ニューラルネットワークのVolterra核推定と構造同定への応用

抄録

This paper proposes a model of nonlinear dynamical systems which consists of a bank of orthogonal filters and a three-layer artificial neural network. The relation of this model and the parametrized Volterra series model is presented. After executing an ordinary learning process on the artificial neural network, the Volterra kernels are directly calculated in terms of the connection weights of the network. One advantage of the present method is that kernels of arbitrary orders can be obtained independently no matter what the order of the Volterra series model is. Another advantage is, by examining the obtained connection weights, it is possible to tell whether the identified system has a special structure referred to a Wiener model which consists of a dynamic linear subsystem followed by a static nonlinear subsystem. The theoretical results are tested by numerical simulations.