Switching probabilistic slow feature extraction for semisupervised industrial inferential modeling

Predicting quality-relevant process variables is of paramount importance in optimizing and controlling chemical processes. Probabilistic Slow Feature Analysis (PSFA), a potent data-driven technique, plays a pivotal role in deducing quality indices by abstracting gradual variations in processes distinctly characterized by pronounced inertia. Nevertheless, PSFA's predictive efficacy encounters a substantial bottleneck due to the assumption of a single operating condition, compromising its accuracy, particularly in industries represented by switching operating conditions. To surmount this limitation, this study proposes an innovative approach that enriches PSFA with multi-operating condition process data and limited labels within a Bayesian framework, effectively combining continuous and discrete first-order Markov chains to capture the processes’ inertia and dynamic shifts. The proposed method updates latent posterior distributions and model parameters iteratively via the Expectation–Maximization algorithm. The effectiveness of the proposed methodology is verified through a numerical case and industrial hydrocracking process data.