  Data-driven soft sensors are essential for achieving accurate perception
through reliable state inference. However, developing representative soft
sensor models is challenged by issues such as missing labels, domain
adaptability, and temporal coherence in data. To address these challenges, we
propose a deep Particle Flow Bayes (DPFB) framework for cross-domain soft
sensor modeling in the absence of target state labels. In particular, a
sequential Bayes objective is first formulated to perform the maximum
likelihood estimation underlying the cross-domain soft sensing problem. At the
core of the framework, we incorporate a physics-inspired particle flow that
optimizes the sequential Bayes objective to perform an exact Bayes update of
the model extracted latent and hidden features. As a result, these
contributions enable the proposed framework to learn a rich approximate
posterior feature representation capable of characterizing complex cross-domain
system dynamics and performing effective time series unsupervised domain
adaptation (UDA). Finally, we validate the framework on a complex industrial
multiphase flow process system with complex dynamics and multiple operating
conditions. The results demonstrate that the DPFB framework achieves superior
cross-domain soft sensing performance, outperforming state-of-the-art deep UDA
and normalizing flow approaches.
