Enhanced Hammerstein Models Identification Using Multiple Hidden Layers Neural Networks

In this paper, a method for Hammerstein model identification using neural networks with multiple hidden layers is proposed. The identification problem is formulated to allow the simultaneous adjustment of the linear and nonlinear parameters of the Hammerstein model. For this purpose, a hybrid neural network model structure is employed, composed of a linear part represented by an autoregressive model with exogenous input and a nonlinear part given by a multilayer perceptron neural network. The model order determination for the linear and nonlinear parts is carried out using Lipschitz quotients and the Akaike information criterion, respectively. From the proposed hybrid structure, it is possible to perform joint optimization of the linear and nonlinear parameters of the models. An iterative gradient-based training procedure with an adaptive learning rate is used. The effectiveness of the proposed method is initially evaluated for a Hammerstein process with a well-defined structure. In addition, the performance of the proposed method is evaluated using simulations of two typical nonlinear industrial processes: a continuous stirred tank reactor and a pH neutralization process. The simulation results show that the proposed method provides a fit up to 25.15% better when compared to alternative methods in the literature.