Physics-informed probabilistic slow feature analysis

This paper presents a novel approach called physics-informed probabilistic slow feature analysis. The probabilistic slow feature analysis method has been employed to extract slowly varying latent patterns from high-dimensional measured data. The extracted slow features have proven effective in industrial applications such as soft sensing and process monitoring. However, industrial processes come with various physical constraints that must be taken into account, such as energy requirements, equipment limitations, and safety considerations. The conventional black-box nature of the slow feature model often leads to physically inconsistent or unacceptable results. To address this issue, we propose integrating physics principles into the probabilistic slow feature model, ensuring that the extracted features adhere to physics laws. Our formulation incorporates two types of physical constraints: linear algebraic equality and inequality constraints. Through an industrial case study, we demonstrate the effectiveness of our methodology, showcasing the advantages of incorporating physics in feature extraction. These advantages include improved interpretability, reduced data dimensionality, and enhanced generalization performance.