Modeling Multiresponse Surfaces for Airfoil Design with Multiple-Output-Gaussian-Process Regression

Response surfaces are frequently used in airfoil design due to less resource requirement compared with direct slow simulations. In many cases, multiple responses need to be modeled to achieve multiple objectives. Considering the correlations between multiple responses in modeling the nonlinear relationship between airfoil shapes and aerodynamic performance, the authors construct multiresponse surfaces for airfoil design with multiple-output-Gaussian-process-regression model. The authors simulate computational data to evaluate the prediction accuracy and stability of the multiple-output Gaussian process in airfoil design, compared with other popular alternative approaches, kriging, and backpropagation and radial-basis-function neural networks. In the experiments, response surfaces from the airfoil shapes, parameterized by the class/shape-function-transformation method, to lift, drag, and pitching-moment coefficients are constructed. The results indicate that the multiple-output Gaussian process receives higher prediction accuracy and stability in modeling multiresponse surfaces than other popular methods when there are significant correlations between responses.