Bayesian robust linear dynamic system approach for dynamic process monitoring

• Bayesian robust linear dynamic system is proposed for dynamic modeling.
• The Gaussian assumption in traditional LDS model has been replaced by Student's t-distribution.
• Expectation–maximization algorithm is employed for parameter learning.
• A fault detection scheme is designed based on the developed model.
• The superiority of the developed method is tested on a benchmark process.

In this paper, a Bayesian robust linear dynamic system approach is proposed for process modeling. Traditional linear dynamic system (LDS) constructed with Kalman filter is designed by Gaussian assumption which can be easily violated in non-Gaussian modeling situations, especially those with outliers. To deal with this issue, the conventional Gaussian-based Kalman filter is modified with heavy tailed Student's t-distribution so as to deal with the non-Gaussian noise and modeling outliers. Then, a variational Bayesian expectation maximization (VBEM) algorithm is developed for learning parameters of the robust linear dynamic system. For process monitoring, traditional monitoring scheme are discussed and the residual space monitoring mechanism has been improved. To explore the feasibility and effectiveness, the proposed method is applied for fault detection, with detailed comparative studies with several other methods through the Tennessee Eastman benchmark.