex,testingforanyinter-actionsbetweencontrolloopswhichmaybeinflatingtheestimateoftherawindexinanabnormalmanner,determiningamodifiedrawindexforaparticularloopintheeventtheinflatedestimatesaredetected,anddistinguishingbetweencontrolloopsthataremalfunctioning,thosethatarenotmalfunctioning,andthosethatarepossiblymalfunctioningandare perturbed by interacting malfunctioning control loops, based of the raw index and the modified raw index.
[0021]Inaccordancewithanotherembodiment,amethodofautomaticassessmentofcontrolloopperformanceofandindustrialmachineiscomprisedof(a)identifyingacurrentcontrolloopinagroupofcontrolloops,(b)obtainingoperatingdataandprioroperatingdataforthecontrolloop,(c)calculatingarawperformanceindexforthecontrolloop,(d)indicatingthecurrentcontrolloopaspotentiallymalfunctioningintheeventtherawperformanceindexisgreaterthanapredeterminedthreshold,(e)intheeventthecontrolloopisindicatedaspotentiallymalfunctioning,computingafastFouriertransformofatrackingerror,andfilterproductsofthetransformtoremovespuriouspeaks,(f)identifyingprimaryandsecondaryspectralpeakscontributingmorethanathresholdvarianceinapredeterminedbandwidthforthecontrolloop,(g)selectinganothercontrolloopinthegroupofcontrolloopsandrepeatsteps(a)-(g)untilalastcontrolloopinthegrouphasbeenprocessed,(h)dividepotentiallymalfunctioningloopswithapproxi-matelycoincidentspectralpeaksintopossiblyinteractingclasses,(i)determineamodifiedperformanceindexforallcontrolloopsbelongingtoaclass,and(j)applyahistogramtesttospectralpeaksofallcontrolloopsinaclasstodetermine a category of malfunction.
[0022]Inaccordancewithanotherembodiment,amethodofdeterminingacategoryofmalfunctionofaprocessiscomprisedoftrackingerrorvariationsofnarrowspectralbandwidthineachofpluralcontrolloopsoftheprocess,comparingspectralpeaksoftheerrorvariationstodetectcoincidencesofpeakswhichareindicativeofinteractionbetweenthepluralcontrolloops,andquantifyingeffectsoftheerrorvariationswhichhavethecoincidencesofpeaks,and as a result determining malfunctioning of a control loop.BRIEF DESCRIPTION OF THE DRAWINGS:[0023]
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Figure1showsaflowdiagramindicatingthesequenceofcalculationsperformedtocalculatetherawindexofperformance for each loop,
Figure2showsaflowdiagramindicatingthegeneralsequenceofcalculationsperformedbythemethodtolocateand diagnose control loop malfunctions,
Figure3showsanexampleofacalculatedpowerspectrum,withprimaryandsecondarypeaksidentified,togetherwith shaded areas corresponding to the variance associated with those peaks over the preset bandwidth,
Figure4showsthehistogramofthetrackingerrorfortheflowcontrollermalfunctionofExample1,whichwasknown to be caused by valve stiction. The statistic used to quantify kurtosis is illustrated,
Figure 5 illustrates grouping of potentially malfunctioning control loops into an interacting equivalence class,Figure6showsasampletextoutputofthemethod,indicatingthepartitionofpotentiallymalfunctioningloopsintoa subgroup where potential mutual interaction may be inflating performance indices,
Figure7showsgraphsdepictingpriorwavelengthestimatesforclosed-looptransferfunctionresonancesforvar-ious process dynamics,
Figures8Aand8Bshowasimulatedrandomlimitcyclewithandwithoutvalvestiction,respectively,withpredicted
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potentialvariabilityimprovementusingstandardmethodsbeingcomparedtothevariabilityimprovementactuallyrealized by removal of the source of simulated stiction,
Figures 9A and 9B show the flow and consistency time-series for Example 1,Figure 10 show the flow and consistency power spectra for Example 1,Figure 11 shows the two level time-series for Example 2,Figure 12 shows the two level power spectra for Example 2,
Figure 13 shows the histogram of the preheater level tracking error in Example 2,Figures 14A and 14B are general block diagrams of an embodiment of the invention,Figure 15 is a block diagram of the diagnostic calculation block of Figure 14,
Figure 16 is a block diagram of the performance evaluation block of Figure 14, andFigure 17 is a block diagram of the spectral peak detector block of Figure 14.DESCRIPTION OF THE PREFERRED EMBODIMENTS:
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[0024]Uponsetupofthecontrolsystemwhichusesthepresentinvention,priororreferenceinformationontheprocessdynamicsshouldbecollectedandorganized.Thisinformationneedbeupdatedonlywheneitherchangesaremadetotheprocessundercontrolortothechoiceofmanipulated/controlledvariablepairing;otherwiseitdoesnotchangeeitherbetweensuccessiveanalysesperformedwiththemethodorbetweenreadjustmentsofthecontroltuningconstants.
[0025]Therearetwostructuresforthispriorinformation,onerelatingtheinter-loopdynamics,theotherrepresentingdynamicinformationabouteachseparateloop.Estimatesofwhichcontrolledvariableshavethepotentialforsignificantmutualinteractionaremadeatstartup,basedonaqualitativeunderstandingoftheprocessbehaviour.Thisinformationisthenusedtopartitioncontrolloopsintogroupswhichmayexhibitsignificantintra-groupmutualinteraction,butwhereinter-groupinteractionislesslikelyorlesspronounced.Thesepartitionsarethenrepresentedbyaseriesoflistscomprisingnamesusedbythecontrolsystemforeachcontrolloopintherespectivegroup.Themethodcollectsandprocessesdatafromcontrolloopsbelongingtoeachlistsimultaneously.Theselistsconstitutethefirstpriorinformationstructure.
[0026]Thesecondpriorinformationstructureisafileassociatedwitheachseparatecontrolloopcontaininganes-timateofthedelaybetweenmanipulatedandcontrolledvariables,theapproximateopen-loopprocesstimeconstant,andthesampletime.Afurtheroptionalitemthatmaybeincludedisanallowablerangeforclosed-loopresonantfrequenciescausedbypoortuningofthecontrol.Upperandlowerboundsonthefrequencyofanyresonancescausedbypoorcontrollertuning,whichareindependentoftheparticularchoiceoftuningconstants,canbefoundfromprioropen-loopdead-timeanddominanttime-constantestimates.Plotsillustratingthedependenceoftheseupperandlowerlimitsondead-timeandopen-looptime-constantareshowninFig.7,andtheformuladescribingthesesurfacesisdescribedlater.Thepurposeofincludingtheselimitsisthatinsomecasestheycanbeusedbythemethodtodistinguishtheeffectsofexternallyandinternallyimposedresonancesinthecontrolledvariable.Additionalpriorinformationper-tainingtoeachindividualloopmayalsobeincludedasneededinthesefiles,suchasoutlierlimitsfordetectingabnormalprocess conditions.
[0027]Themethodusesthepriorinformationtointerpretthedatafromeachcycleofoperatingdataacquisitionandanalysis.AnoverviewofthesequenceofactionstakenduringthiscycleisshowninFig.2.Aftersimultaneousextractionoftheoperatingdatafromalltheloopsinapreselectedgroup,therawindexofperformanceiscalculatedbasedonthecomputedtrackingerror(setpoint-controlledvariable)foreachloop.AgeneralizationoftheindexproposedbyHarris and others is used for this purpose:
observed tracking error variance
------------------------------------------raw generalised index =-------------------------------------------------------------------------------------------------------------------------------minimum achievable variance with linear actuators and sensors
(1)
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[0028]Forcontrolloopswithpredominantlylinearelements,thisindexanditsmethodofcomputationarefunctionallyidenticaltothetechniquetaughtinthepriorart.However,incaseswhereexcessvariationiscausedbylimitcyclesdrivenbyanonlinearity,thetendencyofstandardmethodstounderestimatetheseverityofmalfunctionsisavoidedbyemployingthisgeneralizedformoftheperformanceindexanditsmeansofcomputation(asproposedinthisinven-tion).Forexample,Fig.8Ashowsadynamicsimulationofacontrolloopexhibitingtheeffectsofvalvestiction.Theindexofperformanceascalculatedbythetechniqueproposedinthepriorartis2.1(atthehighendofthenormalrange).Whenthevalvestictionelementwasremovedfromthesimulation,thevariationsinthecontrolledvariableareasshowninFig.8B.Thevariancewasreducedbyafactorof3.6,significantlygreaterthanthefigureof2.1predicatedbythestandardperformanceindex.Therawgeneralizedindex(eq:1)proposedinaccordancewiththepresentinven-tion was 3.3 in this case, providing a more realistic estimate of the excess variation caused by the malfunction.
[0029]ThemethodfordeterminingthegeneralizedrawindexisillustratedinFig.1.Thetechniqueusestheequiv-
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alence:
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and the denominator is approximated by the process described in Fig. 1.
[0030]ThemethodpreferablyalsoperformstwoothermaneouversasshowninFigure2toensureanunbiasedunivariateperformanceestimate.Incaseswherethesampleintervalisshorterthan1/10thoftheestimatedprocesstime-constant,thetrackingerrorislowpassfilteredusinganantialiasingfilterwithacut-offfrequencybetween10-20timesthereciprocaloftheestimatedprocesstime-constant(inradianspersample)andthenresampledwithasamplinginterval0.1-0.2timestheestimateddominantprocesstime-constant.Theoutcomeofthisprocedureisthattheminimumvarianceestimatein(1)isbasedonaminimumvariancecontrollerwithalongerassumedcontrolinterval,equaltothesampleintervaloftheresampleddataratherthanthesampleintervaloftheoriginaldata.Thisavoidsunderesti-matingtheminimumvariancewhenusingdataobtainedwithasampleintervalmuchshorterthantheopen-looptime-constant(stemmingfromanidealcontrolactionwhichwouldhavetoemployunrealisticallylargeandfrequentcontrolmoves), and the consequent upward bias in performance index evaluation.
[0031]Anotherprecautiontakenwhenevaluatingtherawindex,isagainstthebiascausedbyupsetprocesscon-ditions.Astatisticaltestispreferablyappliedtothetrackingerrordatatodetectupsets;iftheresultispositive,eithertheuseriswarnedofthepotentialbiasorthecycleofdataacquisitionrepeatedtocaptureanon-upsetcondition.ThetestmeasuresthestatisticalsignificanceofthestatisticD,whichissensitivetodriftsinthetrackingerrorofdurationgreater than one third of its length that would be associated with upset conditions:
D= maximum of (|m1|, |m3|)
wherem1andm3arethemeansofthefirstandthirdthirdsofthetime-series.ThenullhypothesisisthatthetrackingerrorisastationaryrandomprocesswithapowerspectrumequaltoMtimesthetrackingerrorvarianceoverafrequencyband0topi/M,whereMisapreselectedlargenumber.Suchapowerspectrumdescribesarandomprocesswithsignificantlowfrequencycomponents.Thenullhypothesisisinvalidatedwith95%confidence,andthepresenceofadrift indicated, if:
D > standard dev of tracking error
x square root of 12M/L,
(3)
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where L is the number of samples
[0032]Themaindrawbackofthepriorartiserroneousperformanceassessmentforwellperformingloopswhichareperturbedbydisturbancesfrominteractingmalfunctioningcontrolloops.Theuseofthemodifiedindexofperformancebytheinventiontocounterthiseffectandtracetherootcausesofmalfunctionispredicatedonthecharacterizationanddetectionofabnormaldisturbancestransferredthroughinteraction.Characterizationisbasedonakeyobservation,notknowninthepriorart,whichisvalidunderphysicallyreasonableassumptions:theonlyexternalabnormaldistur-bancestoanormallyfunctioningcontrolloopwhichhavethepotentialtoartificiallyinflatethecalculatedindexofperformancearethosewithanarrowspectralbandwidth.Thischaracterizationisexploitedbytheinventiontodetectinteractionwhichhasthepotentialtocreatebias,withoutrequiringadditionalprocessmodelbuilding.Inparticular,trackingerrorvariationsofnarrowspectralbandwidthcaneasilybeidentifiedbyunivariateFouriertransformmethods,andthespectralpeakscanthenbecomparedtodetectthecoincidenceswhichareindicativeofinteraction.Byquan-tifyingtheeffectsonlyofthoseinter-loopdisturbanceswhichhavethecapabilitytoinduceerrorsinperformanceas-sessment,thetechniqueprovidesmuchgreaterprecisionandsimplicitythanwouldbeavailablewithgeneralcorrelationmethods.
