|Title||Dynamic non-linear system modelling using wavelet-based soft computing techniques|
The enormous number of complex systems results in the necessity of high-level and cost-efficient
modelling structures for the operators and system designers. Model-based approaches offer a very
challenging way to integrate a priori knowledge into the procedure. Soft computing based models
in particular, can successfully be applied in cases of highly nonlinear problems. A further reason
for dealing with so called soft computational model based techniques is that in real-world cases,
many times only partial, uncertain and/or inaccurate data is available.
Wavelet-Based soft computing techniques are considered, as one of the latest trends in system
identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based
approaches to model the non-linear dynamical systems in real world problems in conjunction with
possible twists and novelties aiming for more accurate and less complex modelling structure.
Initially, an on-line structure and parameter design has been considered in an adaptive Neuro-
Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy
rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus
(Monascus ruber van Tieghem) is examined against several other approaches for further
justification of the proposed methodology.
By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have
been introduced. Increasing the accuracy and decreasing the computational cost are both the
primary targets of proposed novelties. Modifying the synoptic weights by replacing them with
Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA)
comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for
the above challenges. These two models differ from the point of view of structure while they share
the same HLA scheme. The second approach contains an additional Multiplication layer, plus its
hidden layer contains several sub-WNNs for each input dimension. The practical superiority of
these extensions is demonstrated by simulation and experimental results on real non-linear
dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT)
whole milk, and consolidated with comprehensive comparison with other suggested schemes.
At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is
presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network
(FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a
modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from
the data by building accurate regression, but also for the identification of complex systems.
The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the
consequent parts of rules. In order to improve the function approximation accuracy and general
capability of the FWNN system, an efficient hybrid learning approach is used to adjust the
parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is
employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which
is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world
application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the