Neurofuzzy Modelling Approaches in System Identification.
: University of Southampton,
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System identification is the task of constructing representative models of processes and has become an invaluable tool in many different areas of science and engineering. Due to the inherent complexity of many real world systems the application of traditional techniques is limited. In such instances more sophisticated (so called intelligent) modelling approaches are required. Neurofuzzy modelling is one such technique, which by integrating the attributes of fuzzy systems and neural networks is ideally suited to system identification. This attractive paradigm combines the well established learning techniques of a particular form of neural network i.e. generalised linear models with the transparent knowledge representation of fuzzy systems, thus producing models which possess the ability to learn from real world observations and whose behaviour can be described naturally as a series of linguistic humanly understandable rules. Unfortunately, the application of these systems is limited to low dimensional problems for which good quality expert knowledge and data are available. The work described in this thesis addresses this fundamental problem with neurofuzzy modelling, as a result algorithms which are less sensitive to the quality of the a priori knowledge and empirical data are developed. The true modelling capabilities of any strategy is heavily reliant on the model's structure, and hence an important (arguably the most important) task is structure identification. Also, due to the curse of dimensionality, in high dimensional problems the size of conventional neurofuzzy models gets prohibitively large. These issues are tackled by the development of automatic neurofuzzy model identification algorithms, which exploit the available expert knowledge and empirical data. To alleviate problems associated with the curse of dimensionality, aid model generalisation and enhance model transparency, parsimonious models are identified. This is achieved by the application of additive and multiplicative neurofuzzy models which exploit structural redundancies found in conventional systems. The developed construction algorithms successfully identify parsimonious models, but as a result of noisy and poorly distributed empirical data, these models can still generalise inadequately. This problem is addressed by the application of Bayesian inferencing techniques; a form of regularisation. Smooth model outputs are assumed and superfluous model parameters are controlled, sufficiently aiding model generalisation and transparency, and data interpolation and extrapolation. By exploiting the structural decomposition of the identified neurofuzzy models, an efficient local method of regularisation is developed. All the methods introduced in this thesis are illustrated on many different examples, including simulated time series, complex functional equations, and multi-dimensional dynamical systems. For many of these problems conventional neurofuzzy modelling is unsuitable, and the developed techniques have extended the range of problems to which neurofuzzy modelling can successfully be applied.
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