[0033]Thedetailsofthisprocedureareasfollows:Foreachloopdeemedpotentiallymalfunctioning(rawindex>presetthreshold)theFouriertransformofthetrackingerrorisevaluated.ItisthenwindowedwithaDanielwindowwhose bandwidth W periodogram ordinates is chosen so that W is the smallest integer which satisfies:
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Wexp(W)>L
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whichaccordingtotheWoodroofeVanNessformula[Priestly],forlongdatalengthsensuresthatthereshouldbenomorethan50%relativeerroratanypointintheestimatedpowerspectrumwithhighprobability.Inordertocharacterizeanyspectralpeaksthefrequencyofthemaximumoftheestimatedpowerspectrumf1isestimated.Thecenterfre-quencyofanysecondarypeakf2isthenevaluatedbytestingforasecondmaxima,overfrequenciesexcludedfromanintervalaroundthefirst.Thevarianceassociatedwithprimaryandsecondarymaximaisevaluatedbycomputingtheareaunderthepowerspectrumestimateoveranintervaloffixedbandwidthbwaboutthetwoestimatedfrequenciesf1andf2(seeFig.3,whereintheshadedareasrepresentvarianceassociatedwithprimaryandsecondaryspectralpeaks).Ifeithervarianceexceedspresetproportionsoftheoveralltrackingerrorvariancethenaspectralresonanceisconsideredtobepresentatthecorrespondingfrequency.Equivalenceclassesofcontrolloopsarethenformedbyassociatingloopswhereeitherprimaryorsecondaryresonantfrequencyiscloserthanasmallfixedamounttoeithertheprimaryorsecondaryresonantfrequencyofanotherloop.AnexampleisshowninFig.5,wherecontrolloops1,2,and4wouldbeassociatedintoasingleequivalenceclassbecauseofacommonresonanceatapproximately0.01Hz.[0034]Inordertodistinguishthesymptomsandthecausesofcontrolloopmalfunctions,amodifiedindexofper-formanceisthencalculatedforloopsbelongingtoeitheroneoftwoclasses:loopsbelongingtoanequivalenceclassofpotentiallyinteractingloops,orloopswherearesonanceisidentifiedoutsidetheprescribedrangeofwavelengthsfortheloopandthatresonanceisnotcausedbyalimitcycleduetothepresenceofaseverenonlinearityintheloop.Intheformercasethemodifiedindexestimatestheperformanceofthecontrolloopifthecommonresonantcomponent(s)ofthevariabilityarise(s)fromdisturbancescontributedbyaninteractingmalfunctioningloopandnotgeneratedinternally.Inthisfirstcasethemodifiedindexestimatestheratiobetweenthevarianceanditsestimatedminimumachievablelevelthatwouldhavebeenobservedpriortotheonsetoftheexternalresonantdisturbances.Thetruelevelofperformanceliessomewherebetweenthemodifiedandrawindicesdependingonthesourceoftheresonantcom-ponent(s)intheobservedvariability.Bycontrast,inthesecondcasethechoiceofrepresentativemeasureofperform-anceismorecertain.Iftheprescribedlimitshavebeensetcorrectlyandthejudgmentoftheabsenceofalimitcycleiscorrectthenanyresonanceoutsidetheprescribedlimitsmustbecontributedbyanexternalmalfunction.Thusbyexcludingtheeffectsoftheresonantvariationoutsidethoselimits,themodifiedindexquantifiestheperformancein-dependentlyoftheabnormalexternaldisturbance.Inbothcasesthemodifiedindexiscalculatedinaccordancewiththe following formula:
Modified index = index x (1-proportion of the
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tracking error variance with resonance suspected of
being imposed externally)
(5)
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[0035]Distinguishingexcessvariationcausedbyrandomlimitcyclesfromothersourcesisfundamentaltoselectingacorrectiveaction.Suchlimitcyclesarecausedbydefectsintheactuator,valveorsensorwhichintroduceaseverenonlinearityinthecontrolloop.Sincethevastmajority,ifnotall,actuatororvalvemalfunctionincreasevariabilitythroughthismechanism,thepresenceofalimitcycleisstronglysuggestiveofsuchacause.Insuchsituationschoosinganalternativecontrolstrategyusingthesamefaultyelement,orretuningthecontrollawisunlikelytoyieldanyglobalimprovementofvariability.Conversely,recognitionofothermechanismsofexcessvariability,suchascyclicalvariationsproducedbyunderdampedclosed-loopdynamics,canallowmaintenancetobefocusedonmoreeasilyrectifiedfactorssuchastuningconstantsandcontrolstrategy.Thephenomenonthattheinventionusestodetectlimitcyclesistheirtendencytoproducenon-Gaussiandistortionofthetrackingerrorhistogram.Ifthedisturbancestoacontrollooparenotcausedbyanabnormalexternalcondition,theirprobabilitydensityfunctionwillbeapproximatelyGaussian.Thisobservationisaconsequenceofthecentrallimittheoremofclassicalstatistics,andhasbeenthoroughlycorroboratedexperimentallyinmanysituations.Iftheopen-loopdynamicsoftheactuator,sensor,andprocessareroughlylinearforvariationsaroundtheset-point(s),itfollowsthatthetrackingerrorwillalsohaveanapproximatelyGaussianprob-abilitydensityfunction.Thiswillbetrueevenifthechoiceoftuningconstantsorcontrolstrategyiscausingexcessvariabilitybyamplifying(orfailingtoattenuate)thedisturbances.Ontheotherhandhighlynon-linearopenloopdy-namicsdue,forexampletovalvehysteresis,thatcauselimitcyclesinclosed-loop,tendtodistorttheGaussianprob-abilitydensityfunctionsofthedisturbancesbysuppressingtherelativefrequencyaroundthemeanvaluerelativetotheGaussianbell,acharacteristicknownaskurtosisorintroduceasymmetryintherelativefrequencyaboutthemean,a characteristic known as skewness.
[0036]AnexampleisshowninFig.4fortheflowtrackingerrortimeseriesshowninFig.9Awherethecharacteris-
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ticallyflattoppedlimitcyclesarecausedbyvalvestiction.ThegeneralityofthisobservationcanbededucedfromresearchresultsreportedbyXueandAthertonandFullerandhasbeenextensivelyverifiedbysimulationandplantobservation.Thisreasoningestablishesthepreferredtechniqueofusingastatisticalmeasureofkurtosis(andoptionallyskewness)asameansofdistinguishinglimitcyclesfromotherpathologicalvariations.Thestatisticusedtomeasurekurtosis is:
K = height of the tracking error histogram bar between + and - W of the mean centered on zero
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- number of samples x area under normal density between + and - W of the mean
[0037]
The statistic used to measure skewness is
Sk= number of tracking error observations greater than 0- half the total number of tracking error time-series observations.
(6)
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[0038]Undertheassumptionsthatdisturbancesaredescribedbystationaryrandomprocessesandthatthedatasetissufficientlylarge,theinventionusesahypothesistesttorecognizestatisticallysignificantdeparturesofKand/orSfrom0.IfanullhypothesisthattrackingerrorvariationshaveGaussianprobabilitydistributionisadopted,thishypothesistestdetectslimitcyclesbymeasuringtheconfidencethattheobservedKand/orSisinconsistentwiththenull hypothesis. The method for performing this test on K proceeds as follows:
1.Ifthesequenceofobservedtrackingerrorsisx(k)wheretheindexkrangesfrom1(thestartofthesequence)to n (the end of the sequence), new sequence y(k) is generated by the following rule:
if x(k) is within the limits of the center bar of the histogramthen y(k):=1 otherwise y(k):=0
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A constant equal to the sample mean of y is then subtracted from each element y(k).
2.Theautocorrelationfunctionforthesequencey(k)iscomputeduptoafixedlagN.Thatsequenceisdenotedby R(j) where j ranges from -N to +N.
Thepreferredmethodofcalculatingtheautocorrelationsequenceistocomputeanautoregressivemodelforthe time-series y using standard least-squares methods, and estimate R from the autoregressive parameters.3.Thesumofthesequencey(k)priortoremovingthesamplemean,definedtobeS,istheheightofthecenterbarofthehistogram.UnderthenullhypothesistheexpectedvalueofSisequaltotheareaundertheGaussianbellintherangeofthecenterhistogrambarmultipliedbythenumberofsamples.ThevarianceofSisgivenbythe formula:
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where R(.) is the estimated autocorrelation sequence,n is the number of samples,
S=thesumofthesequencey(k)priortoremovalofthesamplemean,whichistheheightofthecenterbarofthehistogram,andtheexpectedvalueofSisequaltotheareaundertheGaussiancurveintherangeofthecenter histogram bar multiplied by the number of samples, i.e.
x
nerf(--------------)
1.414
W
sample standard deviation ofχ(k)
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4.IfthereareasufficientnumberofdatapointstheprobabilitydensityfunctionfortherandomvariableSisGaus-sian. Under this assumption the confidence in the null hypothesis can be expressed:
x
confidence =nerf(--------------)
1.414
whereχ=
(8)
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absolutevalueofthedifferencebetweentheexpectedvalueofSanditscomputedvaluedividedbythe estimated standard deviation of S as calculated from (7)
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Negativeorpositiveresultsforthelimitcycletestcanbedecidedbyselectingappropriateconfidencebands.Forexampleifconfidenceislessthan10%thenalimitcycleisdeemedtobepresent,ifconfidenceisgreaterthan70% then a limit cycle is not deemed present, otherwise the result is equivocal.
ThesametestcanbeusedfortheskewnessstatisticSkbyreplacing\"centerbarofthehistogram\"by\"greater
n
than zero\" in steps 1 and 3 and noting that the expected value of S is.
2
[0039]Thekeyfeatureofthisstatisticaltestisthatitaccountsforthecorrelationbetweensuccessivelyobservedtrackingerrormeasurements,aphenomenonwhichinvalidatesthebasicassumptionofclassicalnon-normalitytests.Asecondadvantageisthatthetestquantifiesthemaincharacteristicofthehistogramdistortionproducedbycommonnonlinearitiescausedbyfrictioninactuator/valves,soenhancingthesensitivityandaccuracyofthetest.Themainadvantageofusingthisprocessforon-linecontrolmalfunctiondiagnosisisthatitusesonlynormalclosed-loopoper-ating data, no probing of the process is required.Examples:
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[0040]Thefollowingtwoexamplesdemonstratetwocasesofinteractionanditseffectontheabilityoftheinventionto determine the root cause of a malfunction.
