Interval-Aware Probabilistic Slow Feature Analysis for Irregular Dynamic Process Monitoring With Missing Data

Due to unexpected data transition or equipment failures, irregular data with missing values, which have both irregular sampling intervals and missing values, become very common in industrial processes and bring significant challenges for existing dynamic monitoring methods to explore temporal correlations. Therefore, this article develops an interval-aware probabilistic slow feature analysis (IA-PSFA) method along with the corresponding monitoring strategy to address the above problems for industrial processes. The IA-PSFA method incorporates functions of sampling intervals to adjust the influences of previous samples on the current one when inferring state variables. Specifically, different functions are designed such that the changing temporal correlations between adjacent samples caused by irregular sampling intervals can be tracked effectively. Parameters of the IA-PSFA model are estimated through the expectation-maximization (EM) algorithm with an interval-aware Kalman filter, which addresses the missing variable issue along with irregular sampling intervals. After that, three statistics are constructed based on the state variables, transition and emission errors, and the varying speed of the state variables, to establish comprehensive evaluations of processes. Finally, cases from the Tennessee Eastman (TE) process are provided to validate the effectiveness of the proposed method confronted with different degrees of data irregularity and missing values.