Parameter identification for nonlinear Hammerstein models with stacked sparse autoencoder network

In this paper, a novel parameter identification method is addressed for Hammerstein nonlinear model with stacked sparse autoencoder (SSAE) network. The Hammerstein model presented is composed of a nonlinear block and a linear dynamic block, in which the nonlinear block is modeled by a SSAE network, and the linear dynamic block is established by an autoregression moving average model with exogenous input (ARMAX) model. To estimate the Hammerstein model parameters, step input excitation is used to decouple the nonlinear block from the linear block. Firstly, to identify the ARMAX model parameters, the multi-innovation and recursive extended theories are introduced, then a multi-innovation recursive least squares (MI-RELS) method is proposed, which improves parameter identification accuracy since the current data and past data information are utilized at each recursive computation. Secondly, parameters update of the SSAE network are implemented by layer-wise pre-training process and fine-tuning process, further employing the greedy algorithm and back propagation method to update weight and bias of the SSAE network. The simulation comparison results in numerical case and wind power systems are presented to verify that the feasibility of the developed Hammerstein model identification method.