Deep transfer learning-based model for real-time prediction of multiple injection rate in common rail system for marine engine

Multiple injection in high pressure common rail system (HPCRS) is an advanced technology for energy conservation and emission reduction in modern marine engines. However, the lack of methods capable of real-time and precise prediction of multiple injection rates currently limits the further refinement of air-fuel ratio control and the enhancement of engine performance. In this paper, deep learning and transfer learning were integrated to propose a predictive model architecture for pilot-main injection rates under multiple injection strategies. Initially, the pressure fluctuations at the injector inlet, driving current data, and injection rates were experimentally measured. A single injection rate prediction model based on quantum particle swarm optimization (QPSO) and double-layer bidirectional long short-term memory neural network (DL-BiLSTM) was constructed, which was verified through optimization convergence and ablation study on hidden-layer unit counts. Building upon this foundation, transfer learning models employing three parameter freezing strategies were further developed. Among these, the TDB-F1 model, which freezes the parameters of the first hidden layer while retraining the upper network, achieved high-precision predictions of pilot-main injection rate characteristics in both the time domain and amplitude spectrum on the testing set and non-learning operating conditions set. Real-time prediction experiments demonstrated that the RMSE, MAE, and R2 values for pilot-main injection rate prediction were 18.4391, 8.9811, and 0.9851, respectively. Additionally, the upper limit of the 95 % confidence interval for injection quantity prediction error was less than 4.98 %, while the end-to-end prediction time was approximately 34.07 ms. These results confirm the proposed model's high-precision and stable predictive capability for pilot-main injection characteristics.