Parametric Versus Nonparametric Approach to Wiener Systems Identification

The problem of nonlinear dynamic systems modelling by means of block-oriented models has been strongly elaborated for the last four decades, due to vast variety of applications. The concept of block-oriented models assumes that the real plant, as a whole, can be treated as a system of interconnected blocks, static nonlinearities (N) and linear dynamics (L), where the interaction signals cannot be measured. The most popular in this class are two-element cascade structures, i.e., Hammersteintype (N-L), Wiener-type (L-N), and sandwich-type (L-N-L) representations. Particularly, since in the Wiener system (Figure 8.1) the nonlinear block is preceded by the linear dynamics and the nonlinearity input is correlated, its identification is much more difficult in comparison with the Hammerstein system. However the Wiener model allows for better approximation of many real processes. Such difficulties in theoretical analysis forced the authors to consider special cases, and to take somehow restrictive assumptions on the input signal, impulse response of the linear dynamic block and the shape of the nonlinear characteristic. In particular, for Gaussian input the problem of Wiener system identification becomes much easier. Since the internal signal {xk} is then also Gaussian, the linear block can be simply identified by the cross-correlation approach, and the static characteristic can be recovered e.g. by the nonparametric inverse regression approach ([14]-[16]). Non-Gaussian random input is very rarely met in the literature. It is allowed e.g. in [38], but the algorithm presented there requires prior knowledge of the parametric representation of the linear subsystem. Most of recent methods for Wiener system identification assumes FIR linear dynamics, invertible nonlinearity, or require the use of specially designed input excitations ([2], [12]).