A Causal Knowledge-Assisted Semi-Supervised Dynamical Generative Latent Variable Model for Industrial Quality Index Prediction

Generative latent variable models (GLVMs) are prevalent in developing soft sensors for predicting industrial process quality indices owing to their exceptional capability in extracting features, reducing data dimensionality, and explaining data generation mechanisms. Dynamical GLVMs (DGLVMs) are able to effectively deal with the dynamical characteristics of industrial data changes over time, exhibiting prominence in time-series prediction and dynamical process modeling. However, the existing DGLVM-based soft sensors share an intrinsic imperfection that they focus on capturing the temporal correlations between variables while disregarding the causal relationships between variables. Based on industrial data, it is difficult to recover the causalities between variables from the correlations, resulting in compromised generalization performance of the existing DGLVM-based soft sensors. In light of this limitation, a novel causal knowledge-assisted semi-supervised DGLVM (CK-SsDGLVM) is proposed, and an ad hoc parameter learning method based on the expectation–maximization (EM) algorithm is developed to train the CK-SsDGLVM. The performance of the CK-SsDGLVM is comprehensively evaluated using an artificial numerical case and an actual industrial process. The experimental results demonstrate that the CK-SsDGLVM could achieve superior generalization accuracy and interpretability compared to benchmark models.