CausalSynG: Multivariate Collaborative Causal Inference With Dynamic Knowledge-Data Synergy for Industrial Soft Sensors

Data-driven soft sensor techniques are increasingly being applied in complex industrial environments, enabling the modeling of many previously intractable variables and playing a critical role in ensuring stable industrial operations. However, solely data-driven soft sensor models suffer a certain degree of performance degradation when encountering scenarios with distribution drift. This stems from their exclusive reliance on correlation information for modeling. To enhance the models’ stability in strongly time-varying scenarios, causal information is introduced into the model to enhance its robustness. However, existing causal-enhanced soft sensor models often overlook collaborative causal effects during causal mining and lack dynamic integration of causal information stability and data dynamics. To this end, this paper proposes a novel Causal Synergistic Graph (CausalSynG) network, which developed a multivariate collaborative causal structure inference framework to derive causal topology and incorporated an expert prior correction mechanism based on the contribution of data to endow causal information with data dynamics. Additionally, to fully leverage causal inference results, a causal-enhanced graph structure mechanism based on correlation information is proposed to integrate correlation and causal information. Based on this, a Fused Causal Temporal Graph (F-CausalTG) network is proposed to correctly fuse temporal and causal information to achieve the goal of target variable modeling. Experimental results from petrochemical processes and blast furnaces validate the feasibility and effectiveness of the proposed soft sensor model. In the debutanizer scenario, the proposed method achieved a 17.95% reduction in Mean Absolute Error (MAE) compared to the optimal baseline method, with a 19.44% improvement in the coefficient of determination (R²). In the Blast Furnace Ironmaking Process (BFIP) coke ratio scenario, the Mean Squared Error (MSE) decreased by 7.58%, providing more intuitive evidence of the method’s performance improvement and ensuring the credibility of the conclusions.