An Over-Sampling Amplitude-Limited Variational Bayesian Method for the Identification of Hammerstein Model

Chemical industrial processes involve numerous multivariable nonlinear systems. Nonlinear Muli-Input Muli-Output (MIMO) models seem more suitable to represent most systems and control problems in industrial processes. Furthermore, the outputs of the real systems might be corrupted with the colored noises, which do not satisfy the assumption of the white noises. In order to solve the impact of the colored noises, an Amplitude-Limiting Variational Bayesian (ALVB) method combined with multivariable nonlinear model (Hammerstein model) working in over-sampling closed-loop structure is proposed in this article. This method is the improvement of the Variational Bayesian (VB) method combining Hammerstein model and over-sampling closed-loop structure. Simulation experiments show that for the nonlinear model (Hammerstein model), the proposed algorithm not only overcomes the unidentifiable disadvantage of the traditional structure but also contributes to a higher identification accuracy. Furthermore, even under situation that the processes output noise is a colored noise, the proposed algorithm still maintains and converges to the achieved accuracy.