Identification of Wiener–Hammerstein models based on variational bayesian approach in the presence of process noise

This paper addresses the identification of Wiener–Hammerstein (WH) models in the presence of process and measurement noises, which has not been well studied yet in the existing works. To achieve an unbiased estimation, the model parameters are obtained by maximizing the likelihood function, which is solved in the expectation-maximization framework. Due to the difficulty of computing the posterior distributions of the latent variables of WH models, variational Bayes (VB) is used here, and a method for approximating the posterior distributions based on Monte Carlo integral is proposed in VB framework. To the best of our knowledge, it is the first time to use VB approach for WH model identification. Two simulation examples demonstrate the effectiveness of the proposed method. Moreover, the proposed method is used for a WH benchmark problem, and the results show that it improves the identification performance.