Improved automatic kernel construction for Gaussian process regression in small sample learning for predicting lift body aerodynamic performance

Abstract

A Gaussian process regression (GPR) model based on an improved automatic kernel construction (AKC) algorithm using beam search is proposed to establish a surrogate model between lift body shape parameters and aerodynamic coefficients with various training sets sizes. The precision of our proposed surrogate model is assessed through tenfold cross-validation. The improved AKC-GPR algorithm, polynomial regression, and support vector regression (SVR) are employed to construct the regression model. The interpolation and extrapolation capabilities of the model, as generated by the improved AKC-GPR algorithm, are examined using six shapes beyond the sample set. The results show that the three models perform similarly with a large training set. However, when the training set size is less than 40% sample dataset, the model constructed by the improved AKC-GPR algorithm has better fitting and prediction capabilities than the other models. Specifically, the max relative error of the improved model is one-fourth of that of SVR and one-half of that of polynomial regression with the training set size of 8% of the sample dataset. Furthermore, the lift-to-drag ratio relative error of interpolation is only 3%, and extrapolation error is 6%. In terms of the fitting and prediction abilities for small samples, the lift-to-drag ratio model outperforms the drag coefficient model, while the lift coefficient model performs the poorest. These findings suggest that the proposed AKC-GPR algorithm can be an effective approach for building a surrogate model in the field of aerodynamics.