基于PCA-HicksHenne方法的几何不确定性稳健优化设计

考虑不确定因素的稳健优化设计在飞行器气动外形设计选型中至关重要。针对环境扰动下稳健优化的研究较多，而对几何不确定性的关注则相对较少。为量化几何不确定性，采用主成分分析(PCA)方法，对RAE2822翼型的参数化过程进行了研究，并揭示了翼型的主要几何变形模态。采用敏感度分析方法，指出厚度变形模态、弯度变形模态及上翼面最大厚度位置的轴向位移模态是主要影响模态，并将其作为扰动模态进行稳健优化研究。结果表明: 不考虑扰动的确定优化翼型的升力变化更加剧烈，标准差增大近200%；考虑几何扰动的优化翼型稳健性更高，在平均性能提升的同时，无论是升力还是阻力的变化都比原始RAE2822翼型更小。 

Robust optimization design under geometric uncertainty based on PCA-HicksHenne method

The aerodynamic shape design of an aircraft requires a robust optimization approach that takes uncertainty into account. To the knowledge of the authors, research efforts were more paid to the robust optimization considering environmental perturbations, rather than geometric perturbations. For purpose of quantifying the geometric uncertainty, the principal component analysis (PCA) method was utilized to perform research on the parameterization process of the RAE2822 airfoil. The main geometric transformation modes of the airfoil were revealed subsequently. After that, the sensitivity analysis method was applied, and the thickness deformation mode, the camber deformation mode, and the axial displacement mode of the maximum thickness position on the upper surface were indicated as the main influential modes. Those modes were taken as the perturbation modes in the following robust optimization research. The results show that the lift variation of the deterministic optimal airfoil without consideration of perturbation is much huger, with the standard deviation increased by about 200%. However, the optimal airfoil considering geometric perturbation is more robust. The robust airfoil's variability, whether in lift or drag, are lower than those of the original RAE2822 airfoil along with the improvement in mean performance.