Parameter Identification for the Hammerstein-Wiener Nonlinear Time Delay Systems with Process Noises

In this article, an identification scheme for the Hammerstein-Wiener nonlinear time delay systems with process noises is proposed, which is derived by exploiting special signals and recursive extended technique. The Hammerstein-Wiener time delay system is a linear block with time delay placed between two static nonlinear blocks, in which the two static nonlinear blocks are modeled by two independent neural fuzzy models (NFM), the linear block is represented by time delay autoregressive moving average with extra input (TD-ARMAX). To determine the Hammerstein-Wiener system parameters, the combination of binary and random signals is introduced to fulfill that independent identification of each block. Firstly, the amplitude characteristics of binary signals under a nonlinear system are analyzed, then the output NFM parameters are computed by cluster algorithm and least squares method utilizing two sets of binary signals with different amplitudes. Second, replacing the unknown noise variables in the identified system with colored noise estimates, and the redundant recursive extended least squares method can be used to identify the TD-ARMAX parameters utilizing a set of binary signals. Third, the recursive extended least squares method and cluster method are jointed to estimate parameters of the input NFM depending on random signals. The effectiveness and feasibility of the proposed identification scheme is proved by simulation results.