Application of the Gaussian Process Regression Method Based on a Combined Kernel Function in Engine Performance Prediction

[Image: see text] At present, regression modeling methods fail to achieve higher simulation accuracy, which limits the application of simulation technology in more fields such as virtual calibration and hardware-in-the-loop real-time simulation in automotive industry. After fully considering the abruptness and complexity of engine predictions, a Gaussian process regression modeling method based on a combined kernel function is proposed and verified in this study for engine torque, emission, and temperature predictions. The comparison results with linear regression, decision tree, support vector machine (abbreviated as SVM), neural network, and other Gaussian regression methods show that the Gaussian regression method based on the combined kernel function proposed in this study can achieve higher prediction accuracy. Fitting results show that the R(2) value of engine torque and exhaust gas temperature after the engine turbo (abbreviated as T4) prediction model reaches 1.00, and the R(2) value of the nitrogen oxide (abbreviated as NOx) prediction model reaches 0.9999. The model generalization ability verification test results show that for a totally new world harmonized transient cycle data, the R(2) value of engine torque prediction is 0.9993, the R(2) value of exhaust gas temperature is 0.995, and the R(2) value of NOx emission prediction result is 0.9962. The results of model generalization ability verification show that the model can achieve high prediction accuracy for performance prediction, temperature prediction, and emission prediction under steady-state and transient operating conditions.