To enhance the calibration efficiency, reduce the fuel consumption and improve the emission performance of the engine, a calibration method using Gaussian Process Regression (GPR) is proposed in this work. First, the design of experiment (DoE) is constructed by using the Space-filling method, and the engine bench sampling test is implemented according to results of DoE. Then, the square exponential covariance function is selected through the comparison of four covariance functions, and the corresponding hyper-parameters are optimized by using Newton gradient algorithm. Finally, the GPR model of the engine is established and its calibration performance is validated by the experimental data. The comparison shows that the performance of the developed GPR model is superior to the Polynomial model and Neural Network model, whose coefficient of determination (R²) of Fuel Consumption (FC), NOx emission (NOx) and Soot emission (Soot) are up to 0.9980, 0.9326 and 0.9247. The case study demonstrates that the virtual calibration optimization based on GPR model improves the fuel consumption performance greatly, while taking NOx and Soot emission indicators into account.

为了提高标定效率，减少燃油消耗并改善发动机的排放性能，在这项工作中提出了一种使用高斯过程回归（GPR）的标定方法。首先，采用空间填充法进行实验设计（DoE），并根据实验结果对发动机台架进行试验。然后，通过比较四个协方差函数来选择平方指数协方差函数，并使用牛顿梯度算法对相应的超参数进行优化。最后，建立了发动机的GPR模型，并通过实验数据验证了其标定性能。比较表明，所开发的GPR模型的性能优于多项式模型和神经网络模型，²）燃油消耗（FC），NOx排放（NOx）和烟灰排放（Soot）分别高达0.9980、0.9326和0.9247。案例研究表明，基于GPR模型的虚拟标定优化可以大大提高燃油消耗性能，同时考虑NOx和烟尘排放指标。