Identification of non-linear stochastic systems using a new Hammerstein-Wiener neural network: a simulation study through a non-linear hydraulic process

Abstract

Hammerstein-Wiener models have been proved to be suitable in modelling a class of typical non-linear dynamic systems. This paper aims at developing a Hammerstein-Wiener Neural Network (HWNN) which formulates a Hammerstein-Wiener mathematical model, in order to identify a nonlinear dynamic system operating in a stochastic environment. A central aspect is that a general situation has been considered including non-invertible non-linearity output and correlation of stochastic disturbances after the dynamic linear block. Different from the existing parameter identification methods, the model is developed to handle two types of learning algorithms that can directly obtain the parameters of the unknown time-varying nonlinear system. Firstly, all neural network weights in HWNN are adapted using a Back Propagation-based Gradient algorithm (BPG). The second method, namely Recursive Least Square Back Propagation based Gradient (RLSBPG) is derived from the BPG algorithm to achieve the parametric estimation of the Hammerstein scheme where the remaining parameters are estimated by the least-squares approach based on fuzzy technique to ameliorate the estimation quality. The convergence analysis of the algorithms is presented, and their performances are tested through a simulation study of a nonlinear hydraulic process.