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

Dynamic probabilistic predictable feature analysis for multivariate temporal process monitoring