Dynamic probabilistic predictable feature analysis for multivariate temporal process monitoring

Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring schemes. However, measurement noise is widespread in real-world industrial processes, and ignoring its effect will lead to sub-optimal modeling and monitoring performance. In this article, a probabilistic predictable feature analysis (PPFA) is proposed for multivariate time series modeling, and a multi-step dynamic predictive monitoring scheme is developed. The model parameters are estimated with an efficient expectation-maximum algorithm, where the genetic algorithm and Kalman filter are designed and incorporated. Further, a novel dynamic statistical monitoring index, Dynamic Index, is proposed as an important supplement of $\text{T}^2$ and $\text{SPE}$ to detect dynamic anomalies. The effectiveness of the proposed algorithm is demonstrated via its application on the three-phase flow facility and a medium speed coal mill.