An improved Hammerstein system identification method using Stein Variational Inference and sampling technology

Abstract

This paper considers the identification of the Hammerstein system with immeasurable process noise. The complexity of the Hammerstein system makes it difficult to obtain accurate mathematical expressions of the parameters, or even impossible to obtain accurate mathematical expressions at all. In this contribution, we cast the Hammerstein system parameter identification problem as a posterior parameter estimation problem and take a sampling and Stein variational inference viewpoint to solve it. Improved Stein variational gradient descent(ISVGD)algorithm is proposed in posterior parameter calculation. Compared with other methods, not only the prior distribution of parameters but also the proposal distribution of parameters is considered. In other words, The posterior information is enriched and the parameter identification accuracy is improved. At the same time, ISVGD and reversible jump markov chain monte carlo (RJMCMC) algorithms are used (called ISVGD-RJMCMC algorithm) in the structure detection problem. In the algorithm, the correct basis function number k can be found in the parameter estimation. It tends to be accurate but is slow to converge. Three simulation examples were given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches were analyzed, including parameter estimation accuracy and error, system order estimation and parameter convergence analysis.