Basic concepts of data-based modelling

Abstract

In this chapter we provide the basic model mathematical representations that are used throughout the book. Both parametric and nonparametric models require structural representations which reflect the modeller’s prior knowledge of the underlying process, or is selected so as to provide a form that ensures process identification easily from observed data, or is selected with another end process in mind such as control or condition monitoring. Generally in control and fault diagnosis problems, the model representation is in state space form (see Section 2.2) as knowledge of the unknown systems states are required for detection of process faults, or for state feedback control, or for state vector data fusion (see Section 9.3). Fundamental to this book is the representation of nonlinear observable processes by additive basis function expansions for which the basis functions are locally defined (i.e. have compact local support) rather than global basis functions such as general polynomials. In the sequel this representation coupled with linearly adjustable parameters is shown to have many knowledge and computational based advantages such as parameterisation via linear optimisation, easy incorporation of prior knowledge, and model transparency with direct links to fuzzy rule base representations.

“Never let your data get in the way of analysis.” — T. J. Lowi