Probabilistic multivariate statistical process control

Abstract

Fault detection has become a fast-growing area of research to ensure the reliability and safety of industrial processes. Conventional machine learning techniques for fault detection often struggle with optimizing a large number of parameters and do not provide uncertainty quantification. To overcome these limitations, a novel probabilistic framework is developed for fault detection in this thesis. This framework provides uncertainty-aware control charts improving fault detection performance. Kernel parameters are estimated with uncertainty estimates and posterior inference using Gaussian process regression and Markov chain Monte Carlo. The optimized kernel parameters are then used in the calibration of probabilistic control charts for process monitoring. Two Gaussian kernel forms, squared exponential kernel and automatic relevance determination squared exponential kernel, are compared. The Tennessee Eastman Process dataset is used to evaluate the proposed methodology. The results show that both kernel cases turned out effective for fault detection. Comparatively, a kernel that learns an individual length scale for each process variable achieves more accurate fault detection and yields narrower predictive uncertainty envelopes. Overall, the proposed methodology results in a probabilistic approach that improves multivariate statistical process control-based monitoring and supports more informed decision-making in complex industrial processes.