Parameter learning for Wiener systems with time-delay state-space model

Abstract

This paper discusses a novel scheme for learning the Wiener output error nonlinear system with time-delay state-space model. In the Wiener system, the dynamic linear block is approximated by time-delay state-space model, and the static nonlinear block is established using neural fuzzy network. Combined signals designed including separable signal and random signal are devoted to achieving parameters separation learning of the Wiener system, that is, the two blocks are learned independently. Firstly, using the properties of shift operator and transforming state-space model with time-delay into a representation with input and output, then linear dynamic block parameters are learned by the virtue of correlation analysis method in the condition of Gaussian signals. Moreover, a recursive extended least squares estimation is carried out to learn parameters of static nonlinear block and colored noise model under the condition of random signals. The efficiency and accuracy of proposed scheme are confirmed on experiment results of a numerical simulation and a typical practical nonlinear process, and experimental simulation results demonstrate that the learning scheme proposed obtains good learning precision.