A Novel Causal Robust Soft Sensor for Industrial Processes With Data Distribution Drift

Modern industrial systems require real-time prediction for critical variables that are expensive or impossible to measure online. Existing soft sensing approaches suffer from catastrophic performance degradation under distribution shifts and sensor perturbations. This study develops a novel framework that bridges causal inference with robust optimization for reliable industrial soft sensing. We propose a causal robust soft sensor (CRSS) framework that employs spatiotemporal filtering to extract Granger-causal features that capture predictive temporal relationships reflecting fundamental process mechanisms. The framework incorporates explicit robustness constraints via regularization that penalizes sensitivity to bounded perturbations. Extensive experimental verification on real industrial refinery control system data demonstrates that CRSS achieves the best predictive accuracy (RMSE$=0.42$,$R^{2}=0.90$). It maintains stable performance under 20% sensor noise with small degradation, and remains robust under complete sensor outages, nonlinear distortions, and heavy-tailed perturbations beyond the Gaussian model. CRSS provides theoretically grounded prediction error bounds, offering a practical solution for industrial soft sensing applications with interpretable Granger-causal insights.