Towards hybrid modeling with mechanistic and real-time data embed iterative co-optimization for industrial processes

This paper addresses the hybrid modeling challenges arising from incomplete mechanistic models and operational data noise interference in process industries, proposing a two-layer joint iterative optimization framework for updating parameters of hybrid models integrating mechanistic and data-driven models. The framework achieves real-time anomaly elimination through an outlier screening algorithm, while employing a bidirectional feedback algorithm to enable continuous collaboration and mutual constraints between mechanistic and data-driven models during parameter identification and iterative updates, ensuring robust hybrid model predictions. The proposed method resolves hybrid modeling and updating under conditions of mechanistic model information deficiency. Additionally, by incorporating model uncertainty and prior knowledge, it accomplishes a knowledge-incorporated hybrid modeling process, demonstrating significant practical value. Unlike conventional hybrid modeling approaches where mechanistic knowledge merely guides the modeling process, our method achieves dynamic co-evolution between mechanistic and data-driven models. This paper elaborates on three key aspects: (1) using mechanistic models to screen anomalous data; (2) incorporating mechanistic parameter uncertainty and prior knowledge through Bayesian methods to design knowledge-guided parameter updating method; (3) implementation details of the two-layer joint iterative optimization algorithm. Comparative experiments validate the method’s superior performance under multiple operating conditions and anomalies, demonstrating its scientific validity and practical value in dynamic optimization processes. • A joint iterative optimization framework with bidirectional feedback is proposed, enabling real-time collaboration between the mechanistic and data-driven models. • An anomaly detection and filtering method based on the Median Absolute Deviation (MAD) is used to improve data quality. • A optimization strategy is employed to dynamically update the parameters of both mechanistic and data-driven models. • The integration of mechanistic knowledge with real-time data improves model prediction and robustness in dynamic operating conditions.