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.

本文讨论了在存在过程和测量噪声的情况下识别 Wiener-Hammerstein (WH) 模型，这在现有工作中尚未得到很好的研究。为了实现无偏估计，模型参数通过最大化似然函数获得，该函数在期望最大化框架中求解。由于WH模型潜变量的后验分布计算困难，这里采用变分贝叶斯（VB），并在VB框架中提出了一种基于蒙特卡罗积分的后验分布逼近方法。据我们所知，这是第一次使用 VB 方法进行 WH 模型识别。两个仿真例子证明了所提出方法的有效性。此外，所提出的方法用于 WH 基准问题，