[0041]Case1:Fig.9showstwotimeseriesdepictingtwocontrolledvariablesonapapermachine:theflowrateandconsistency(drysolidsmassperunitliquidmass)oftheflowofbrokepulptotheblendingtankaheadofthemachine.Theflowcontrolloopandtheconsistencycontrolloopcomprisedthesetofloopswhoseperformanceindicesweregreaterthanthepresetthreshold(dubbed\"potentiallymalfunctioning\"),amongthelargerpreselectedlistofloopsfromwhichdatawasanalyzed.TheperformanceindicesascalculatedbythemethodshowninFig.1were9.65and2.51.ThepowerspectraestimatesobtainedfromthesmoothedFouriertransform(withDanielwindowsizegivenbyeq:4)areshowninFig.10.Boththeflowtrackingerrorandtheconsistencytrackingerrorexhibitaprimarycyclicalvariationatafrequencyof0.0081Hz.Theproportionofthevariancewithinabandwidthof+/-0.00125Hz(+/-1%oftheentirerange)oftheprimarypeakis80%fortheflowtrackingerrorand57%fortheconsistencytrackingerror;boththesevaluesareabovethethresholdlevelfordesignationofaprimaryresonance.Nosecondarypeakhassufficientvariancewithina+/-0.00125Hzbandwidthtobedesignatedasecondaryresonance.Inaccordancewiththepreferredembod-iments, the two control loops are assigned to the same single equivalence class of potentially interacting loops.
[0042]Applicationofeq:5yieldsmodifiedindicesofperformance1.92and1.09respectively.Inneithercaseisthefrequencyoftheresonanceoutsidethepre-computedlimits,andsoineithercasethe\"real\"indexcouldlieanywherebetweenthemodifiedandunmodifiedindex.Sincebothofthemodifiedindicesareinthe\"normal\"rangeof1-2,theresultsdonotdefinitelyisolateeitherloopasasourceofmalfunctionindependentlyoftheother,andamanualbumptest is required to make the distinction.
[0043]Thehypothesistestonthetrackingerrorhistogramrevealeda3%confidenceinthenullhypothesisfortheflowloopanda45%confidencefortheconsistencyloop.Consequentlytheconclusionismadethatiftheflowloopisthesourceofthemalfunction,thecauseisanonlinearityintheloopsuchasadefectivevalveoractuator,andiftheconsistencyloopisthesourceofthemalfunctionthenthecauseisalinearphenomenonsuchaspoorchoiceoftuningconstants.Subsequenttestsidentifiedthefirstloopasthecauseoftheproblemandconfirmedthediagnosticproducedby the method. Repair of the valve position and realignment of the valve resolved the malfunction.
[0044]Case2:Fig.11showstwotimeseriesdepictingtwocontrolledvariablesoninathermomechanicalpulpmill:thelevelofwoodchipsinapreheaterandthelevelofliquidpressateintheplugscrewfeederthatreceiveschipsfromthepreheater.Asincase1thepreheaterlevelcontrolloopandtheplugscrewlevelcontrolloopcomprisedthesetof\"potentiallymalfunctioning\"loopsamongthelistofloopsfromwhichdatawasanalyzed.Intheformercasetheper-formanceindexwas348.7andinthelatteritwas4.27.ThewindowedpowerspectrumestimatesareshowninFig.12.Asincase1primaryresonancesoccurinbothloops,bothatafrequency0.005Hz,accountingfor73%and32%ofthevariancerespectively.Forthepreheaterlevel,nosecondarypeakhassufficientvariancewithina+/-0.00125Hzbandwidthtobedesignatedasecondaryresonance.Howeverfortheplugscrewlevelasecondaryresonanceat0.183Hzwasdetectedwithanassociatedrelativevarianceof3%withabandwidth+/-0.000125Hz.Thecoincidenceofthe
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twoprimaryresonancescausesthemethodtoassociatebothloopswiththesamesingleequivalenceclassofpotentiallyinteractingloops,asincase1.Themodifiedindicesofperformanceare93.91and2.93respectively,andinneithercaseistheresonanceoutsidethepresetlimits.Howeverincontrasttocase1,bothmodifiedindicesareabovethelevelofnormallyfunctioningloops,anditcanthusbeconcludedthatbothloopsaremalfunctioningindependentlyoftheevidentinteractionbetweenthem.Thehistogramtestrevealsconfidencesof32%and65%inthenullhypothesis,and so both malfunctions are likely caused by linear defects.
[0045]Priorestimatescanbeobtainedfortheclosed-loopresonantfrequenciesoftwocommonlyoccurringclassesof process dynamics:
a)Selfregulatingprocesseswithlineardynamicswhichareapproximatelydescribedbyafirstorderstabletransferfunction and a delay;
b) Non-self regulating processes with negligible delay.
[0046]Thetwoestimateswhichfollowareindependentofthecontrollertuningconstants:Foraprocesswhosedynamicsaredescribedbya),anyclosed-loopresonantfrequencyisboundedbelowbythesmallestfrequencyw(inradians per sample) which satisfies
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whereα is the open loop time-constant and d is the open loop dead-time.
[0047]Foraprocesswhosedynamicsaredescribedbyb),anyclosedloopresonantfrequencyisboundedaboveby:30/(timeforprocessvariabletochange1%fora1%changeinthemanipulatedvariable).Thequantityonthedenominatoraboveisconsideredtobeageneralizationofthetime-constantfornon-selfregulatingprocesseswhensettingupthepriorinformationfilesforthoseloops.BoththeseboundsarederivedfromclassicalNyquistfrequencyresponsemethodsandsomeassumptionsabouttheactuatorinthelattercase.Other,similarboundscanbederivedin the same manner for different assumptions.
[0048]Figure14Aillustratesapapermakingmachine101,whichhasplurallocalcontrolunits103controllingdifferentpartsofthemachine.Thecontrolunitsarecomprisedofvariousclosedloopcontrolloopsofwellknownstructure.Thelocalcontrolunitsareconnectedtoadistributedcontrolsystembus105,whichbusisconnectedviaacomputergateway 107 and a network link 109 to a computer 111, having a display.
[0049]Inoperation,astreamofdatacomprisedofameasurementbythelocalcontrolunitsofavariablebeingcontrolledbyeachcontrolloop,andatargetorsetpointforeachcontrolloop,ispassedviathelocalcontrolunits103viathebus105,gateway107andnetworklink109tothecomputer111,wheretheremainderoftheprocessalreadydescribed is further carried out.
[0050]ItshouldbeunderstoodthattheprocesscanbecarriedoutusingthestructureandelementstobedescribedbelowwithreferencetoFigures14B,15,16and17.Alternatively,thecomputer111cansimulatethestructurestobedescribed below.
[0051]Figure14Billustratesabasicblockdiagramofastructurewhichcanimplementtheinventiveprocess.Theaforenotedvariablesbeingcontrolledandthetargetorsetpointsaresampledbythelocalcontrolunits,andarecon-vertedbyanalogtodigitalconverters113foreachofthencontrolloopstodigitalform,andthelastNsamplesofeacharestoredinabuffers115.Themeasuredvalueofeachcontrolledvariableisthensubtractedfromtheassociatedsetpointincorrespondingsubtractors117,toobtainasequenceofdigitaldatavaluesignalsrepresentingthetrackingerror for each loop.
[0052]Thetrackingerrorsignalsforeachloopareappliedtoadiagnosticevaluator119whichisdescribedinmoredetailwithreferencetoFigure15,toaperformanceindexdeterminator121whichisdescribedinmoredetailwithrespecttoFigure16,andtoaspectralpeakdetectorwhichisdescribedinmoredetailwithrespecttoFigure17.Theoutputs of these subsystems are signals representing single values rather than data sequences.
[0053]Anoutputsignalofthediagnosticblock119isafigureofconfidenceinthenullhypothesisthattheprobabilitydensityfunctionoftheinputsequenceisnormallydistributed,i.e.thatithasapurelyGaussiandistribution.Tointerpretthisfigureofconfidence,thissignaliscomparedwithtwolimits(confidencelowlimit,andconfidencehighlimit)inrespectivecomparators125and127,thelimitsbeingprovidedbyconstantsignalgenerators131and133.Thethresh-oldorlimitsignalsappliedbygenerators131and133arecomparedwiththefigureofconfidencesignalincomparators125and127respectively,andanoutputsignalsaregeneratedtosignalpaths129and135respectivelyindicatethat
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the indexes exceed the limit signals.
[00]ThesignalsindicatingexceedingoftheconfidencehighandlowlimitsaresimultaneouslyappliedtoNORgate145,ANDgate137,andexclusiveORgate134.TheoutputsignalofNORgate145isappliedtoasignalpath147,whichwhenhighindicatesanon-linearmalfunctioninthecontrolloop.TheoutputsignaloftheANDgate137isappliedtosignalpath141,whichwhenhighindicatesalinearmalfunctionofthecontrolloop.TheoutputsignaloftheexclusiveORgate134isappliedtosignalpath143,whichwhenhighindicatesthatthereisnostatisticalsignificanceof the null hypothesis form the diagnostic evaluator.
[0055]Theoutputsignaloftheperformanceindexdeterminator121online149isthenonlinearperformanceindexfor the control loop in question.
[0056]Thespectralpeakdetector123providesfouroutputsignals:thefrequenciesofanysecondaryandprimaryspectralpeaks,andtheproportionofthetotalvariance(withinapresetbandwidth)accountedforbythoseprimaryandsecondary peaks.
[0057]ThepairoftheoutputsignalsofthespectralpeakdetectorrepresentingtheproportionofthetotalvarianceaccountedforbythoseprimaryandsecondarypeaksarepassedthroughrespectiveswitchesXandY(foreachloop)andareappliedtoadder150.Theoutputissubtractedfrom\"1\"insubtractor151,andtheresultismultipliedinmultiplier152fromtheperformanceindexoutputfromperformanceindexdeterminator121online149,toprovideamodifiedindex of performance on line 153.
[0058]Theseoutputsignalsforallofthenspectralpeakdetectorsareassignedintoequivalenceclasses,asfollows.[0059]Grouplogic155receivesthefrequenciesofthespectralpeakoutputsignalsfromtheeachofthespectralpeak detectors 123, and assigns loops into equivalence classes, according to the following conditions:
(a)Aprimaryspectralpeak(accountingformorethanapredeterminedproportionofthevariance)foroneloopcoincideswitheitheraprimaryorsecondaryspectralpeakinanotherloop(thataccountsformorethanaprede-termined proportion of the variance);
(b)Asecondaryspectralpeak(accountingformorethanapredeterminedproportionofthevariance)foroneloopcoincideswitheitheraprimaryorsecondaryspectralpeakinanotherloop(thataccountsformorethanaprede-termined proportion of the variance);
(c)Ifcriteria(a)issatisfiedforagivenloop,thenswitchXisclosedforthatloop.Ifcriteria(b)issatisfiedforagiven loop, then switch Y is closed for that loop.
[0060]Thisactionhastheeffectofsettingthemodifiedperformanceindexonline153equaltotheperformanceindexscaleddownbythevarianceproportionofanysignificantspectralpeak(s)whichareincommonwithotherloopsand cause the loop in question to be assigned to an equivalence class.
