WaveARX Neural Network Development for System Identification Using a Systematic Design Synthesis

Abstract

The WaveARX network, a new neural network architecture, is introduced. Its development was motivated by the opportunity to capitalize on recent research results that allow some shortcomings of the traditional artificial neural net (ANN) to be addressed. ANN has been shown to be a valuable tool for system identification but suffers from slow convergence and long training time due to the globalized activation function. The structure of ANN is derived from trial and error procedures, and the trained network parameters often are strongly dependent on the random selection of the initial values. There are not even guidelines on the number of neurons needed. Also, few identification techniques are available for distinguishing linear from nonlinear contributions to a system's behavior. The WaveARX integrates the multiresolution analysis concepts of the wavelet transform and the traditional AutoRegressive eXternal input model (ARX) into a three-layer feedforward network. Additional network design problems are solved as the WaveARX formalisms provide a systematic design synthesis for the network architecture, training procedure, and excellent initial values of the network parameters. The new structure also isolates and quantifies the linear and nonlinear components of the training data sets. The wavelet function is extended to multidimensional input space using the concept of a norm. The capabilities of the network are demonstrated through several examples in comparison with some widely used linear and nonlinear identification techniques. Separately, the wavelet network of the WaveARX model is shown for the example investigated to have a better performance than two other existing wavelet-based neural networks.