A novel Extreme Learning Machine-based Hammerstein-Wiener model for complex nonlinear industrial processes

Abstract In this paper, a novel extreme learning machine (ELM) based Hammerstein-Wiener model is developed for the approximation of complex nonlinear systems. The proposed model has two static ELM networks surround a dynamic linear part. Estimation of this model can be summarized into the following three aspects: The first one is to approximate the static nonlinear elements of Hammerstein-Wiener model with two independent ELM networks, which are single-hidden layer feedforward network (SLFN) essentially. The second one is to estimate the structure of linear part of the proposed model using lipschitz quotient criterion with respect to the measurements. The final one is to determine the parameters of the two SLFNs and the linear block using ELM algorithm. To evaluate the generalization performance, Rademacher complexity will be used to give the generalization bound of the proposed model with theoretical proof. The proposed model can track and handle the strong nonlinearity and time-varying dynamics over the whole operating domain for its inherent two nonlinear structure. Furthermore, with ELM algorithms, the proposed model can achieve fast learning speed and less computation complexity. Simulations on two typical industrial thermal processes demonstrate the accuracy and efficiency of the researched model.