[0061]Thedetailsofanembodimentofthediagnosticevaluator119isillustratedinFigure15.Thetrackingerrorsignalfromsubtractor117(Figure14B)isappliedtoapairofcomparators157and159(Figure15).Alsoappliedtocomparator157isaconstantsignalrepresenting+0.1standarddeviationofzero,andalsoappliedtocomparator159isasignalrepresenting-0.1ofastandarddeviationofzero.Comparator157outputsasignalwhichis1whenthetrackingerrorissmallerthan+0.1standarddeviationsofzeroandzerootherwiseandcomparator159outputsasignalwhichis1whenthetrackingerrorislargerthan-0.1standarddeviationofzero.Theoutputsofthecomparators157and159whicharesequencescomprisingzeroesandonesareappliedtoANDgate161,whichhasanoutputsignalthatisonewhenthetrackingerroriswithinthe+0.1and-0.1standarddeviationboundsofzeroandiszerootherwise,intheformofasequenceofonesandzeros,withthevalueofonewhenthetrackingerroriswithintheaforenotedbounds.
[0062]Thissignalisappliedtoprocessor163whichdeterminesthestandarddeviationofthestatistick,inaccordancewith equation (7) described earlier.
[0063]Thesequenceofonesandzerosisalsosummedinaccumulator165,resultinginanoutputsignaltherefromthatrepresentsasinglenumberwhichisequaltothenumberofpointsintheoriginalinputsequencehavingabsolutevalue within the +/- 0.1 standard deviations bounds of zero.
[00]Thetrackingerrorisalsoappliedtoarootmeanssquarecalculator167,wherestandarddeviationiscalcu-lated,theresultingsignalbeingprocessedinprocessor169bye(0.1/(1.414xinput))(where\"input\"istheoutputsignalofcalculator167)andthenmultipledbythetotalnumberofsamples,toprovideanestimateoftheexpectedvalueoftheoutputofaccumulator165underthenullhypothesisthattheprobabilitydensityfunctionofthetrackingerrorisnormal.[0065]TheestimateofKsignalisobtainedastheoutputofsubtractor171,whichisthedifferencebetweenthesignalwhichistheoutputofthecalculationblock169andthesignalwhichisoutputfromaccumulator165.Thissignalisappliedtodivider173.Theestimatedstandarddeviationofthestatistickobtainedinprocessor163isalsoappliedtodivider173,whereitisdividedintothesignaloutputfromsubtractor171.Theresultisprocessedthroughprocessor175whereitistransformedby50(1-e(input/1.414)),where\"input\"istheoutputsignalfromdivider173,theresultbeingthe estimate of K relative to its estimated standard deviation.
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[0066]TheratioKtoitsestimatedstandarddeviationasprocessedinprocessor175isasignalrepresentingtheconfidence figure described earlier with reference to Figure 14B.
[0067]Theprocessor163canberealizedbymultiplyingtheoutputsignalfromANDgate161withitselfandpro-gressivelydelayedversionsthereof,andaccumulatingtheresultinrespectiveaccumulators.Theoutputoftheaccu-mulatorofthenondelayedmultipliedoutputsignal,andtheoutputsoftheotheraccumulatorsmultipliedby2(n-x)/n(wherexrepresentsthenumberofdelayelementsinseriesandnrepresentsthenumberofpointsintheoriginalinputsequence) are added together and the result forms the standard deviation of the tracking error signal.
[0068]Figure16illustratesanembodimentofaperformanceindexdeterminator121(Figure14B).Theinputsignalfrom subtractor 117 is stored in a buffer 177.
[0069]Whentriggered,thebuffertransmitsthestoredsignaltoasquarer179,toasigndetector181,andtoamultiplier by 1, 183.
[0070]Theoutputsofthesquarer179,signdetector181andmultiplier183areappliedtotappeddelaylines185A,185Band185C,whereintappingweights187arevariableundercontrolofanoptimizerprocessor1.Theoptimizerprocessor 1 varies the tapping weights to minimize its input signal.
[0071]Theoutputsignalsfromdelayline,weightedbythetappingweights,aresummedinadders1,andtheresulting sums are added to the undelayed input signal from the output of multiplier by 1, 183.
[0072]Itshouldbenotedthatthefirstdelayelementofthetappeddelaylinedelaystheinputsignalsbyd+1samples,where d is the dead-time of the control loop under consideration.
[0073]Thevarianceoftheresultingsequenceofsumsisthencomputed,bydividingthermssquared(inmultiplier192)ofthesignalstoredinthebuffer177bytheoutputsignalfromrmscalculator191,individer193.Thequotient,representingtheindexofperformance,isinverselyrelatedtotheaccuracyofpredictionofcurrentobservationsoftheinputsequenceof183or117bylinearcombinationsasrepresentedbytappingweightsofthealgebraicfunctionsofpast observations.
[0074]Theoptimizer1thenrepeatsthecyclefornewvaluesofthetappingweights,retriggeringthebuffer177torecalltheinputsequence,recalculatingtheapproximationerrorformodifiedtappingweights,untilthevarianceofthesumsequence194isminimized.Uponcompletionoftheoptimizationthevarianceoftheinputsignalisdividedbytheminimumvarianceofthesumsequencetoyieldtheperformanceindex,whichisthefinaloutputoftheperformanceindex determinator block 121.
[0075]Anembodimentofthespectralpeakdetector123(inFigure14B)isillustratedinFigure17.Theinputsignalfromthesubtractor117isappliedtoadigitalspectralanalyzer195,whoseoutputsignalsareasequenceofsquaredabsolutevaluesoftheFouriertransformof.theinputsignalandthesequenceofcorrespondingfrequencies.Thefirstoutputsignalispassedthroughasymmetricalnon-causalmovingaveragedigitalfilter197,thewidthofthemovingaverage of which is set by a smallest integer k which satisfies ke(k)[0076]Theoutputsignalofthefilter197andthesecond(frequency)outputofthespectralanalyzer195areappliedtoamaximumdetector199,whichcomputesthefrequencyofthemaximumpointofthefilteredspectrum.Thispeakis then identified with the primary spectral peak. [0077]Thefilteredspectrumfromfilter197andthesequenceoffrequenciesarethenstoredinanotherbuffer201.Allspectralvaluesofthesignalstoredinthisbufferthatarewithinacertainbandwidthofthefrequencyoftheprimaryspectral peak are then set to zero by a sequence of operations to be described below. [0078]Thefrequencyatthemaximumofthismodifiedspectrumisthencomputedbyasecondmaximumdetector,andthisfrequencyisidentifiedwiththesecondaryspectralmaximumwhichisoutputfromdetector203.Frequenciesarethenmultipliedby(2/(datalengthxsampletime)),toobtainthefrequenciesofthesecondaryandprimaryspectralpeaks, which are one pair of the output signals of spectral peak detector 123. [0079]Theelementsinthedashedlineblock205calculatetheproportionofthevariancewithinapresetbandwidthofthecalculatedfrequenciesoftheprimaryandsecondaryspectralpeaks,theotherpairofoutputsignalsofthespectralpeak detector 123. [0080]Settingthespectralvalueswithinacertainbandwidthofthefrequencyoftheprimaryspectratozeroisobtainedbyprovidingasignalfromaprocessingcircuit207whichrepresentstheminimumpeakwidthincyclespersamplex(datalength)/2,inperiodogramordinates.Thissignalisaddedtotheoutputsignalofthemaximumdetector199inadder209andissubtractedfromthesamesignalinsubtractor211.Theresultiscomparedwiththesecondfrequencysequence output signal of the spectral analyzer 195 in comparators 213 and 215. [0081]Ifanyelementoftheoutputofthespectralanalyzerislessthanthecorrespondingoutputofsubtractor211,thecorrespondingoutputofthecomparator213isone,otherwiseitiszero.Ifanyelementoftheoutputofthespectralanalyzer195isgreaterthanthecorrespondingoutputoftheadder209,theoutputofcomparator215isone,otherwiseitiszero.Theoutputsofcomparators213and215thenmultiplythefirstoutputofbuffer201inmultipliers217and219. The result, and the output of the buffer 201, are applied to the maximum detector 203. [0082]Theproportionofthevariancewithinapresetbandwidthofthecalculatedfrequenciesoftheprimaryandsecondaryspectralpeaksaredeterminedbyapplyingtheoutputofthemaximumdetector199toadder221andto 5 10 15 20 25 30 35 40 45 50 55 13 EP0 907 913B1 subtractor223towhichasignalisappliedrepresentingthe(peakvariancebandwidth)x(datalength)/2.Theoutputsignalofthemaximumdetector203isappliedtosubtractor223andtosubtractor227towhichthesignalisappliedrepresentingthe(peakvariancebandwidth)x(datalength)/2.Theoutputsignalsofsubtractors223and227areappliedtorespectivecomparators229and231,towhichthesecond(frequency)outputofthedigitalspectralanalyzer195isapplied. [0083]Intheeventthatthissignalexceedstheoutputofsubtractor223or227theoutputoftherespectivecomparator229 or 231 is one, otherwise it is zero. [0084]Similarly,theoutputsofadders221and225areappliedtoinputsofcomparators233and235towhichthesameoutputofthedigitalspectralanalyzer195isapplied.Intheeventthatthissignalislessthantheoutputofadder221or225,theoutputoftherespectivecomparator233or235isone,otherwiseitiszero.Theoutputsofcomparators229,233,231and235aremultipliedinrespectivemultipliers137,141,139and143withthefirst(spectrum)outputsignal of the spectral analyzer 195. [0085]Theresultingoutputsofmultipliers141and143areappliedtorespectivemultipliers145and147wheretheyaresquaredandthesequencessummed.Theresultingsignalsaredividedindividers151and153bythesumofthesquares of the input signal to the spectral analyzer calculated by processor 149. [0086]Theoutputsignalsofthedividers151and153representthevarianceproportionoftheprimaryandsecondaryspectralpeaks,andtheoutputofprocessor204providesthefrequenciesoftheprimaryandsecondaryspectralpeaks,which are the four output signals, noted in the earlier description of Figure 14B, from spectral peak detector 123.[0087]Apersonunderstandingthisinventionmaynowconceiveofalternativestructuresandembodimentsorvar-iations of the above. 5 10 15 20 Claims 25 1. 30 Amethodofdiagnosticdifferentiationbetweentwoormorepotentialsourcesofamalfunctionrelatingtoaclosedloopcontrolloopofaprocesscontrolsystemwhichincludesatleastoneclosedloopcontrolloopcomprisingmeasuringahistogramoftrackingerrorofsaidcontrolloop,determiningdistortionofsaidtrackingerrorrelativetoaGaussiandistribution,andindicatingamalfunctionintheprocessintheeventadeviationfromsaidGaussiandistributionofsaidtrackingerrorexceedspredeterminedlimits,whereinsaiddistortion(K)ismeasuredbysub-tractingfromaheightofatrackingerrorhistogrambarofsaidhistogramcenteredonzero,anumberofsamplesmultipliedbyanareabetweenapairoflimitsdefininganormaldensityaboutameanofsaidhistogram,andthenindicating a malfunction in the process in the event a value of K is different from 0 by a predetermined amount.A method as defined in claim 1 in which the malfunctioning indicating step is carried out by: (a)ifasequenceofobservedtrackingerrorsisx(k),wheretheindexkrangesfrom1(thestartofthesequence)to n (the end of the sequence), generate a new sequence y(k) by the following rule: ifx(k)iswithinthecenterbarofthehistogram,theny(k):=1,otherwisey(k):=0,thensubtractthesamplemean of y from each element y(k), (b)computeanautocorrelationfunctionforthesequencey(k)uptoafixedlagN,whereinanautocorrelationfunction sequence is R(j) where j ranges from -N to +N,(c) determine a variance using the transform 2. 