Identification of Volterra systems with a polynomial neural network

The Volterra series finds wide application in the general representation of nonlinear systems. A method of identifying linear and second-order time-invariant nonlinear systems is proposed using a variation of the group method of data handling (GMDH) algorithm, a polynomial network, employing a combination of quadratic polynomial and linear layers. The principal advantage of this method is that the degree of nonlinearity and the memory of the system do not have to be known a priori and are determined recursively. The GMDH method allows a Volterra series to be modeled solely from a set of input-output data. System identification using GMDH consists of applying a set of input-output data to train the network by computing the necessary coefficient sets and to select the optimum combination of these coefficient sets to obtain the model parameters