TABLE OF CONTENTS Nonlinear models are required in a variety of different tasks. They are needed for system analysis, simulation, optimisation and fault diagnosis of nonlinear processes. Furthermore, they are the basis for nonlinear model-based control approaches. These models can be obtained by theoretical or experimental modelling [1]. Theoretical models are based on first principles and are also called white-box models because of their transparency. In experimental modelling (or identification), the model is solely built from measurement data. Since these models usually lack physical interpretability, they are called black-box models. To make such models more transparent, grey-box models [2] try to incorporate prior physical knowledge in some way and therefore combine black-box and white-box modelling.
Contrary to linear systems [3] , [4], general methods for nonlinear identification are not available because a large number of different nonlinearities and a variety of nonlinear model architectures exist, e.g. Hammerstein and Wiener models, Volterra series and Kolmogorov Garbor polynomials. Generally, a nonlinear model has a flexible structure, and its parameters are adjusted by an optimisation algorithm to capture the desired nonlinear behaviour. In recent years, also neural network and fuzzy logic approaches have been successfully applied.
Artificial neural networks (ANNs) are motivated by biological neural structures regarding learning and information processing. They consist of a large number of simple but strongly interconnected units: the neurons. ANNs belong to the class of black-box models and usually require nonlinear optimisation methods to adapt their parameters. Three...
