A Deep Probabilistic Flow-Based Framework for Unsupervised Cross-Domain Soft Sensing

Industrial soft sensing is crucial for accurate process monitoring through reliable inference of dominant sensor variables. However, developing effective data-driven soft sensor models presents challenges, such as achieving domain adaptability, addressing incomplete sensor labels, and learning stochastic data variability. To overcome these challenges, we propose a deep variational potential flow (DVPF) framework for cross-domain soft sensor modeling, taking into account the lack of sensor labels in the target domain. Our framework introduces sequential variational Bayes with recurrent neural network (RNN) parameterization to address the maximum likelihood estimation problem that characterizes cross-domain soft sensing. Central to the framework is a potential flow that performs unsupervised Bayesian inference on the RNN-extracted features to obtain an exact representation of the intractable posterior distribution. Together, these DVPF components learn domain-adaptable features that effectively capture complex cross-domain process dynamics and data variability. We validate the proposed DVPF on a real industrial multiphase flow process across varying operating modes. The results show that the DVPF demonstrates superior performance in cross-domain soft sensing compared to existing deep feature-based domain adaptation methods.