35 40 45 50 55 where R(.) is the estimated autocorrelation sequence,n is the number of samples, S=thesumofthesequencey(k)priortoremovalofthesamplemeanin(a),whichistheheightofthecenterbarofthehistogram,andtheexpectedvalueofSisequaltotheareaundertheGaussiancurveintherange of the center histogram bar multiplied by the number of samples,(d) determine a confidence value C, x where C =nerf(),1.414 14 EP0 907 913B1 χ = absolute value of the difference between the expected value of S andits computed value divided by the estimated standard deviation of S, and (e) set confidence bands and determine whether C is contained within the bands. 5 3. Amethodofdiagnosticdifferentiationbetweentwoormorepotentialsourcesofunsatisfactorycontrolloopper-formance of an industrial machine which includes a plurality of closed loop control loop comprising: (a)collectingoperatingdatacomprisingtimeseriesofcontrolledvariablemeasurementsandcontrolloopsetpointssimultaneouslyfrompredeterminedcontrolloops,foraperiodofatleastapproximately100timesalongest time constant of said predetermined control loops, (b) subtracting measured variable data from set point data to obtain tracking errors, (c)determininganamountbywhichobservedvarianceofatrackingerrorexceedsaminimumvalue,afternon-linearelementshavebeenremovedfromaloop,exploitingpriorestimatesofprocesstimeconstantanddead-time to provide a raw index, (d)testingforanyinteractionsbetweencontrolloopswhichmaybeinflatinginanabnormalmanneranestimateof said raw index, (e)determiningamodifiedrawindexforaparticularloopintheeventsaidinflatedestimatesaredetected,and(f)distinguishingbetweencontrolloopsthataremalfunctioning,thosethatarenotmalfunctioning,andthosethatarepossiblymalfunctioningandareperturbedbyinteractingmalfunctioningcontrolloops,basedonsaidraw index and said modified raw index. 10 15 20 4. 25 A method as defined in claim 1 or 2 further comprising: (i) computing said histogram of the tracking error for each loop of said system; (ii)quantifyingkurtosisofeachhistogrambydeterminingheightofacenterbarofsaidhistogramrelativetoanexpectedheightwhereintheexpectedheightisdeterminedbyanassumptionthattrackingerrorisnormallydistributed with a sample mean and sample variance, (iii)calculatingastatisticalsignificanceofsaidkurtosisinadownwarddirection,takingintoaccountanyinter-sample correlation of tracking error time-series, and (iv) displaying said statistical significance as a diagnostic measure indication. 30 5. 35 Amethodasdefinedinclaim3,inwhichsaidrawindex(IN)isdeterminedbyobservingtrackingerrorvariation(O)insaidloop,determiningavarianceofconditionalexpectation(V)frommeasurementsandsamplesinthepast, and processing O/V to obtain IN. A method as defined in claim 5, wherein V is determined by: (a) subtracting a measured variable from a set point to obtain a tracking error,(b) extracting prior measured variable data for said loop, (c)intheeventasampletimeTofsaidvariableisatleastapproximately0.1timesthedominantopenlooptimeconstantofsaidloop,findingbestleastsquaresapproximationofavectoroftrackingerrorobservationswithlinearcombinationsoftrackingerrorsandsuccessivetrackingerrorsdelayedbysuccessivesampleperioddelays, and (d)intheeventasampletimeofsaidvariableissmallerthanapproximately0.1timessaiddominantlooptimeconstant,resamplesaidvariableatasampleintervalapproximately5-10timesshorterthansaiddominantopen loop time constant, and then find the best least squares approximation as in step (c). 6. 40 45 7. 50 Amethodasdefinedinclaim6inwhichthestepofcalculatingsaidrawperformanceindexiscomprisedofdeter-mininganamountbywhichobservedvarianceofatrackingerrorexceedsaminimumvalue,afternon-linearelements have been removed from a loop, from prior estimates of process delayed time constant. Amethodasdefinedinclaim6inwhichstep(d)iscomprisedofdigitalantialiasfilteringsaidvariableandresamplingsaidvariableatalongersampleintervalIwhichisapproximately5-10timesshorterthansaidopenlooptimeconstant, and expressing said longer sample intervals as said sample intervals. Amethodasdefinedinclaim8inwhichacutofffrequencyoftheantialiasingfilterisbetween10-20timesthereciprocaloftheopenlooptimeconstantinradianspersample,andinwhichtheresamplingintervalisapproxi- 8. 55 9. 15 EP0 907 913B1 mately 0.1 - 0.2 times an estimated process time constant. 10.Amethodasdefinedinclaim6includingthestepofdeterminingtheexistenceofdriftintrackingerrorusinga statisticDwhereinD=maximumof(|m1|,|m3|)whereinm1andm3aremeansofthefirstthirdandthirdthirdofatimeseriesofsaidtrackingerror,andprovidingawarningsignalifD>standarddeviationofthetrackingerrorx(12M/L)1/2, where m is a predetermined large number and L is the number of samples in the time series.11.A method as defined in claim 3characterised by 10 5 15 (a)inrelationtoacontrolloopofagroupofloopscontrolindicatedaspotentiallymalfunctioning,computingafastFouriertransformofatrackingerror,andfilteringproductsofsaidtransformtoremovespuriouspeaks,(b)identifyingprimaryandsecondaryspectralpeakscontributingmorethanathresholdvarianceinaprede-termined bandwidth for said control loop, (c)selectinganothercontrolloopinsaidgroupofcontrolloopsandrepeatingsteps(a)and-(b)untilalastcontrol loop in said group has been processed, (d)dividingpotentiallymalfunctioningloopswithapproximatelycoincidentspectralpeaksintopossiblyinter-acting classes, and (e) determining a modified performance index for all control loops belonging to a class. 12.Amethodasdefinedinclaim11includingdeterminingadriftofsaidoperatingdata,andindicatingfromavalue oratrendofsaiddriftwhetheranupsetconditionexists,andintheeventanupsetconditionexists,providingawarning indication.13.Amethodasdefinedinclaim12includingcarryingoutthestepofdeterminingthepresenceofsaiddriftbydeter-miningastatisticDforthedrifttrackingerrorofsaidloop,whereinD=maximumof(|m1|,|m3|),whereinm1andm3aremeansofafirstthirdandthirdthirdofatimeseriesoftrackingerror,andindicatinganupsetconditionifD>standarddeviationofthetrackingerrorx(12M/L)1/2whereMisapredeterminedlargenumberandListhenumber of samples in the tracking error time eries.14.A method as defined in claim 3characterised by (a)trackingerrorvariationsofnarrowspectralbandwidthineachofsaidpredeterminedcontrolloopsofsaidprocess, (b)comparingspectralpeaksofsaiderrorvariationstodetectcoincidencesofpeakswhichareindicativeofinteraction between said predetermined control loops, and (c)quantifyingeffectsofsaiderrorvariationswhichhavesaidcoincidencesofpeaks,andasaresultdeter-mining malfunctioning of a control loop. 15.A method as defined in claim 14 performed on each control loop deemed to be malfunctioning, inwhichsaiderrorvariationtrackingstepiscomprisedofevaluatingaFouriertransformofsaidtrackingerrorvariations,windowingproductsoftheFouriertransformation,choosingaDanielwindowhavingbandwidthWper-iodogram ordinates such that W is a smallest integer which satisfies WexpW > L, andinwhichthespectralpeakcomparingstepiscomprisedofestimatingthefrequencyf1ofafirstmaximumoftheestimatedpowerspectrum,evaluatingacenterfrequencyf2ofanycenterpeakbytestingforasecondmaximumoverfrequenciesexcludedfromanintervalaroundthefirstmaximum,evaluatingavarianceassociatedwithsaidprimaryandsecondarymaximabycomputinganareaunderthepowerspectrumestimateoveranintervaloffixedbandwidthaboutsaidfrequenciesf1andf2,andindicatingthepresenceofaspectralresonanceatacorrespondingfrequencyf1orf2intheeventeithervarianceexceedspredeterminedproportionsofoveralltrackingerror variance.16.Amethodasdefinedinclaim15includingthestepofformingclassesofcontrolloopsbyassociatingcontrolloops inaclass,whereinsaidfrequenciesf1andf2ofacontrolloopareadjacenttoeithersaidf1orf2ofanothercontrolloop by a small predetermined amount. 20 25 30 35 40 45 50 55 17.Amethodasdefinedinclaim7includingdeterminingacategoryofmalfunctionofaprocesscarriedoutbysaid industrial machine comprising: (a) tracking error variations of narrow spectral bandwidth in each of plural control loops of said process, 16 EP0 907 913B1 (b)comparingspectralpeaksofsaiderrorvariationstodetectcoincidencesofpeakswhichareindicativeofinteraction between said plural control loops, and (c)quantifyingeffectsofsaiderrorvariationswhichhavesaidcoincidencesofpeaks,andasaresultdeter-mining malfunctioning of a control loop. 5 10 15 18.A method as defined in claim 17 performed on each control loop deemed to be malfunctioning, inwhichsaiderrorvariationtrackingstepiscomprisedofevaluatingaFouriertransformofsaidtrackingerrorvariations,windowingproductsoftheFouriertransformation,choosingaDanielwindowhavingbandwidthWper-iodogram ordinates such that W is a smallest integer which satisfies wexpW > L, andinwhichthespectralpeakcomparingstepiscomprisedofestimatingthefrequencyf1ofafirstmaximumoftheestimatedpowerspectrum,evaluatingacenterfrequencyf2ofanycenterpeakbytestingforasecondmaximumoverfrequenciesexcludedfromanintervalaroundthefirstmaximum,evaluatingavarianceassociatedwithsaidprimaryandsecondarymaximabycomputinganareaunderthepowerspectrumestimateoveranintervaloffixedbandwidthaboutsaidfrequenciesf1andf2,andindicatingthepresenceofaspectralresonanceatacorrespondingfrequencyf1orf2intheeventeithervarianceexceedspredeterminedproportionsofoveralltrackingerror variance.19.Amethodasdefinedinclaim18includingthestepofformingclassesofcontrolloopsbyassociatingcontrolloops inaclass,whereinsaidfrequenciesf1andf2ofacontrolloopareadjacenttoeithersaidf1orf2ofanothercontrolloop by a small predetermined amount.20.Amethodasdefinedinclaim10includingthestepsofdeterminingamodifiedindexofperformanceasadeter-minationofmalfunctionforcontrolloopsbelongingtoeitheraclassofpotentiallyinteractingcontrolloopsoraclassofcontrolloopsinwhicharesonanceisidentifiedtobeoutsideapredeterminedrangeofwavelengthswhichresonanceiscausedbyotherthanalimitcyclegeneratedduetothepresenceofaseverenonlearityinacontrolloop.21.Amethodasdefinedinclaim20inwhichsaiddeterminingstepiscomprisedofprocessingthesignalvalues: (modifiedindex)=(rawindex)x(1-proportionofthetrackingerrorvarianceassociatedwitharesonancesuspectedof being imposed externally to a control loop).22.A method as defined in claim 1 further comprising in combination the method as defined in claim 3. 