Construction of composite models from observed data

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Abstract
Most processes of realistic complexity cannot be described by simple linear relationships. An alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collection of simple models along with rules concerning when to use which one. In this paper we describe a method for constructing such composite models from observed data. It is assumed that the dynamics of the process changes with some 'operating-point vector’, which is assumed to be a measurable quantity. Based on input-output measurements and measurements of the operating-point vector, a composite model is constructed which consists of piecewise linear models. Different regions of the operating point space thus give different linear dynamics. The dynamics as well as the region boundaries are determined from the data. The basic idea is to utilize a method from recursive identification, which is able to track slow as well as rapid dynamic changes. A classification procedure is then applied to the models produced by this identification procedure, and finally borders are created between the different classified models. Techniques for supervised pattern recognition are used for the latter step. The whole construction procedure is illustrated with an example.

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