Hammerstein-Wiener Model Robust Identification Method

There are a large number of nonlinear processes in the increasingly complex actual production process.The linear model often used in process research has been difficult to meet the description of the production process,and there are too many restrictions.The Hammerstein-Wiener model is a typical block-oriented model.This model approximates the actual production process by combining input nonlinear modules,linear modules,and output nonlinear modules.At present,the identification algorithm derivation process of Hammerstein-Wiener model is mostly based on the least square criterion function.However,when there are spike noises or abnormal points,the noise distribution does not meet the normal distribution.Due to the existence of the square term in the least squares criterion function,the identification results will be biased,and even cannot be effectively identified.In view of the shortcomings of the least square criterion function,the least absolute criterion function can be used as the objective function.However,because the least absolute criterion function does not have the conditions for direct derivation,this paper proposes to replace the least absolute criterion function with a deterministic derivable function to make the objective function derivable and reduce the amount of calculation.In this paper,the Hammerstein-Wiener model is studied.First of all,take the approximate least absolute objective function as the entry point of the improved algorithm,a stochastic gradient descent method based on the approximate least absolute deviation is given.The common Hammerstein-Wiener model is identified,and the influence of the forgetting factor on the convergence speed and stability of the identification algorithm is discussed.Then,two identification methods are discussed for the Hammerstein-Wiener model with time delay: augmented matrix method and two-step iterative method.The augmented matrix method can identify model parameters and time delay parameters at the same time,but its anti-interference ability is poor.The two-step iterative method separately estimates the model parameters and the time delay parameters,and by changing the objective function to approximate the least absolute deviation function,the robustness of the algorithm is obviously improved.Finally,for the Hammerstein-Wiener model with load disturbance,the stochastic gradient method is used for identification based on the separation strategy and the least absolute deviation function,and the appropriate forgetting factor is selected to improve the robustness of the algorithm and speed up the convergence speed.After the completion of the algorithm derivation of each part of this paper,simulation experiments are used to verify the algorithm.By adding different noise conditions,the algorithm proposed in this paper is compared with the algorithm based on the least square criterion,which fully demonstrates that the algorithm in this paper has strong stability and robustness,and has application value in the field of nonlinear identification.