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The complexity of probability estimation has limited the application of Bayesian learning in nonlinear system identification. This paper addresses Wiener-Hammerstein (WH) nonlinear process identification in the presence of process noise and measurement noise, we propose a Stochastic Variational Inference (SVI) method inspired by stochastic optimization. The SVI method leverages probabilities of intermediate variables to estimate natural gradients of model parameters and updates the posterior probabilities of hidden variables. Compared to the traditional Variational Inference (VI) method, our proposed approach significantly reduces computational complexity. The effectiveness of the SVI method is verified by two numerical simulations and the WH benchmark problem, thereby providing a fresh perspective for efficiently identifying nonlinear systems with large-scale uncertain data.

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Identification of Wiener-Hammerstein Model Using Stochastic Variational Bayesian Learning

  • 会议论文

  • 发表日期：

    2025年

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  • Junhao Li,
  • Fukai Zhang,
  • Cong Wang,
  • Yuehu Liu

摘要

The complexity of probability estimation has limited the application of Bayesian learning in nonlinear system identification. This paper addresses Wiener-Hammerstein (WH) nonlinear process identification in the presence of process noise and measurement noise, we propose a Stochastic Variational Inference (SVI) method inspired by stochastic optimization. The SVI method leverages probabilities of intermediate variables to estimate natural gradients of model parameters and updates the posterior probabilities of hidden variables. Compared to the traditional Variational Inference (VI) method, our proposed approach significantly reduces computational complexity. The effectiveness of the SVI method is verified by two numerical simulations and the WH benchmark problem, thereby providing a fresh perspective for efficiently identifying nonlinear systems with large-scale uncertain data.