Predicting Transient Soot Emissions in Diesel Engines Using Physical and Machine Learning Models

In recent years, diesel engine emissions regulations have been strengthened worldwide, necessitating the evaluation of regulatory values under transient conditions. Consequently, the need to assess transient states in the development of diesel engines has increased significantly. The evaluation using MBD (Model Based Development) is considered a promising method for achieving both low fuel consumption and simultaneous reduction of NOx and soot emissions. However, the mechanism of soot formation is complex, making it challenging to model mathematically directly. In this paper, hybrid machine learning approaches combining a physical model and a machine learning model are used to validate the prediction of soot emissions under transient conditions in a diesel engine with an EGR system. Various parameters such as fuel consumption and emissions predicted by the physical model are compared with measurements to validate the accuracy of the physical model. The prediction of soot emissions by the physical model is based on the Hiroyasu model. From these results, it is demonstrated that the physical model has sufficient accuracy to be used in hybrid machine learning approaches. However, it is shown that the physical model is inadequate as a prediction approach for soot emissions. Gaussian Process Regression (GPR), Support Vector Regression (SVR), Random Forest (RF), and Gradient Boosting Decision Tree (GBDT) are used to develop the machine learning models, and each model is trained on data under steady-state conditions. The prediction accuracy of each model and the physical model is compared and validated. The results show that the hybrid machine learning approaches have higher predictive accuracy than the physical model for soot emissions predictions in both steady-state and transient conditions. The GPR model with the highest prediction accuracy shows a test R² of 0.87 under steady-state conditions and relative errors with the measured values of less than 10% for both Non-load Transient Cycle (NRTC) and Low Load Cycle (LLC), which are engine test cycles.