Nonlinear singular spectrum analysis and its application in multivariate statistical process monitoring

Krishnannair, Syamala (2016-03)

Thesis (PhD)--Stellenbosch University, 2016

Thesis

ENGLISH ABSTRACT: Multivariate statistical process control (MSPC) approaches based on principal component analysis (PCA), partial least squares (PLS) and related extensions are now widely used for process monitoring and diagnosis in process systems where observed correlated measurements are readily available. However, highly nonlinear (dynamic) processes pose a challenge for MSPC methods as a large set of nonlinear features are typically required to capture the underlying characteristic behaviour of the process in the absence of faults. Several extensions of basic (PCA) methods have previously been proposed to handle features such as autocorrelation in data, time-frequency localization, and nonlinearity. In this study multivariate statistical process monitoring methods based on nonlinear singular spectrum analysis which use nonlinear principal component analysis, multidimensional scaling and kernel multidimensional scaling are proposed. More specifically, singular spectrum analysis using covariance and dissimilarity scale structure are proposed to express multivariate time series as the sum of identifiable components whose basis functions are obtained from the process measurements. Such an approach is useful for extracting trends, harmonic patterns and noise in time series data. Using nonlinear SSA decomposition of time series data, a multimodal representation is obtained that can be used together with existing statistical process control methods to develop novel process monitoring schemes. The advantages of these approaches are demonstrated on simulated multivariate nonlinear data and compared with those of classical PCA and multimodal SSA on base metal flotation plant data and the Tennessee Eastman process benchmark data. The nonlinear SSA methods better captured the nonlinearities in the observed data. Consequently, this yielded improved detection rates for various faults in nonlinear data over those obtainable by alternative competing multivariate methods.

AFRIKAANSE OPSOMMING: Meerveranderlike statistiese prosesbeheer (MSP) benaderings gebaseer op hoofkomponentontleding, gedeeltelike kleinste kwadrate en verwante uitbreidings, word tans wyd gebruik in prosesmonitering en –diagnose van prosesstelsels waar waargenome gekorreleerde metings geredelik beskikbaar is. Hoogs nie-lineêre (dinamiese) prosesse is egter ’n uitdaging vir MSP metodes, aangesien ’n groot stel nie-lineêre kenmerke tipies benodig word om die onderliggende karakteristieke gedrag van die proses vas te vang in die afwesigheid van foute. Verskeie uitbreidings van basiese hoofkomponentonledingsmetodes is voorheen voorgestel om kenmerke, soos outokorrelasie, tyd-frekwensielokalisering en nie-lineariteit in die data te hanteer. In die studie, word meerveranderlike statistiese prosesmoniteringsmetodes voorgestel, gebaseer op nie-lineêre enkelvoudige spektrumontleding wat nie-lineêre hoofkomponentontleding, meerdimensionele skalering en kern- multidimensionele skalering gebruik. Meer spesifiek, enkelvoudige spektrumontleding wat kovariansie- en andersheidskaalstrukture gebruik, word voorgestel om meerveranderlike tydreekse uit te druk as die som van identifiseerbare komponente, wat se basisfunksies van prosesmetings verkry kan word. So ’n benadering is nuttig vir die ekstraksie van tendense, harmoniese patrone en geraas in die tydreeksdata. Deur nie-lineêre enkelvoudige spektrumontleding te gebruik vir ontbinding van die tydreeksdata, word ’n multimodale verteenwoordiging verkry wat gebruik kan word saam met bestaande statistiese prosesbeheermetodes om nuwe prosesmoniteringskemas te ontwikkel. Die voordele van die benaderings word gedemonstreer en vergelyk met die van klassieke hoofkomponentontleding en multimodale nie-lineêre enkelvoudige spektrumontleding op gesimuleerde meerveranderlike nie-lineêre data, data van ’n basismetaalflottasie-aanleg en die Tennessee Eastman prosesykingsdata. Die nie-lineêre enkelvoudige spektrumontledingsmetodes het die nie-lineariteite in die waargenome prosesdata beter beskryf. Gevolglik het dit tot beter foutopsporingstempo’s gelei, as wat behaal kon word met alternatiewe kompterende meerveranderlike metodes. Stellenbosch University https://scholar.sun.ac.za

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/98605
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