Adversarial Training-Based Deep Layer-Wise Probabilistic Network for Enhancing Soft Sensor Modeling of Industrial Processes

Improving the robustness of the soft sensor model of industrial processes is an important yet challenging problem for a large amount of noise interference and missing data in practical industrial data. In this article, an adversarial training-based deep supervised variational autoencoder (Adv-DSVAE) is proposed to enhance the performance of industrial soft sensor models. Specifically, a supervised variational autoencoder (SVAE) is first designed to extract the quality-relevant feature representation. Then, a deep SVAE (DSVAE) model is constructed by stacking the hidden features extracted by SVAE, such that a high-level output-related feature representation can be captured. In this way, the missing data situation can be handled by the probabilistic latent feature representation extracted in DSVAE. To improve the robustness of a DSVAE-based soft sensor model, an adversarial training method is designed, in which adversarial examples are generated by adding perturbations to the last hidden feature of DSVAE, such that the model can perform well on both clean and perturbed feature representations. We further provide theoretical convergence analysis for the proposed Adv-DSVAE to guarantee its successful practical application. The ablation studies confirm that industrial quality prediction using the adversarial training strategy can ensure better robustness. Case studies on both the debutanizer column process and the real-world aluminum electrolysis process validate the superiority of Adv-DSVAE.