Abstract: To address the limitations in accuracy and reliability of existing methods, a dynamic warning approach that integrates mechanistic knowledge with uncertainty analysis is proposed. The method begins by constructing a mechanistic model based on MESH (Material balance, Equilibrium, Summation, and Heat balance) equations. A Bayesian Gated Recurrent Unit (BD-GRU) is then employed to capture the residuals of the mechanistic model, to enable dynamic correction and enhance prediction accuracy. Subsequently, a double Monte Carlo sampling strategy is implemented to quantify the total prediction uncertainty, which is decomposed into epistemic uncertainty and aleatoric uncertainty.Finally, a dynamic threshold mechanism, informed by this uncertainty quantification, is designed to improve the system's adaptability to operational fluctuations.Experimental results show that the constructed hybrid model achieves high prediction accuracy and reliability, with a mean absolute percentage error（MAPE）as low as 3.6% and a prediction interval coverage probability of 94.5%. Compared with the traditional fixed-threshold method, the fault detection rate of the proposed method increases from 82% to 95%, and the false alarm rate decreases from 16.2% to 4.8%, significantly improving the accuracy and reliability of the early warning system.

Key words: crude oil distillation process, fault early warning, hybrid modeling, uncertainty analysis, dynamic early-warning threshold