Quality-Relevant Modeling and Monitoring of Industrial Cyber-Physical Systems: The Semi-Supervised Dynamic Latent Variable Models

In modern industrial cyber-physical systems, a mass of process variables has been obtained by the high-sampling online sensors. Meanwhile, the key quality indexes are usually obtained infrequently from the laboratory. Hence, these quality variables are with low sampling rate. To avail of the complete process and quality variables with various sampling rates in the dynamic processes, a set of semi-supervised dynamic latent variable models are proposed for dynamic modeling and quality-relevant monitoring. The proposed models have built a unified structure to consider both the auto-correlations and cross-correlations between the process and quality variables with unbalanced sampling sizes. Hence, the feature extraction of the time series data is dynamically adjusted under the guidance of the quality variables. Then, the quality-relevant monitoring schemes are proposed, which is validated by a numerical case and an actual wastewater treatment process.