Bridging Physics and Data: Hybrid Modelling of NOx and Soot Emissions in Alternative-Fuel Diesel Engine

In this study, a basic machine learning approach based on fuel type for estimating NOx and soot emissions in diesel engines was comparatively evaluated against a physics-based model incorporating physical indicators related to the combustion process. Experimental data were obtained from a single-cylinder, four-stroke diesel engine under single and dual fuel conditions using diesel, biodiesel, and ammonia. Quantities derived from the in-cylinder pressure signal, including IMEP, maximum pressure rise rate, maximum pressure, the crankshaft angle corresponding to maximum pressure, the CA10–CA90 combustion interval, ignition delay and total combustion duration, were integrated into the model as quantitative indicators representing the engine’s thermodynamic behaviour and combustion evolution, and the resulting framework is referred to in this study as a physically informed model. With the inclusion of these parameters, physical information reflecting combustion intensity, heat release dynamics, and mixture formation characteristics has been incorporated into the data-driven structure. Models developed using linear regression, Random Forest, and Gradient Boosting methods were compared using R2, RMSE, and MAE metrics. The findings revealed that the baseline model exhibited significant deviations, particularly at high NOx and medium-high soot levels. The physics-based model significantly reduced error across all algorithms, narrowed the distribution, and largely eliminated systematic bias. The highest accuracy was achieved with the Gradient Boosting method, where the physics-based model elevated the R2 value to 0.99 for NOx predictions and again to 0.99 for soot predictions. The results obtained demonstrate that integrating in-cylinder combustion indicators into the model significantly improves emission prediction performance and that combining physical processes with data-driven approaches provides a robust and reliable prediction framework.