Deep Variable-Wise Probabilistic Principal Component Analysis for Industrial Process Monitoring in the Presence of Missing Data

Data-driven process monitoring is widely used for assessing the operational status of industrial processes. However, missing values in process data can severely degrade the performance of such methods. To address this issue, a deep variable-wise probabilistic principal component analysis (DVPPCA) model is proposed, allowing monitoring under incomplete data. DVPPCA is constructed through a two-stage training process: a greedy layer-wise pretraining phase, followed by a unified end-to-end fine-tuning phase. The pretraining phase builds a hierarchical deep architecture directly from raw data with missing values, while the fine-tuning phase establishes an end-to-end mapping from incomplete raw inputs to high-level features, further enhancing the model's representational ability. Missing values in both training and testing datasets can be handled directly by DVPPCA. Rather than relying on external imputation as a separate preprocessing step, DVPPCA incorporates probabilistic estimation of missing variables within its unified model framework, avoiding potential error propagation. DVPPCA can generate accurate monitoring statistics for samples with missing values. Experimental results on the Tennessee Eastman (TE) process demonstrate that DVPPCA achieves superior monitoring accuracy and efficiency compared to state-of-the-art methods, even under high missing rates.