Airfoils play significant roles in aerodynamic engineering as they are important devices in designing aircraft and engines. For airfoils, geometric design variables often deviate from nominal values that deteriorate airfoil quality. Thus, the design optimization of airfoils under the noises of design variables is important. However, the existing literature does not consider functional responses that can more adequately describe airfoil performances than univariate and multivariate responses. To fill in this gap and further improve airfoil quality, we develop a surrogate-based robust parameter design methodology for the design optimization of airfoils with functional responses. A new optimization criterion that involves both location and dispersion effects associated with the functional feature of quality losses, noises of design variables, and emulator uncertainty is proposed. A Gaussian process (GP) model with functional responses is employed as a surrogate/emulator. An efficient method for computing the proposed criterion is developed. The proposed methodology is applied to a typical airfoil design optimization problem to demonstrate that better and more robust solutions are obtained with the proposed criterion for airfoils, and the computing time is significantly reduced with the proposed estimation method.

翼型在空气动力学工程中发挥着重要作用，因为它们是设计飞机和发动机的重要设备。对于翼型，几何设计变量通常会偏离标称值，从而降低翼型质量。因此，翼型在设计变量噪声下的设计优化很重要。然而，现有文献并未考虑比单变量和多变量响应更能充分描述翼型性能的功能响应。为了填补这一空白并进一步提高翼型质量，我们开发了一种基于代理的稳健参数设计方法，用于具有功能响应的翼型设计优化。一种新的优化标准，涉及与质量损失、设计变量噪声、并提出了仿真器不确定性。具有功能响应的高斯过程 (GP) 模型被用作代理/模拟器。开发了一种计算建议标准的有效方法。将所提出的方法应用于典型的翼型设计优化问题，以证明使用所提出的翼型标准可以获得更好、更稳健的解决方案，并且使用所提出的估计方法显着减少了计算时间。