Empirical state space modelling with application in online diagnosis of multivariate non-linear dynamic systems

Barnard, Jakobus Petrus (Stellenbosch : Stellenbosch University, 1999-12)

Thesis

ENGLISH ABSTRACT: System identification has been sufficiently formalized for linear systems, but not for empirical identification of non-linear, multivariate dynamic systems. Therefore this dissertation formalizes and extends non-linear empirical system identification for the broad class of nonlinear multivariate systems that can be parameterized as state space systems. The established, but rather ad hoc methods of time series embedding and nonlinear modeling, using multilayer perceptron network and radial basis function network model structures, are interpreted in context with the established linear system identification framework. First, the methodological framework was formulated for the identification of non-linear state space systems from one-dimensional time series using a surrogate data method. It was clearly demonstrated on an autocatalytic process in a continuously stirred tank reactor, that validation of dynamic models by one-step predictions is insufficient proof of model quality. In addition, the classification of data as either dynamic or random was performed, using the same surrogate data technique. The classification technique proved to be robust in the presence of up to at least 10% measurement and dynamic noise. Next, the formulation of a nearly real-time algorithm for detection and removal of radial outliers in multidimensional data was pursued. A convex hull technique was proposed and demonstrated on random data, as well as real test data recorded from an internal combustion engine. The results showed the convex hull technique to be effective at a computational cost two orders of magnitude lower than the more proficient Rocke and Woodruff technique, used as a benchmark, and incurred low cost (0.9%) in terms of falsely identifying outliers. Following the identification of systems from one-dimensional time series, the methodological framework was expanded to accommodate the identification of nonlinear state space systems from multivariate time series. System parameterization was accomplished by combining individual embeddings of each variable in the multivariate time series, and then separating this combined space into independent components, using independent component analysis. This method of parameterization was successfully applied in the simulation of the abovementioned autocatalytic process. In addition, the parameterization method was implemented in the one-step prediction of atmospheric N02 concentrations, which could become part of an environmental control system for Cape Town. Furthermore, the combination of the embedding strategy and separation by independent component analysis was able to isolate some of the noise components from the embedded data. Finally the foregoing system identification methodology was applied to the online diagnosis of temporal trends in critical system states. The methodology was supplemented by the formulation of a statistical likelihood criterion for simultaneous interpretation of multivariate system states. This technology was successfully applied to the diagnosis of the temporal deterioration of the piston rings in a compression ignition engine under test conditions. The diagnostic results indicated the beginning of significant piston ring wear, which was confirmed by physical inspection of the engine after conclusion of the test. The technology will be further developed and commercialized.

AFRIKAANSE OPSOMMING: Stelselidentifikasie is weI genoegsaam ten opsigte van lineere stelsels geformaliseer, maar nie ten opsigte van die identifikasie van nie-lineere, multiveranderlike stelsels nie. In hierdie tesis word nie-lineere, empiriese stelselidentifikasie gevolglik ten opsigte van die wye klas van nielineere, multiveranderlike stelsels, wat geparameteriseer kan word as toestandveranderlike stelsels, geformaliseer en uitgebrei. Die gevestigde, maar betreklik ad hoc metodes vir tydreeksontvouing en nie-lineere modellering (met behulp van multilaag-perseptron- en radiaalbasisfunksie-modelstrukture) word in konteks met die gevestigde line ere stelselidentifikasieraamwerk vertolk. Eerstens is die metodologiese raamwerk vir die identifikasie van nie-lineere, toestandsveranderlike stelsels uit eendimensionele tydreekse met behulp van In surrogaatdatametode geformuleer. Daar is duidelik by wyse van 'n outokatalitiese proses in 'n deurlopend geroerde tenkreaktor getoon dat die bevestiging van dinamiese modelle deur middel van enkelstapvoorspellings onvoldoende bewys van die kwaliteit van die modelle is. Bykomend is die klassifikasie van tydreekse as 6f dinamies Of willekeurig, met behulp van dieselfde surrogaattegniek gedoen. Die klassifikasietegniek het in die teenwoordigheid van tot minstens 10% meetgeraas en dinamiese geraas robuust vertoon. / Vervolgens is die formulering van In bykans intydse algoritme vir die opspoor en verwydering van radiale uitskieters in multiveranderlike data aangepak. 'n Konvekse hulstegniek is V:oorgestel en op ewekansige data, sowel as op werklike toetsdata wat van 'n binnebrandenjin opgeneem is, gedemonstreer. Volgens die resultate was die konvekse hulstegniek effektief teen 'n rekenkoste twee grootte-ordes kleiner as die meer vermoende Rocke en Woodrufftegniek, wat as meetstandaard beskou is. Die konvekse hulstegniek het ook 'n lae loopkoste (0.9%) betreffende die valse identifisering van uitskieters behaal. Na aanleiding van die identifisering van stelsels uit eendimensionele tydreekse, is die metodologiese raamwerk uitgebiei om die identifikasie van nie-lineere, toestandsveranderlike stelsels uit multiveranderlike data te omvat. Stelselparameterisering is bereik deur individuele ontvouings van elke veranderlike in die multidimensionele tydreeks met die skeiding van die gesamenlike ontvouingsruimte tot onafhanklike komponente saam te span. Sodanige skeiding is deur middel van onafhanklike komponentanalise behaal. Hierdie metode van parameterisering is suksesvc1 op die simulering van bogenoemde outokatalitiese proses toegepas. Die parameteriseringsmetode is bykomend in die enkelstapvoorspelling van atmosferiese N02-konsentrasies ingespan en sal moontlik deel van 'n voorgestelde omgewingsbestuurstelsel vir Kaapstad uitmaak. Die kombinasie van die ontvouingstrategie en skeiding deur onafhanklike komponentanalise was verder ook in staat om van die geraaskomponente in die data uit te lig. Ten slotte is die voorafgaande tegnologie vir stelselidentifikasie op die lopende diagnose van tydsgebonde neigings in kritiese stelseltoestande toegepas. Die metodologie is met die formulering van 'n statistiese waarskynlikheidsmaatstaf vir die gelyktydige vertolking van multiveranderlike stelseltoestande aangevul. Hierdie tegnologie is suksesvol op die diagnose van die tydsgebonde verswakking van die suierringe in 'n kompressieontstekingenj in tydens toetstoestande toegepas. Die diagnostiese resultate het die aanvang van beduidende slytasie in die suierringe aangedui, wat later tydens fisiese inspeksie van die enjin met afloop van die toets, bevestig is. Die tegnologie sal verder ontwikkel en markgereed gemaak word.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/51258
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