Peak in-cylinder pressure virtual sensor based on hybrid modeling framework

Accurate onboard measurement of peak in-cylinder pressure (PCP) is essential for optimizing engine performance, enhancing combustion efficiency, and supporting emissions control in internal combustion engines. This study introduces a hybrid modeling framework, designed as a virtual sensor, combining Robust Iterated Local Search with Ordinary Least Squares (RILS-ROLS), a white-box model based on symbolic regression, with black-box models to improve PCP prediction accuracy across diverse operating conditions. The optimal hybrid model, combining RILS-ROLS and Categorical Boosting (CatBoost), enhances prediction accuracy, particularly under extreme conditions, achieving error reductions of up to 55.2% compared to standalone models while maintaining lower complexity. By correcting residuals from the physics-informed RILS-ROLS model with the adaptive CatBoost model, the approach effectively captures nonlinearities, outperforming traditional methods that typically exhibit errors exceeding 5%–10%. Validation with real-world data demonstrated strong agreement between measured and predicted cycle-to-cycle PCP values, with coefficient of determination R2 values above 0.99 and an F1-score of 0.944 at a ±5 bar margin. The hybrid framework also prioritizes real-time processing, computational efficiency, and fault tolerance through cross-verification across four distinct driving cycles, offering a robust and reliable solution for cycle-to-cycle PCP estimation in advanced engine control applications.