20 25 30 35 Patentansprüche1. VerfahrenzurDiagnosedifferenzierungzwischenzweiodermehrmöglichenQuelleneinerStörungbeieinemge-schlossenenRegelkreiseinesProzeßregelungssystems,dasmindestenseinengeschlossenenRegelkreisent-hält,umfassenddasMesseneinesHistogrammsderRegelabweichungdesgenanntenRegelkreises,dasBestim-menderAbweichungderRegelabweichungvoneinerGaußverteilungunddasAnzeigeneinerStörungindemProzeßfürdenFall,daßeineAbweichungderRegelabweichungvonderGaußverteilungvorgegebeneGrenzwerteüberschreitet,wobeidiegenannteAbweichung(K)dadurchgemessenwird,daßvonderHöheeinesumNullzentriertenRegelabweichungs-HistogrammbalkensdesgenanntenHistogrammsdieAnzahlvonStichprobenmul-tipliziertmiteinerFlächezwischenzweiGrenzwerten,durchdieeineNormaldichteumdenMittelwertdesgenann-tenHistogrammsfestgelegtwird,abgezogenwird,undanschließendesAnzeigeneinerStörungindemProzeßfür den Fall, daß der Wert für K um einen vorgegebenen Betrag von 0 abweicht. Verfahren nach Anspruch 1, wobei der Schritt des Anzeigens einer Störung ausgeführt wird durch: (a)ErzeugeneinerneuenFolgey(k),auseinerFolgex(k)vonbeobachtetenRegelabweichungenx(k),wobeider Index k von 1 (dem Start der Folge) bis n (dem Ende der Folge) reicht, anhand der folgenden Regel: wennx(k)innerhalbdesMittelbalkensdesHistogrammsliegt,dannisty(k):=1,andernfallsy(k):=0,danach wird der Stichprobenmittelwert von y von jedem Element y(k) subtrahiert, 40 45 2. 50 55 (b)BerechneneinerAutokorrelationsfunktionderFolgey(k)biszueinemfestgesetztenZeitabstandN,wobeiR(j) eine Autokorrelationsfunktionsfolge ist, bei der j von -N bis +N reicht, 17 EP0 907 913B1 (c) Bestimmen der Varianz unter Verwendung der Transformation 5 10 wobei R(.) die geschätzte Autokorrelationsfolge ist,n die Anzahl der Stichproben ist, S=dieSummederFolgey(k)vordemAbziehendesStichprobenmittelwertesbei(a)ist,welchederHöhedesMittelbalkensdesHistogrammsentspricht,undderErwartungswertvonSgleichderFlächeunterderGaußkurve im Bereich des Mittelbalkens des Histogramms multipliziert mit der Anzahl von Stichproben ist,(d) Bestimmen eines Vertrauenswertes C,wobei 15 20 25 X = Absolutwert der Differenz von dem Erwartungswert von Sund seinem berechneten Wert dividiert durch die geschätzte Standardabweichung von S ist, und(e) Festlegen von Vertrauensbereichen und Ermitteln, ob C in den Bereichen enthalten ist. 30 3. VerfahrenzurDiagnosedifferenzierungzwischenzweiodermehrmöglichenQuellenunzufriedenstellenderRe-gelkreisleistung einer industriellen Maschine, die eine Vielzahl von Regelkreisen enthält, umfassend: (a)gleichzeitigesSammelnvonBetriebsdaten,dieZeitreihenvonRegelgrößen-MessungenundRegelkreis-Sollwertenenthalten,vonfestgelegtenRegelkreisen,füreinenZeitraum,dermindestensetwadashundert-fache der längsten Zeitkonstante der festgelegten Regelkreise beträgt, (b)SubtrahierengemessenerveränderlicherDatenvonSollwertdaten,umRegelabweichungenzuermitteln,(c)BestimmendesBetrages,umdendiebeobachteteVarianzderRegelabweichungeinenMindestwertüber-steigt,nachdemnichtlineareElementeausdemRegelkreisentferntwordensind,wobeifrühereSchätzwerteder Prozeßzeitkonstante und der Totzeit ausgenutzt werden, um einen Rohindex bereitzustellen, (d)PrüfenaufetwaigeWechselwirkungenzwischenRegelkreisen,dieeinenSchätzwertdesgenanntenRohin-dex möglicherweise auf abnorme Weise übermäßig steigern, 35 40 45 (e)BestimmeneinesmodifiziertenRohindexfüreinenbestimmtenRegelkreis,fürdenFall,daßdiegenanntenübermäßig gesteigerten Schätzwerte ermittelt werden, und (f)UnterscheidenzwischenRegelkreisen,diefehlerhaftfunktionieren,solchen,dienichtfehlerhaftfunktionie-ren,undsolchen,diemöglicherweisefehlerhaftfunktionierenunddurchwechselwirkendefehlerhaftfunktio-nierende Regelkreise gestört werden, auf der Basis des Rohindex und des modifizierten Rohindex. 4. 55 50 Verfahren nach Anspruch 1 oder 2, ferner umfassend: (i) Berechnen des Histogramms der Regelabweichung für jeden Regelkreis des Systems, (ii)QuantifizierenderKurtosiseinesjedenHistogrammsdurchBestimmenderHöhedesMittelbalkensdesHistogrammsrelativzueinerErwartungshöhe,wobeidieErwartungshöhebestimmtwirddurchdieAnnahme, 18 EP0 907 913B1 daßdieRegelabweichungnormalverteiltistmiteinemStichproben-MittelwertundeinerStichproben-Varianz,(iii)BerechneneinerstatistischenSignifikanzdergenanntenKurtosisineinerAbwärtsrichtung,unterBerück-sichtigung jeglicher Stichprobenkorrelationen von Regelabweichungs-Zeitreihen, und 5 (iv) Anzeigen der genannten statistischen Signifikanz als diagnostisches Maß. 5. 10 VerfahrennachAnspruch3,beidemdergenannteRohindex(IN)dadurchbestimmtwird,daßdieRegelabwei-chungsveränderung(O)indemgenanntenRegelkreisbeobachtetwird,eineVarianzbedingterErwartung(V)ausden früheren Messungen und Stichproben bestimmt wird, und O/V verarbeitet wird, um IN zu erhalten.Verfahren nach Anspruch 5, wobei V bestimmt wird durch: (a) Subtrahieren einer gemessenen Größe von einem Sollwert, um eine Regelabweichung zu erhalten, 6. 15 (b)ExtrahierenvonDatenfürveränderlicheGrößen,diefrüherfürdengenanntenRegelkreisgemessenwur-den, (c)fürdenFall,daßeineStichprobenzeitTdergenanntenveränderlichenGrößemindestensetwa0,1malderdominierendenOffener-Regelkreis-ZeitkonstantedesgenanntenRegelkreisesist,Herausfindenderbe-stenApproximationeinesVektorsvonRegelabweichungsbeobachtungenmitLinearkombinationenvonRe-gelabweichungenundsukzessiven,durchsukzessiveStichprobenperiodenverzögerungenverzögerteRegel-abweichungen nach der Methode der kleinsten Quadrate, und (d)fürdenFall,daßdieStichprobenzeitdergenanntenveränderlichenGrößekleineralsetwa0,1maldergenanntendominierendenRegelkreis-Zeitkonstanteist,erneuteStichprobennahmedergenanntenveränder-lichenGrößemiteinemStichprobennahmeabstand,deretwa5bis10malkürzeristalsdiegenanntedomi-nierendeOffener-Regelkreis-Zeitkonstante,andanschließendesHerausfindenderbestenApproximationnach der Methode der kleinsten Quadrate wie bei Schritt (c). 7. VerfahrennachAnspruch6,beidemderSchrittdesBerechnensdesRohleistungsindexausdemBestimmendesBetragesbesteht,umdendiebeobachteteVarianzeinerRegelabweichungeinenMindestwertübersteigt,nachdemnichtlineareElementeauseinemRegelkreisentferntwordensind,ausfrüherenSchätzwertenderprozeß-verzö-gerten Zeitkonstante. VerfahrennachAnspruch6,beidemderSchritt(d)darausbesteht,daßdiegenannteveränderlicheGrößemiteinemAnti-Aliasing-FilterdigitalgefiltertwirdunddiegenannteveränderlicheGrößemiteinemlängerenStichpro-bennahmeabstand1,deretwa5bis10malkürzeralsdieOffener-Regelkreis-Zeitkonstanteist,emeuteinerStich-probennahmeunterzogenwird,undAusdrückendergenanntenlängerenStichprobennahmeabständealsdiege-nannten Stichprobennahmeabstände. VerfahrennachAnspruch8,beidemeineGrenzfrequenzdesAnti-Aliasing-Filtersdas10bis20-fachedesKehr-wertsderOffener-Regelkreis-ZeitkonstanteinRadiantenproStichprobeist,undbeidemderStichprobennahme-abstand der erneuten Stichprobe etwa 0,1 bis 0,2 mal eine geschätzte Prozeßzeitkonstante ist. 20 25 30 35 8. 40 9. 45 50 10.VerfahrennachAnspruch6,umfassenddenSchrittdesErmittelnsderExistenzeinerDriftderRegelabweichung unterVerwendungeinerStatistikD,wobeiD=Maximalwertvon(|m1|,|m3|)ist,wobeim1undm3MittelwertedeserstenDrittelsunddrittenDrittelseinerZeitreihedergenanntenRegelabweichungsind,unddasBereitstelleneinesWarnsignals,wennD>StandardabweichungderRegelabweichungx(12M/L)1/2ist,wobeimeinevorgege-bene große Zahl und L die Anzahl der Stichproben in der Zeitreihe ist.11.Verfahren nach Anspruch 3,gekennzeichnet, durch (a)inZusammenhangmiteinemRegelkreisauseinerGruppevonRegelkreisen,diealsmöglicherweisefeh-lerhaftfunktionierendangezeigtwerden,BerechnenderschnellenFourierTransformiertenderRegelabwei-chung, und Filtern von Produkten der genannten Transformierten, um unechte Spitzen zu entfernen,(b)IdentifizierenvonerstenundzweitenspektralenSpitzen,diemehralseineSchwellenvarianzineinervor- 55 19 EP0 907 913B1 gegebenen Bandbreite für den genannten Regelkreis beitragen, (c)AuswähleneinesanderenRegelkreisesausdergenanntenGruppevonRegelkreisenundWiederholender Schritte (a) und (b), bis ein letzter Regelkreis aus der genannten Gruppe verarbeitet worden ist, 5 (d)EinteilenmöglicherweisefehlerhaftfunktionierenderRegelkreisemitnäherungsweisezusammenfallendenspektralen Spitzen in möglicherweise wechselwirkende Klassen, und (e) Bestimmen eines modifizierten Leistungsindex für alle Regelkreise, die zu einer Klasse gehören. 10 12.VerfahrennachAnspruch11,einschließlichdesErmitteinseinerDriftdergenanntenBetriebsdaten,undausge-hendvoneinemWertodereinemTrenddergenanntenDrift,desAnzeigens,obeinStörungszustandvorliegt,undfür den Fall, daß ein Störungszustand vorliegt, des Bereitstellens einer Warnungsanzeige. 