Wavenet identification of dynamical systems by a modified PSO algorithm

Abstract

This paper presents a new method for the identification of nonlinear dynamical systems employing a wavelet neural network (wavenet) coupled to an infinite impulse response filter (WIIR). It is well known that a neural network trained by a gradient method is susceptible to fall in a minimum local. In order to solve this problem, we train the wavenet with a modified particle swarm optimization (mPSO) evolutionary algorithm, which integrates an elitist selection in order to conserve the best qualified particles. This approach is called mPSOWIIR algorithm. Basically, the idea is that the mPSO generates different sets of parameters that are evaluated in the dynamical system to be identified in order to obtain the fitness of every set. The best one and the best historical values of every set are taken into account to improve the set of parameters, keeping the diversity of new solutions and training the wavenet only with the first time steps of the dynamical system. This approach is able to reduce the number of possible solutions, avoid local minima and extend the search space of the wavenet; eluding the problem of finding good initial parameters by trial and error. One of the main features of the proposed method is that the number of parameters remains constant in all the training process. The mPSOWIIR algorithm is applied to identify nonlinear dynamical systems commonly used in specialized literature, obtaining satisfactory results.