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

[摘要] ENGLISH ABSTRACT:System identification has been sufficiently formalized for linear systems, but not for empiricalidentification of non-linear, multivariate dynamic systems. Therefore this dissertationformalizes and extends non-linear empirical system identification for the broad class of nonlinearmultivariate systems that can be parameterized as state space systems. The established,but rather ad hoc methods of time series embedding and nonlinear modeling, using multilayerperceptron network and radial basis function network model structures, are interpretedin context with the established linear system identification framework.First, the methodological framework was formulated for the identification of non-linear statespace systems from one-dimensional time series using a surrogate data method. It was clearlydemonstrated on an autocatalytic process in a continuously stirred tank reactor, that validationof 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 samesurrogate data technique. The classification technique proved to be robust in the presence ofup to at least 10% measurement and dynamic noise.Next, the formulation of a nearly real-time algorithm for detection and removal of radialoutliers in multidimensional data was pursued. A convex hull technique was proposed anddemonstrated on random data, as well as real test data recorded from an internal combustionengine. The results showed the convex hull technique to be effective at a computational costtwo orders of magnitude lower than the more proficient Rocke and Woodruff technique, usedas 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 methodologicalframework was expanded to accommodate the identification of nonlinear state space systemsfrom multivariate time series. System parameterization was accomplished by combiningindividual embeddings of each variable in the multivariate time series, and then separatingthis combined space into independent components, using independent component analysis.This method of parameterization was successfully applied in the simulation of the abovementionedautocatalytic process. In addition, the parameterization method was implementedin the one-step prediction of atmospheric N02 concentrations, which could become part of anenvironmental control system for Cape Town. Furthermore, the combination of the embedding strategy and separation by independent component analysis was able to isolatesome of the noise components from the embedded data.Finally the foregoing system identification methodology was applied to the online diagnosisof temporal trends in critical system states. The methodology was supplemented by theformulation of a statistical likelihood criterion for simultaneous interpretation of multivariatesystem states. This technology was successfully applied to the diagnosis of the temporaldeterioration of the piston rings in a compression ignition engine under test conditions. Thediagnostic results indicated the beginning of significant piston ring wear, which wasconfirmed by physical inspection of the engine after conclusion of the test. The technologywill be further developed and commercialized.

[发布机构] Stellenbosch University