A Matrix Block-Based Physics-Informed Probabilistic Quality-Relevant Monitoring Model

Area of Science:

• Industrial Process Monitoring
• Statistical Modeling
• Quality Control

Background:

• Physical laws are crucial for enhancing reliability in industrial processes.
• Existing models often lack the integration of physical principles, leading to potential inconsistencies.
• Quality-relevant monitoring requires robust methods that account for process dynamics.

Purpose of the Study:

• To develop a probabilistic linear latent variable model incorporating physical knowledge for quality-relevant monitoring.
• To enhance model reliability and prevent physically inconsistent results in industrial applications.
• To improve the sensitivity of monitoring for both process- and quality-related anomalies.

Main Methods:

• A probabilistic linear latent variable model named Physical Information-guided Probabilistic Quality Monitoring (PI-PQM) was developed.
• A block-matrix structure was employed, imposing physical principles (boundedness, monotonicity) as inequation constraints using skew normal distributions.
• Variational inference (VI) was used for estimating latent variables and model parameters.

Main Results:

• Physical constraints were shown to improve convergence accuracy to the true data structure.
• The integration of physical information enhanced monitoring sensitivity for process- and quality-related anomalies.
• Comparative analysis demonstrated the effectiveness of constrained versus unconstrained variables.

Conclusions:

• Incorporating physical knowledge into probabilistic models significantly enhances industrial quality monitoring.
• The PI-PQM model offers a reliable framework for detecting anomalies by adhering to physical laws.
• The method provides a robust approach for improving both process control and product quality assurance.