Hybrid PDE-RNN model for SCR inlet temperature simulation in diesel engines
Yong Li, Yuchen Yang, Hongjun Hui, Shiyu Liu, Shijin Shuai, Xingjian Li
Accurate prediction of Selective Catalytic Reduction (SCR) inlet temperature is critical for effective thermal management of diesel aftertreatment systems and for complying with increasingly stringent emission regulations. Traditional physics-based models formulated as partial differential equations (PDEs) capture the main heat transfer dynamics but are computationally intensive and rely on simplifying assumptions that neglect effects such as wall temperature variations and chemical reactions. In contrast, data-driven models can represent complex nonlinear relationships but typically require long input sequences and generalise poorly to unseen operating conditions. This study proposes a hybrid PDE + RNN modelling framework that integrates a one dimensional PDE based physical model with a recurrent neural network (RNN) trained to learn residual prediction errors. The PDE component models the dominant thermal behaviour along the exhaust line, while the RNN compensates for unmodelled effects, improving both prediction accuracy and interpretability. The proposed model is validated using experimental data from three diesel engines (light, medium, and heavy duty) under multiple test cycles, including the World Harmonised Transient Cycle (WHTC) and the World Harmonised Steady-state Cycle (WHSC). Results demonstrate that the hybrid model consistently outperforms PDE-only, RNN-only and standard LSTM approaches, achieving an average root mean squared error (RMSE) of approximately