Methods, Algorithms and Tools for System Identification Based on Prior Knowledge

University dissertation from Linköping : Linköping University

Abstract: One of the most challenging problems in system identification is that of model structure selection. In this thesis we investigate how three different kinds of prior process knowledge can be utilized to deal with this fundamental issue.The material is presented in four parts. The first one reviews some basic modeling and identification concepts, algorithms and ideas from which the following main three parts take off.The second part considers linear model structures that benefit from prior knowledge about the time constants and resonance frequencies of the underlying system. The idea is to generalize FIR modeling by replacing the delay operator with discrete so-called Laguerre or Kautz filters. While the nice properties of the FIR structure (stability, linear regression formulation, good approximation capability, etc.) are retained, the prior is used to reduce the number of parameters typically needed in the models. Tailored and efficient identification algorithms for these structures are developed and analyzed. The usefulness of the proposed methods is also demonstrated through a number of concrete simulation and application studies.The next approach is termed semi-physical modeling. Starting with simple physical insight into the application, often in terms of a set of unstructured equations, we are here looking for suitable nonlinear transformations of the raw measurements, so as to come up with a reasonable model structure. The suggested modeling procedure shows a first step where symbolic computations are employed to determine a set of physically motivated regressors. We discuss and show how constructive tools from commutative and differential algebra can be applied for this. Then, to avoid unnecessarily complex models, we address the intertwined problem of selecting a "good" subset of these regressors and how to estimate the corresponding parameters. More informal tools such as the programming environment are also treated.The fourth part concerns fuzzy identification where the prior structural knowledge comes in terms of a set of linguistic production rules. We emphasize the close connections between a particular fuzzy model structure on one hand and neural networks, model trees, etc. on the other hand. Several estimation related issues for this fuzzy structure are discussed, e.g., what algorithms to use, the need for regularization, and so on. It is also shown that the expert knowledge easily can be lost in the estimation procedure, unless special parameter restrictions are imposed. In addition, we propose a simplified fuzzy model structure customized to reflect a monotone steady-state behavior. Two applications, a tank and a water heating system, are investigated and successfully modeled within this framework.Finally and quite importantly, prototype software tools supporting the suggested approaches have been designed and implemented. The usefulness of these is illustrated in a number of identification applications.

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