15 20 13.VerfahrennachAnspruch12,umfassenddasDurchführendesSchrittesdesErmittelnsderExistenzdergenannten DriftdurchdasBestimmeneinerStatistikDfürdieDrift-RegelabweichungdesgenanntenRegelkreises,wobeiD=Maximalwertvon(|m1|,(|m3|)ist,wobeim1undm3MittelwertedeserstenDrittelsunddesdrittenDrittelseinerZeitreihederRegelabweichungsind,unddesAnzeigenseinesStörungszustandes,wennD>Standardabwei-chungderRegelabweichungx(12M/L)1/2ist,wobeiMeinevorgegebenegroßeZahlundLdieAnzahlderStich-proben in der Regelabweichungs-Zeitreihe ist.14.Verfahren nach Anspruch 3,gekennzeichnet, durch (a)AufspürenvonFehlervariationenschmalerspektralerBandbreiteinjedemdergenanntenvorgegebenenRegelkreise des genannten Prozesses, (b)VergleichenvonspektralenSpitzendergenanntenFehlervariationen,umÜbereinstimmungenvonSpitzenfestzustellen,dieeineWechselwirkungzwischendengenanntenvorgegebenenRegelkreisenanzeigen,und 25 30 (c)QuantifizierenvonEffektendergenanntenFehlervariationen,diediegenanntenÜbereinstimmungenvonSpitzen aufweisen, und resultierend Bestimmen einer Störung eines Regelkreises. 15.VerfahrennachAnspruch14,dasanjedemRegelkreisdurchgeführtwird,derfürfehlerhaftfunktionierenderachtet wird, beidemderSchrittdesAufspürenseinerFehlervariationdarausbesteht,daßmaneineFourier-TransformiertedergenanntenRegelabweichungsvariationenauswertet,ProduktederFourier-Transformationfensterartigdar-stellt,einDaniel-FenstermitBandbreiteWPeriodogramm-Ordinatenauswählt,sodaßWdiekleinsteganzeZahlist, die WexpW > L erfüllt, undbeidemderSchrittdesVergleichensderspektralenSpitzendarausbesteht,daßmandieFrequenzf1eineserstenMaximalwertesdesgeschätztenLeistungsspektrumsschätzt,eineMittelfrequenzf2irgendeinerMittelspitzedurchPrüfenaufeinenzweitenMaximalwertuntersolchenFrequenzen,dieauseinemIntervallumdenerstenMaximalwertherumausgeschlossensind,auswertet,daßmaneineVarianzauswertet,diemitdemgenanntenerstenunddemgenanntenzweitenMaximalwertverknüpftist,indemmandieFlächeunterdemgeschätztenLeistungsspektrumübereinIntervallfestgesetzterBandbreiteumdiegenanntenFrequenzenf1undf2berechnet,unddaßmandasVorhandenseineinerspektralenResonanzbeieinerentsprechendenFrequenzf1oderf2fürdenFallanzeigt,daßeinederVarianzenvorgegebeneAnteileeinerGesamtregelabweichungsvarianzübersteigt.16.VerfahrennachAnspruch15,umfassenddenSchrittderBildensvonKlassenvonRegelkreisendurchZuordnen vonRegelkreisenzueinerKlasse,inderdiegenanntenFrequenzenf1undf2einesRegelkreisesumeinenkleinenvorgegebenen Betrag an einer der genannten f1 oder f2 eines anderen Regelkreises angrenzen.17.VerfahrennachAnspruch7,umfassenddasBestimmeneinerKategorievonStörungeneinesProzesses,dervon der genannten industriellen Maschine durchgeführt wird, umfassend: 35 40 45 50 55 (a)AufspürenvonFehlervariationenschmalerspektralerBandbreiteinjedemauseinerMehrzahlvonRegel-kreisen in dem genannten Prozeß, (b)VergleichenvonspektralenSpitzendergenanntenFehlervariationen,umÜbereinstimmungenvonSpitzen 20 EP0 907 913B1 festzustellen, die eine Wechselwirkung zwischen den genannten mehrzahligen Regelkreisen anzeigen, und(c)QuantifizierenvonEffektendergenanntenFehlervariationen,diediesegenanntenÜbereinstimmungenvon Spitzen aufweisen, und resultierend Bestimmen einer Störung eines Regelkreises. 5 10 15 18.VerfahrennachAnspruch17,dasanjedemRegelkreisdurchgeführtwird,derfürfehlerhaftfunktionierenderachtet wird, beidemderSchrittdesAufspürensderFehlervariationdarausbesteht,daßmaneineFourier-TransformiertederRegelabweichungsvariationenauswertet,ProduktederFourier-Transformationfensterartigdarstellt,einDaniel-FenstermiteinerBandbreiteWPeriodogramm-Ordinatenauswählt,sodaßWdiekleinsteganzeZahlist,dieWexpW > L erfüllt, undbeidemderSchrittdesVergleichensderspektralenSpitzendarausbesteht,daßmandieFrequenzf1eineserstenMaximalwertesdesgeschätztenLeistungsspektrumsschätzt,eineMittelfrequenzf2irgendeinerMittelspitzedurchPrüfenaufeinenzweitenMaximalwertuntersolchenFrequenzen,dieauseinemIntervallumdenerstenMaximalwertherumausgeschlossensind,auswertet,daßmaneineVarianzauswertet,diemitdemerstenunddemzweitenMaximalwertverknüpftist,indemmandieFlächeunterdemgeschätztenLeistungsspektrumübereinIntervallfestgesetzterBandbreiteumdiegenanntenFrequenzenf1undf2berechnet,unddaßmandasVor-handenseineinerspektralenResonanzbeieinerentsprechendenFrequenzf1oderf2fürdenFallanzeigt,daßirgendeine Varianz vorgegebene Anteile der Gesamtregelabweichungsvarianz übersteigt.19.VerfahrennachAnspruch18,umfassenddenSchrittdesBildensvonKlassenvonRegelkreisendurchZuordnen vonRegelkreisenzueinerKlasse,inderdiegenanntenFrequenzenf1undf2einesRegelkreisesaneinedergenannten f1 oder f2 eines anderen Regelkreises um einen kleinen vorgegebenen Betrag angrenzen. 20 25 30 20.VerfahrennachAnspruch19,umfassenddieSchrittedesBestimmenseinesmodifiziertenLeistungsindexalsein BestimmungsmitteleinerStörungfürRegelkreise,dieentwederzueinerKlassevonmöglicherweisewechselwir-kendenRegelkreisenoderzueinerKlassevonRegelkreisengehören,beideneneineResonanzfestgestelltwird,dieaußerhalbeinesvorgegebenenBereichesvonWellenlängenliegt,wobeidieResonanzdurchetwasanderesverursachtwirdalseinenGrenzzyklus,deraufgrunddesVorhandenseinseinerstarkenNichtlinearitätineinemRegelkreis erzeugt wird.21.VerfahrennachAnspruch20,beidemdergenannteSchrittdesBestimmensausdemVerarbeitenderSignalwerte besteht:(modifizierterIndex)=Rohindex)x(1-AnteilderRegelabweichungsvarianz,diemiteinerResonanzverknüpft ist, von der man vermutet, daß sie einem Regelkreis von außen auferlegt worden ist). 35 22.Verfahren nach Anspruch 1, ferner in Kombination umfassend das Verfahren nach Anspruch 3. Revendications 40 1. 45 50 Procédédedifférenciationdiagnostiqueentredeuxsourcespotentielles,ouplus,dedéfautdefonctionnementconcernantuneboucledecommandeenboucleferméed'unsystèmedecommandedeprocessusquicomporteaumoinsuneboucledecommandeenbouclefermée,comprenantlamesured'unhistogrammed'erreurdesuivideladiteboucledecommande,ladéterminationd'unedistorsiondeladiteerreurdesuiviparrapportàunedistributiondeGauss,etl'indicationd'undéfautdefonctionnementduprocessusdanslecasoùunécartparrapportàladitedistributiondeGaussdeladiteerreurdesuividépassedeslimitesprédéterminées,danslequelladitedistorsion(K)estmesuréeensoustrayantd'unehauteurd'unebarred'histogrammed'erreurdesuividudithistogramme,centréesurzéro,unnombred'échantillonsmultipliéparunesurfaceentredeuxlimitesdéfinissantunedensiténormaleautourd'unemoyennedudithistogramme,undéfautdefonctionnementduprocessusétantensuite indiqué dans le cas où une valeur de K diffère de zéro, d'une quantité prédéterminée. Procédéselonlarevendication1,danslequell'étaped'indicationdedéfautdefonctionnementesteffectuéecommesuit: (a)siuneséquenced'erreursdesuiviobservéesestx(k),oùl'indice(k)vade1(ledébutdelaséquence)àn (la fin de la séquence), on génère une nouvelle séquence y(k) par la règle ci-après: six(k)estdanslabarrecentraledel'histogramme,alorsy(k):=1,sinony(k):=0,etonsoustraitalorsla 2. 55 21 EP0 907 913B1 moyenne des échantillons de y de chaque élément de y(k), (b)oncalculeunefonctiond'autocorrélationpourlaséquencey(k)jusqu'àundécalagefixeN,desortequ'uneséquence de fonction d'autocorrélation est R(j) où j va de -N à +N,(c) on détermine une variance au moyen de la transformation 5 10 15 où R(.) est la séquence d'autocorrélation estimée, n est le nombre d'échantillons, Sestlasommedelaséquencey(k)avantlasoustractiondelamoyennedeséchantillonsdans(a),quiestlahauteurdelabarrecentraledel'histogramme,etlavaleurattenduedeSestégaleàlasurfacesouslacourbe de Gauss dans la plage de la barre centrale d'histogramme multipliée par le nombre d'échantillons,(d) on détermine une valeur de confiance C, où x C =nerf(--------------), 1.414 X=valeurabsoluedeladifférenceentrelavaleurattenduedeSetsavaleurcalculéediviséeparl'écartstandard estimé de S, et (e) on établit des bandes de confiance et on détermine si C est contenu dans les bandes. 20 25 3. Procédédedifférenciationdiagnostiqueentredeuxsourcespotentiellesouplusdefonctionnementnonsatisfaisantd'uneboucledecommanded'unemachineindustriellequiinclutunepluralitédebouclesdecommandeenbouclefermée, comprenant: (a)lacollectededonnéesdefonctionnementcomprenantdessérieschronologiquesdemesuresd'uneva-riablecontrôléeetdepointsdeconsignedeboucledecommandesimultanémentàpartirdebouclesdecom-mandeprédéterminées,pendantunepérioded'aumoins100foisenvironunepluslongueconstantedetempsdes dites boucles de commande prédéterminées, (b)lasoustractiondesdonnéesdevariablemesuréesdesditesdonnéesdepointdeconsigne,pourobtenirdes erreurs de suivi, (c)ladéterminationd'unegrandeurdontlavarianceobservéed'uneerreurdesuividépasseunevaleurmini-male,aprèséliminationdesélémentsnonlinéairesd'uneboucle,etl'exploitationd'estimationsantérieuresdela constante de temps et du temps mort du processus, pour obtenir un indice brut, (d)letestdesinteractionséventuellesentrebouclesdecommande,quipeuventgonflerd'unemanièreanor-male une estimation du dit indice brut, (e)ladéterminationd'unindicebrutmodifiépouruneboucleparticulièredanslecasoùondétectedesditesestimations gonflées, et (f)ladifférenciation,entrelesbouclesdecommande,decellesquisontendéfautdefonctionnement,decellesquinesontpasendéfautdefonctionnementetdecellesquisontéventuellementendéfautdefonctionnementetquisontperturbéesparinteractionavecdesbouclesdecommandeendéfautdefonctionnement,surlabase du dit indice brut et du dit indice brut modifié. 30 35 40 45 4. 50 Procédé selon la revendication 1 ou 2, comprenant en outre: (i) le calcul du dit histogramme de l'erreur de suivi pour chaque boucle du dit système, (ii)laquantificationdel'aplatissementdechaquehistogrammepardéterminationdelahauteurd'unebarrecentraledudithistogrammeparrapportàunehauteurattendue,lahauteurattendueétantdéterminéeparunehypothèsequ'uneerreurdesuiviestnormalementdistribuéeavecunemoyenned'échantillonetunevariance d'échantillon, (iii)lecalculd'unesignificationstatistiqueduditaplatissementdansunedirectiondescendante,entenantcompte de toute corrélation inter-échantillon des séries chronologiques d'erreur de suivi, et(iv) l'affichage de la dite signification statistique comme une indication de mesure diagnostique. 