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
posted on 2021-12-09, 10:08authored byAitshaam Shahzad
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.
History
School
Aeronautical, Automotive, Chemical and Materials Engineering