Generalised additive multiscale wavelet models constructed using particle swarm optimisation and mutual information for spatio-temporal evolutionary system representation

A new class of generalised additive multiscale wavelet models (GAMWMs) is introduced for high dimensional spatio-temporal evolutionary (STE) system identification. A novel two-stage hybrid learning scheme is developed for constructing such an additive wavelet model. In the first stage, a new orthogonal projection pursuit (OPP) method, implemented using a particle swarm optimisation(PSO) algorithm, is proposed for successively augmenting an initial coarse wavelet model, where relevant parameters of the associated wavelets are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be a redundant model. In the second stage, a forward orthogonal regression (FOR) algorithm, implemented using a mutual information method, is then applied to refine and improve the initially constructed wavelet model. The proposed two-stage hybrid method can generally produce a parsimonious wavelet model, where a ranked list of wavelet functions, according to the capability of each wavelet to represent the total variance in the desired system output signal is produced. The proposed new modelling framework is applied to real observed images, relative to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, and the associated identification results show that the new modelling framework is applicable and effective for handling high dimensional identification problems of spatio-temporal evolution sytems.