Algorithms and tools for system identification using prior knowledge

摘要

One of the hardest problems in system identification is that of model structure selection. In this thesis two different kinds of a priori process knowledge are used to address this fundamental problem. Concentrating on linear model structures, the first prior advantage of is knowledge about the systems' dominating time constants and resonance frequencies. The idea is to generalize FIR modelling by replacing the usual delay operator with discrete so-called Laguerre or Kautz filters. The generalization is such that stability, the linear regression structure and the approximation ability of the FIR model structure is retained, whereas the prior is used to reduce the number of parameters needed to arrive at a reasonable model. Tailorized and efficient system identification algorithms for these model structures are detailed in this work. The usefulness of the proposed methods is demonstrated through concrete simulation and application studies. The other approach is referred to as semi-physical modelling. The main idea is to use simple physical insight into the application, often in terms of a set of unstructured equations, in order to come up with suitable nonlinear transformation of the raw measurements, so as to allow for a good model structure. Semi-physical modelling is less ''ambitious'' than physical modelling in that no complete physical structure is sought, just combinations of inputs and outputs that can be subjected to more or less standard model structures, such as linear regressions. The suggested modelling procedure shows a first step where symbolic computations are employed to determine a suitable model structure - a set of regressors. We show how constructive methods from commutative and differential algebra can be applied for this. Subsequently, different numerical schemes for finding a subset of ''good'' regressors and for estimating the corresponding linear-in-the-parameters model are discussed. 107 refs, figs, tabs. (Atomindex citation 26:006790)