APSF-Net: A deep adversarial slow feature extraction network for industrial inferential modeling

Process industries rely on inferential models to provide real-time estimates of quality variables. Among the various types of inferential models, the slowness preference approach stands out as effective in mimicking chemical processes by encapsulating system inertia. This study proposes a new deep generative model, grounded in Bayesian principles, which leverages the slowness representation to identify slow and nonlinear patterns in sequential industrial data. Notably, the model characterizes a variable attention mechanism that adaptively identifies quality-related input variables. Moreover, a min–max game theoretical adversarial learning strategy is designed to enhance the model's robustness and the ability to effectively approximate the real data distribution. The mathematical formulation of the model is presented within a semi-supervised framework, accommodating scenarios with limited labeled data. Finally, this study unequivocally showcases the superior performance of the proposed model in predicting carbon monoxide content in the recycled gas using data from a real coal-to-ethylene glycol process.