Pruned hierarchical local model networks for nonlinear system identification : neuro-fuzzy local model network-based nonlinear system identification using maximum likelihood partitioned hierarchical model trees and backward elimination pruning for structure optimisation

Mathematical models form the basis of application in a multitude of processes and disciplines. With there being a recent and general trend of increased system complexity through added dimensionality and new innovations in technology, conventional characterisation methods fall short in many key areas. Consequently, it is necessary to address these shortcomings through the development of modelling methods which allow for the characterisation and investigations of the features of these systems. Local Model Networks (LMNs), a subset of the Neuro-Fuzzy modelling method, have become increasingly popular as a solution to this problem of Nonlinear System Identification. This thesis introduces a novel procedure for the identification of such systems, which returns a Pruned Hierarchical Network. Herein referred to as PRUHINET, the algorithm operates using hierarchical tree construction and returns a structure which is constituted of neurons containing local models each with an associated region of activation. The operational input space of the system is partitioned using an axis-oblique strategy, however unlike previous deployments, the employed partition method is predicated upon Maximum Likelihood Estimation (MLE). Analytical gradients are used to speed up the required nonlinear optimisation process. PRUHINET proposes various LMNs of varying complexity levels and utilises Information Theoretic Criterion (ITC) for the determination of the optimal network structure. This is addressed through the termination of the model build and the removal of redundant neurons via a Backward Elimination Pruning (BEP) approach. Multi-Model Inference (MMI) is used across the candidate LMNs to further mitigate model selection uncertainty and provide final response prediction. PRUHINET also allows for the consideration of systematic correlations within the supplied dataset by whitening the model errors through an iterated Feasible Generalised Least Squares (FGLS) approach external to the LMN build. The utility of the approach is shown through the identification of various dataset examples consisting of static and dynamic elements. The static simulation results illustrate the functionality of PRUHINET as an evolution of traditional approaches, providing superior performance and also being able to return results representative of classical methods under certain configurational assumptions. Validation results for the dynamic dataset showed the approach was able to identify the given system to an accuracy greater than 95% in all cases. Finally, the PRUHINET approach was shown to allow scrutinisation of the identified local models, which is of benefit in application.