Structure and parameter identification for Bayesian Hammerstein system

Abstract

In this paper, we consider the structure and parameter identification problem for Bayesian Hammerstein system. A structure identification algorithm is proposed, in which the system order, system parameters and regularization parameters are all unknown in the considered system. The joint posterior distribution of system parameters and the value of basis functions $$k$$ are obtained via sampling theory. The proposed identification algorithm is based on the reversible jump Markov chain Monte Carlo method. There are two main characteristics of the algorithm: (i) By using the birth move and death move strategy, the parameter $$k$$ is searched quickly in the number of basis functions space until the suitable value of $$k$$ is found. (ii) The distributions of system parameters are changed with the value of $$k$$ in the Bayesian framework, and the parameters are successfully found after the value of $$k$$ is stable. Two examples are provided to show the effectiveness of the proposed algorithm. The performances of the algorithm are validated with the results of statistical analyses including parameter estimate error, MSE, NRMSE, MAD, Theils inequality coefficient, etc.