Recursive hierarchical parametric identification of Wiener-Hammerstein systems based on initial value optimization

In this paper, a novel recursive hierarchical parametric identification method based on initial value optimization is proposed for Wiener-Hammerstein systems subject to stochastic measurement noise. By transforming the traditional Wiener-Hammerstein system model into a generalized form, the system model parameters are uniquely expressed for estimation. To avoid cross-coupling between estimating block-oriented model parameters, a hierarchical identification algorithm is presented by dividing the parameter vector into two subvectors containing the coupled and uncoupled terms for estimation, respectively. To guarantee consistent estimation on these parameters, an auxiliary block model is designed to predict the inner unmeasurable variables of the Wiener-Hammerstein system for computational iteration. Furthermore, two adaptive forgetting factors are designed to accelerate the convergence rates on estimating both coupled and uncoupled parameters. To overcome the issue of initial value sensitivity involved with the traditional recursive least-squares based algorithms for parameter estimation, a particle swarm optimization (PSO) algorithm based on two different excitation signals is given for initial value optimization of the proposed recursive identification algorithm. Meanwhile, the convergence property of the proposed algorithm is clarified with a proof. Finally, an illustrative example and experiments on a micro-positioning stage are performed to validate the merit of the proposed method.