55 22 EP0 907 913B1 5. Procédéselonlarevendication3,danslequelleditindicebrut(IN)estdéterminéparobservationd'unevariationd'erreurdesuivi(O)dansladiteboucle,déterminationd'unevarianced'uneprévisionconditionnelle(V)àpartirde mesures et d'échantillons antérieurs, et traitement de O/V pour obtenir IN.Procédé selon la revendication 5, dans lequel V est déterminé par: (a) soustraction d'une variable mesurée d'un point de consigne pour obtenir une erreur de suivi,(b) extraction de données antérieures de la variable mesurée pour la dite boucle, (c)danslecasoùuntempsd'échantillonTdeladitevariableestaumoinsapproximativement0,1foislaconstantedetempsenboucleouvertedominantedeladiteboucle,recherchedelameilleureapproximationdesmoindrescarrésd'unvecteurd'observationsd'erreurdesuiviavecdescombinaisonslinéairesd'erreursdesuivietd'erreursdesuivisuccessivesretardéespardesretardsdepériodesd'échantillonsuccessives,et(d)danslecasoùuntempsd'échantillondeladitevariableestpluspetitqu'environ0,1foisladiteconstantedetempsdeboucledominante,nouveléchantillonnagedeladitevariableàunintervalled'échantillonenviron5à10foispluscourtqueladiteconstantedetempsenboucleouvertedominante,puisrecherchedelameilleure approximation de moindres carrés comme dans l'étape (c). 7. 20 5 6. 10 15 Procédéselonlarevendication6,danslequell'étapedecalculduditindicedeperformancebrutcomprendladéterminationd'unequantitéparlaquellelavarianceobservéed'uneerreurdesuividépasseunevaleurminimale,aprèséliminationdesélémentsnonlinéairesd'uneboucle,àpartird'estimationsantérieuresd'uneconstantedetemps retardée du processus. Procédéselonlarevendication6,danslequell'étape(d)comprendunfiltrageanti-crénelagenumériquedeladitevariableetunnouveléchantillonnagedeladitevariableàunpluslongintervalled'échantillonIquiestapproxi-mativement5à10foispluscourtqueladiteconstantedetempsenboucleouverte,etl'expressiondesditspluslongs intervalles d'échantillon comme dits intervalles d'échantillon. Procédéselonlarevendication8,danslequelunefréquencedecoupuredufiltreanti-crénelageestcompriseentre10et20foisl'inversedelaconstantedetempsenboucleouverte,enradiansparéchantillon,etdanslequell'intervalledunouveléchantillonnageestapproximativementde0,1à0,2foisuneconstantedetempsdeprocessusestimée. 8. 25 9. 30 35 10.Procédéselonlarevendication6;incluantl'étapededéterminationdel'existenced'unedérivedel'erreurdesuivi aumoyend'unestatistiqueD,danslequelDestégalaumaximumde(|m1|,|m3|)oùm1etm3sontlesmoyennesdupremiertiersetdutroisièmetiersd'unesériechronologiquedeladiteerreurdesuivi,etdefournitured'unsignald'alertesiDestplusgrandquel'écartstandarddel'erreurdesuivix(12M/L)1/2,oùMestungrandnombrepré-déterminé et L est le nombre d'échantillons dans la série chronologique.11.Procédé selon la revendication 3,caractérisé en ce que: 40 45 50 (a)enrelationàuneboucledecommanded'ungroupedebouclesdecommandeindiquéescommepoten-tiellementendéfautdefonctionnement,oncalculeunetransformationrapidedeFourierd'uneerreurdesuiviet on filtre les produits de la dite transformation pour éliminer les pics parasites, (b)onidentifiedespicsspectrauxprimaireetsecondairecontribuantàplusqu'unevarlancedeseuildansune largeur de bande prédéterminée, pour la dite boucle de commande, (c)onchoisituneautreboucledecommandedansleditgroupedebouclesdecommandeetonrépètelesétapes (a) et (b) jusqu'à ce qu'une dernière boucle de commande dans le dit groupe ait été traitée, (d)onséparelesbouclespotentiellementendéfautdefonctionnementayantdespicsspectrauxapproxlma-tivement en coïncidence, en classes éventuellement en interaction, et (e)ondétermineunindicedeperformancemodifiépourtouteslesbouclesdecommandeappartenantàuneclasse. 12.Procédéselonlarevendication11,incluantladéterminationd'unedérivedesditesdonnéesdefonctionnement, etl'indication,àpartird'unevaleuroud'unetendancedeladitedérive,decequ'ilexisteounonunétatdedé-faillance, et, dans le cas où un état de défaillance existe, la fourniture d'une indication d'alerte.13.Procédéselonlarevendication12;incluantl'exécutiondel'étapededéterminationdelaprésencedeladitedérive pardéterminationd'unestatistiqueDpourladérivedel'erreurdesuivideladiteboucle,oùDestégalaumaximum 55 23 EP0 907 913B1 de(|m1|,|m3|),etm1etm3sontlesmoyennesd'unpremiertiersetd'untroisièmetiersd'unesériechronologiquedel'erreurdesuivi,etl'indicationd'unétatdedéfautsiDestplusgrandquel'écartstandarddel'erreurdesuivix(12M/L)1/2oùMestungrandnombreprédéterminéetLestlenombred'échantillonsdanslasériechronologiquede l'erreur de suivi. 5 14.Procédé selon la revendication 3,caractérisé par: (a)l'examendesvariationsd'erreurdesuiviayantuneétroitelargeurdebandespectrale,danschacunedesdites boucles de commande prédéterminées du dit processus, (b)lacomparaisondespicsspectrauxdesditesvariationsd'erreurpourdétecterlescoïncidencesdepicsquisont indicatives d'une interaction entre les dites boucles de commande prédéterminées, et (c)laquantificationdeseffetsdesditesvariationsd'erreurquiprésententlesditescoïncidencesdepicset,comme résultat, la détermination d'un défaut de fonctionnement d'une boucle de commande. 15.Procédéselonlarevendication14,effectuésurchaqueboucledecommandesupposéeêtreendéfautdefonc-tionnement, danslequelladiteétaped'examendesvariationsd'erreurdesuivicomprenduneévaluationd'unetransfor-mationdeFourlerdesditesvariationsd'erreurdesuivi,l'établissementdefenêtresdesproduitsdelatransformationdeFourier,lechoixd'unefenêtredeDanielayantuneordonnéedepériodogrammedelargeurdebandeWtelleque W est un plus petit entier qui satisfait à WexpW > L, etdanslequell'étapedecomparaisondespicsspectrauxcomprendl'estimationdelafréquencef1d'unepremièrevaleurmaximaleduspectred'énergieestimé,l'évaluationd'unefréquencecentralef2detoutpiccentralparessaipourunedeuxièmevaleurmaximaleparmidesfréquencesexcluesd'unintervalleautourdelapremièrevaleurmaximale,l'évaluationd'unevarianceassociéeauxditesvaleursmaximalesprimaireetsecondaireparcalculd'unesurfacesousl'estimationdespectred'énergiedansunintervalledelargeurdebandefixeautourdesditesfréquencesf1etf2,etl'indicationdelaprésenced'unerésonancespectraleàunefréquencecorrespondantef1ouf2danslecasoul'uneoul'autredesvariancesdépassedesproportionsprédéterminéesdelavarianced'erreur de suivi globale.16.Procédéselonlarevendication15,incluantl'étapedeformationdeclassesdebouclesdecommandeparasso-ciationdebouclesdecommandedansuneclasse,danslequellesditesfréquencesf1etf2d'uneboucledecommandesontprochesd'unequelconquedesditesfréquencesf1ouf2d'uneautreboucledecommande,d'unepetite quantité prédéterminée.17.Procédéselonlarevendication7,incluantladéterminationd'unecatégoriededéfautdefonctionnementd'un processus exécuté par la dite machine industrielle, comprenant: (a)l'examendesvariationsd'erreurdesuiviayantunelargeurdebandespectraleétroite,danschacuned'unepluralité de boucles de commande du dit processus, (b)lacomparaisondespicsspectrauxdesditesvariationsd'erreurpourdétecterdescoïncidencesdepicsqui sont indicatives d'une interaction entre les dites plusieurs boucles de commande, et (c)laquantificationdeseffetsdesditesvariationsd'erreurquiontlesditescoïncidencesdepicset,commerésultat, la détermination d'un défaut de fonctionnement d'une boucle de commande. 18.Procédéselonlarevendication17,appliquésurchaqueboucledecommandejugéecommeétantendéfautde fonctionnement, danslequelladiteétaped'examendesvariationsd'erreurcomprendl'évaluationd'unetransformationdeFourierdesditesvariationsd'erreurdesuivi,l'établissementdefenêtresdesproduitsdelatransformationdeFourier,lechoixd'unefenêtredeDanielayantuneordonnéedépériodogrammedelargeurdebandeWtellequeW est un plus petit entier qui satisfait à Wexpw > L, etdanslequell'étapedecomparaisondespicsspectrauxcomprendl'estimationdelafréquencef1d'unpremiermaximumduspectred'énergieestimé,l'évaluationd'unefréquencecentralef2detoutpiccentralparessaipourundeuxièmemaximumdansdesfréquencesexcluesd'unintervalleautourdupremiermaximum,l'éva-luationd'unevarianceassociéeauxditsmaximaprimaireetsecondaireparcalculd'unesurfacesousl'estimationdespectred'énergiedansunintervalledelargeurdebandefixeautourdesditesfréquencesf1etf2,etl'indicationdelaprésenced'unerésonancespectraleàunefréquencecorrespondantef1ouf2danslecasoùl'uneoul'autrevariance dépasse des proportions prédéterminées de la variance d'erreur de suivi globale. 10 15 20 25 30 35 40 45 50 55 24 EP0 907 913B1 19.Procédéselonlarevendication18,incluantl'étapedeformationdeclassesdebouclesdecommandeparasso-ciationdebouclesdecommandedansuneclasse,danslequellesditesfréquencesf1etf2d'uneboucledecommandesontprochesdel'uneoul'autredesditesfréquencesf1ouf2d'uneautreboucledecommande,d'unepetite quantité prédéterminée. 5 10 20.Procédéselonlarevendication19,incluantlesétapesdedéterminationd'unindicedeperformancemodifiecomme déterminationd'undéfautdefonctionnementpourlesbouclesdecommandeappartenantàuneclassedebouclesdecommandepotentiellementeninteractionouàuneclassedebouclesdecommandedanslaquelleuneréso-nanceestidentifiéecommeétantendehorsd'uneplageprédéterminéedelongueursd'onde,cetterésonanceétantprovoquéeparautrechosequ'uncyclelimiteengendrédufaitdelaprésenced'unefortenonlinéaritédansune boucle de commande.21.Procédéselonlarevendication20,danslequelladiteétapededéterminationcomprendletraitementdesvaleurs designal:(indicemodifié)=(indicebrut)x(1-proportiondelavarianced'erreurdesuiviassociéeàunerésonancesuspectée d'être imposée de façon extérieure à une boucle de commande).22.Procédé selon la revendication 1, comprenant en outre en combinaison le procédé selon la revendication 3. 15 20 25 30 35 40 45 50 55 25 EP0 907 913B1 26 EP0 907 913B1 27 EP0 907 913B1 28 EP0 907 913B1 29 EP0 907 913B1 30 EP0 907 913B1 31 EP0 907 913B1 32 EP0 907 913B1 33 EP0 907 913B1 34 EP0 907 913B1 35 EP0 907 913B1 36 EP0 907 913B1 37 EP0 907 913B1 38 EP0 907 913B1 39 EP0 907 913B1 40 EP0 907 913B1 41 EP0 907 913B1 42 因篇幅问题不能全部显示，请点此查看更多更全内容
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