Stochastic Variational Bayesian Learning of Wiener Model in the Presence of Uncertainty

Nonlinear system identification in multiple uncertain environment is an open problem. Bayesian learning has significant advantages in describing and dealing with uncertainties and has been widely used in linear system identification. However, the use of Bayesian learning for nonlinear system identification has not been well studied, confronted with the complexity of the estimation of the probability and the high computational cost. Motivated by these problems, this paper proposes a nonlinear system identification method based on stochastic variational Bayesian for Wiener model, a typical nonlinear model. First, the process noise, measurement noise and parameter uncertainty are described in terms of probability distribution. Then, the posterior estimation of model parameters is carried out by using the stochastic variational Bayesian approach. In this framework, only a few intermediate variables are used to estimate the natural gradient of the lower bound function of the likelihood function based on the stochastic optimization idea. Compared with classical variational Bayesian approach, where the estimation of model parameters depends on the information of all the intermediate variables, the computational complexity is significantly reduced for the proposed method since it only depends on the information of a few intermediate variables. To the best of our knowledge, it is the first time to use the stochastic variational Bayesian to system identification. A numerical example and a Benchmark problem of Wiener model are used to show the effectiveness of this method in the nonlinear system identification in the presence of large-scale data. © 2024 Science Press. All rights reserved.