Time-Specific Thresholds for Batch Process Monitoring: A Study Based on Two-Dimensional Conditional Variational Auto-Encoder

Abstract

This paper studies the use of varying threshold in the statistical process control (SPC) of batch processes. The motivation is driven by how when multiple phases are implicated in each repetition, the distributions of the features behind vary with phases or even the time; thus, it is inconsistent to uniformly bound them by an invariant threshold. In this paper, we paved a new path for learning and monitoring batch processes based on an efficient framework integrating a model termed conditional dynamic variational auto-encoder (CDVAE). Phase indicators are first used to split the data and are then separated, serving as an extra input for the model in order to alleviate the learning complexity. Dissimilar to the routine using features across all timescales, only features relevant to local timestamps are aggregated for threshold calculation, producing a varying threshold that is more specific for the process variations occurring among the timeline. Leveraged upon this idea, a fault detection panel is devised, and a deep reconstruction-based contribution diagram is illustrated for locating the faulty variables. Finally, the comparative results from two case studies highlight the superiority in both detection accuracy and diagnostic performance.