Virtual Calibration of Steady-State Emissions for Heavy-Duty Diesel Engines Based on Regression Models

To promote the green and low-carbon transition and achieve sustainable development in the transportation sector, virtual calibration technology was employed for the efficient and precise control of emissions from heavy-duty diesel engines and aftertreatment systems. A data-driven, semi-empirical and semi-physical simulation modeling method was proposed. By constructing core modules based on physical mechanisms and refining empirical parameters using experimental data, the method improves computational efficiency while maintaining the prediction accuracy of key parameters. Additionally, a collaborative architecture combining physical actuators and virtual sensor signals was introduced, laying the foundation for the validity of virtual calibration. By innovatively introducing a closed-loop system with real actuators and virtual sensors, the dynamic response characteristics of the control system are faithfully reproduced, providing a reliable environment for validating the results of virtual calibration. Under steady-state conditions, the results demonstrated an average relative error of 1.7% for brake-specific fuel consumption (BSFC) and 6.1% for NOx emissions. An open-loop system for the virtual calibration testing platform was constructed for steady-state calibration. Using the main injection timing and common rail pressure as independent variables, a D-optimal design was utilized to generate 43 sets of experimental points, from which a polynomial regression model was established (R2 ≥ 98%). Under the constraints of NOx and pre-turbine temperature, fuel consumption in the low-load range is reduced by 0.5–3 g/kW·h, aftertreatment NOx emissions are reduced by 0.5–3 g/kW·h, and exhaust temperature is increased by 10 °C. This study establishes a complete development workflow consisting of “operating condition design-virtual optimization-bench validation,” significantly enhancing calibration efficiency and engineering applicability. This method shortens the calibration cycle and reduces the number of physical bench tests, providing the industry with a comprehensive calibration methodology tailored to engine operating conditions that is both reproducible and scalable.