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 suboptimal modeling and monitoring performance. In this article, a probabilistic predictable feature analysis (PPFA) is proposed for multivariate time series modeling, and a multistep dynamic predictive monitoring scheme is developed. The model parameters are estimated with an efficient expectation–maximization algorithm, where the genetic algorithm and the Kalman filter are designed and incorporated. Furthermore, a novel dynamic statistical monitoring index, the dynamic index, is proposed as an important supplement of T2 and 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.

Particle erosion is a commonly occurring phenomenon, and it plays a significantly important role in service life. However, few simulations have replicated erosion, especially the detailed evolution process. To address this complex issue, a new method for establishing the solution of the erosion evolution process was developed. The approach is introduced with the erosion model and the dynamic mesh. The erosion model was applied to estimate the material removal of erosion, and the dynamic mesh technology was used to demonstrate the surface profile of erosion. Then, this method was applied to solve a typical case—the erosion surface deformation and the expiry period of an economizer bank in coal-fired power plants. The mathematical models were set up, including gas motion, particle motion, particle-wall collision, and erosion. Such models were solved by computational fluid dynamics (CFD) software (ANSYS FLUENT), which describes the evolution process of erosion based on the dynamic mesh. The results indicate that: (1) the prediction of the erosion profile calculated by the dynamic mesh is in good agreement with that on-site; (2) the global/local erosion loss and the maximum erosion depth is linearly related to the working time at the earlier stage, but the growth of the maximum erosion depth slows down gradually in the later stage; (3) the reason for slowing down is that the collision point trajectory moves along the increasing direction of the absolute value of θ as time increases; and (4) the expiry period is shortened as the ash diameter increases.