Volterra neural network construction in the nonlinear dynamic systems modeling problem

Abstract

The features of using the theory of Volterra series and neural networks in problems of nonlinear dynamic systems modeling are considered. A comparative analysis of methods for constructing models of nonlinear dynamic systems based on the theory of Volterra series and neural networks is carried out; areas of effective application of each method are indicated. The problem statement is formulated, consisting in the creation of a mathematical apparatus for transforming models of nonlinear dynamic systems derived from the Volterra series apparatus into an artificial neural network of a certain structure. The three-layer structure of a direct signal propagation neural network has been substantiated and investigated for represent nonlinear dynamic systems. It is outlined a class of systems that can be efficiently approximated by this network. The dependence of the Volterra kernels coefficients and the weighting coefficients of the hidden layer of the three-layer forward-propagation neural network is established. An algorithm for constructing an artificial neural network based on the Volterra series is given. The results of computer simulation of nonlinear dynamic systems using the Volterra neural network and direct signal propagation neural network are presented. The analysis of experimental data confirms the effectiveness of using Volterra neural networks in problems of modeling nonlinear dynamic systems. Conclusions and recommendations on the effective use of Volterra neural networks for modeling nonlinear dynamic systems are made.