A Domain Knowledge-Supervised Framework Based on Deep Probabilistic Generation Network for Enhancing Industrial Soft Sensing

Soft sensors have been widely used in many industrial processes for monitoring and optimization. Existing soft-sensing methods rely on high-quality data. However, the intrinsic patterns of data might deviate from process mechanisms due to an adverse environment, leading to a decrease in accuracy. To address these challenges, we propose a domain knowledge-supervised framework based on a deep probabilistic generative network (DKSF-DPGN). The contributions of this work are below. A domain knowledge network is designed to extract features from expert knowledge and process mechanisms. An attention mechanism is then applied to obtain a shared latent feature representation. Supervised by the features aligned with domain knowledge, a deep generative regression network (DGRN) is developed to construct a predictive regression model, enhancing both soft-sensing accuracy and interpretability. The proposed soft-sensing model based on DKSF-DPGN is validated by Tennessee Eastman process, continuous stirred tank heater, and aluminum electrolysis process. Experimental results demonstrate that our model exhibits outstanding accuracy, as measured by mean absolute error (MAE), mean squared error (mse), root-mean-squared error (RMSE), coefficient of determination ( $ R^{2} $ ), and mean absolute percentage error (MAPE).