Variational Bayesian State Space Model for dynamic process fault detection. (April 2023) - Zhang, Qi; Lu, Shan; Xie, Lei; Gu, Shaowu; Su, Hongye
Abstract: Industrial processes are subject to various noise disturbances that lead to the stochastic nature of the modeled system and the uncertainty of the model parameters. In this paper, a variational Bayesian State Space Model (VBSSM) model is developed for dynamic process monitoring, allowing the uncertainty of parameters to be described by probabilities. The conjugate prior allows the posterior distribution of the parameters to be estimated iteratively through the Rauch Tung Striebel (RTS) smoothing estimation with the VB framework. The next state can be better predicted even in the presence of noisy perturbations, and imperceptible correlations among multiple variables can be found. By maximizing the lower bound of the objective function to approximate the true posterior distribution of the parameters, the fault detection index is constructed by the corresponding residual. Finally, the effectiveness and superiority of the proposed method is verified by numerical simulations, Tennessee Eastman process and hot rolling industry examples. Highlights: This work develops variational Bayesian state space model (VBSSM) based on variational Bayes, where the dynamic properties of the data are described directly through the SSM. The increased dimensionality of the state space due to the Cholesky decomposition is avoided. The developed VBSSM method describes the parameter uncertainty probabilistically instead of point estimation and therefore avoids overfitting.