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

TL;DR

The paper tackles cross-domain soft sensing under unlabeled target domains by marrying a probabilistic RNN-based sequential variational Bayes objective with a deep, flow-driven Bayesian update. The Deep Variational Potential Flow (DVPF) uses a Gaussian RNN parameterization for likelihoods and a diffeomorphic particle flow guided by a scalar potential $\phi$ to obtain an exact posterior $p^{+}(z_t,h_t)$, bypassing Gaussian/mean-field limitations. This yields a domain-adaptable latent representation that generalizes across operating modes without target labels, validated on real multiphase flow (MFP) and the Tennessee Eastman process (TEP). Results show superior cross-domain soft sensing performance, robust latent representations, and favorable computational efficiency, demonstrating a practical unsupervised domain adaptation approach for industrial process monitoring. The method advances soft sensing by integrating sequential variational inference with a flow-based Bayesian update to handle nonstationary, multi-mode data in practice.

Abstract

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.

Figures (6)

• Figure 1: Overall diagram of the proposed DVPF. The probabilistic RNN is used first to extract prior latent and hidden features $(z_{t},h_{t})$. The potential flow (\ref{['eq:particle_flow']}) then performs unsupervised Bayesian inference on these RNN-extracted features $(z_{t},h_{t})$. The dashed outlines of $y^{\mathcal{S}}_{t}$ indicate that sensor labels are only available within the source domain.
• Figure 2: Graphical illustrations of the overall DVPF framework and its operations. The dashed outlines of $y^{\mathcal{S}}_{t}$ indicate that sensor labels are only available within the source domain.
• Figure 3: Process flow diagrams for the (a) TEP and (b) MFP facilities.
• Figure 4: Comparisons between ground truths and predictions of the two best models for the first MFP domain adaptation task. The unshaded regions represent the labeled source domain, and the shaded regions represent the unlabeled target domain.
• Figure 5: Comparison of t-SNE embeddings between the ground-truth sensor labels and the model predictions of the MFP output variables on transfer task: {0.0278, 0.0347} → {0.0208, 0.0417}.