Reducing the number of parameters in a Wiener-Schetzen model

Abstract The class of Wiener-Schetzen models can describe a large variety of nonlinear systems. In this paper the dynamical part of these models is formulated in terms of orthonormal basis functions, while the nonlinearity is modeled through a multivariate polynomial. The parameters of the model are the coefficients of this polynomial. Generally this polynomial contains a relatively large number of significant terms, resulting in a large number of parameters. This paper considers a reduction of the significant parameters, by replacing one of the basis functions by the so-called best linear approximation of the system. It is shown that in this way the number of relevantly contributing terms in the multivariate polynomial is significantly reduced. Simulation results show a major reduction in the number of parameters, with only a minor increase in the rms error on the simulated output.