System identification using neural networks

Abstract

A mathematical model is a helpful representation of a process system used to understand, explain, control and forecast system behaviour. However, it is often difficult, if not impossible, to build mathematical models directly from the basic scientific (e.g. physical or chemical) laws for some complicated systems. These include, for example, the natural environment, economics, and certain process engineering systems.System identification is that area of investigation which determines system behaviour from the input and output (and/or state) records of the system. The parametric method in system identification is an approach to modelling system behaviour and building a mathematical model which describes the system. The model has a certain structure and certain parameters. There are mature parameter estimation methods for linear-inparameter (polynomial) models in conventional system identification. However, the efficient development of reliable system models intimately depends on the determination (or selection) of the model structure, and the estimation of the structure of polynomial models still needs further investigation. In addition, the various nonlinear-in-parameter (nonpolynomial) systems make it necessary and important to generally identify arbitrary non-polynomial models.One of the approaches offering most potential for further investigation is the area of artificial neural networks which have recently been successfully applied in fuzzy signal processing, simulation and control of nonlinear dynamic systems.The goal of this thesis is to investigate and develop new and generic methodologies for identification of the structure and parameters of polynomial and non-polynomial systems. In this work, multilayer neural networks have been developed into a universal framework of system models with new tools for system simulation and identification. The contributions of this thesis to both system identification and artificial neural networks are:♦ presentation of a new concept of complexity for the whole process of system identification, and new performance criteria for estimation of model structure and parameters (Chapter 4);♦ presentation of a new method using a new recurrent multilayer neural network for the direct identification of structure of linear state-space models from input-output data only (Chapter 7);♦ presentation of new methodologies using the basic multilayer neural network for the identification of polynomial and linear systems in terms of input-output and state-space forms (Chapters 5 and 6);♦ presentation of generic methodologies using multilayer neural networks with and without recurrent links for the representation and identification of arbitrary non-polynomial systems (Chapters 8);♦ generalisation of various error back propagation learning methods and the classical prediction error identification method, and analyses of convergence and stability conditions of the learning methods (Chapter 3);♦ development of a new two-step learning method which may be more stable and quicker in training multilayer neural networks than basic and adaptive methods (Chapter 3); and♦ development of a software package, INNATE 2.0, for system simulation and identification, pattern recognition and classification. A note on the application of the package is described in Appendix B.