A Physical Causality-Informed Variational Autoencoder for Industrial Virtual Sensing

Deep learning models, with their excellent modeling capabilities for large-scale and nonlinear data, have played a significant role in the intelligent perception of quality-related variables. Nevertheless, the majority of current deep learning models are purely data-based black-box models, ignoring the causal dependence of process variables in industrial processes, which severely undermines the interpretability performance. To address these issues, this paper proposes a variational autoencoder model based on physical causal information. Moreover, in response to the problem of scarce labeled samples due to issues such as mismatched measurement frequencies and data loss in industrial processes, a semi-supervised physical causal information variational autoencoder, namely PCI-SsVAE, is introduced. Finally, a comprehensive performance evaluation of PCI-SsVAE is conducted through numerical and industrial case studies. The results indicate that the proposed method exhibits superior predictive performance and explainability compared with existing soft measurement approaches.