A local model network approach to nonlinear modelling
This thesis describes practical learning systems able to model unknown nonlinear dynamic processes from their observed input-output behaviour. Local Model Networks use a number of simple, locally accurate models to represent a globally complex process, and provide a powerful, flexible framework for the integration of different model structures and learning algorithms. A major difficulty with Local Model Nets is the optimisation of the model structure. A novel Multi-Resolution Constructive (MRC) structure identification algorithm for local model networks is developed. The algorithm gradually adds to the model structure by searching for 'complexity' at ever decreasing scales of 'locality'. Reliable error estimates are useful during development and use of models. New methods are described which use the local basis function structure to provide interpolated state-dependent estimates of model accuracy. Active learning methods which automatically construct a training set for a given Local Model structure are developed, letting the training set grow in step with the model structure - the learning system 'explores' its data set looking for useful information. Local Learning methods developed in this work are explicitly linked to the local nature of the basis functions and provide a more computationally efficient method, more interpretable models and, due to the poor conditioning of the parameter estimation problem, often lead to an improvement in generalisation, compared to global optimisation methods. Important side-effects of normalisation of the basis functions are examined. A new hierarchical extension of Local Model Nets is presented: the Learning Hierarchy of Models (LHM), where local models can be sub-networks, leading to a tree-like hierarchy of softly interpolated local models. Constructive model structure identification algorithms are described, and the advantages of hierarchical 'divide-and-conquer' methods for modelling, especially in high dimensional spaces are discussed. The structures and algorithms are illustrated using several synthetic examples of nonlinear multivariable systems (dynamic and static), and applied to real world examples. Two nonlinear dynamic applications are described: predicting the strip thickness in an aluminium rolling mill from observed process data, and modelling robot actuator nonlinearities from measured data. The Local Model Nets reliably constructed models which provided the best results to date on the Rolling Mill application.