关键词: 气动外形优化, 翼型参数化, 主成分分析, 几何参数化, 本征正交分解

Abstract:

Geometry parametrization plays a significant role in Aerodynamic Shape Optimization （ASO）. A succinct， accurate， and efficient geometric presentation method can effectively improve the optimization efficiency and the design results. Principal Component Analysis （PCA） is a common way to extract data features and reduce data dimension. In this paper， an airfoil geometry parameterization method based on the PCA is firstly introduced. Then， the influences of sampling space， sample number， sampling method and geometric reconstruction method on PCA dimension reduction ability， base mode characteristics and geometric presentation ability are analyzed. Furthermore， the presentation ability of the PCA method on aerodynamic characteristics is also studied based on computation fluid dynamics. Simulation results show that： the PCA method could effectively describe the airfoil geometry shape with preferable accuracy and relatively few， physically meaningful parameters； based on a specific sampling method， the PCA mode， the dimension reduction ability and the geometric accuracy are little affected by the sampling space and the sample number， though they are sensitive to the parameters of the sampling method； the PCA method described in this paper could not only accurately describe the geometry shape， but also ensure the accuracy of the aerodynamic forces to a certain degree， which has certain guiding significance in ASO applications.

Key words: aerodynamic shape optimization, airfoil parametrization, principal component analysis, geometry parametrization, proper orthogonal decomposition