Impact of geometric forms on the effectiveness and physical features of POD-based geometric parameterization

Abstract

Effective geometric parameterization is crucial in aerodynamic shape optimization for enabling flexible surface deformation while maximizing design space coverage. This paper studies the impact of different geometric forms (closed and open curves) on the effectiveness of Proper Orthogonal Decomposition (POD) geometric parameterization and explores the information of physical features contained in the POD bases. The efficiency and design space coverage which are the main indicators of effectiveness. These indicators of two POD-based parameterization methods are tested on a hybrid database and four typical airfoils. The convergence of aerodynamic properties is also investigated in typical airfoils. In addition, a modified application criterion for POD bases is established by the recursive feature elimination method. A feature importance-based explainable AI (xAI) method is also developed, combining Shapley additive explanations (SHAP) and modified application criterion to explore the physical information contained in POD bases. The results indicate that the POD-based parameterization method constructed from open curves can reconstruct database with better efficiency and design space coverage. Additionally, compared to geometric errors, more POD bases may be required to cover the airfoil design space in order to achieve superior aerodynamic accuracy. Significant differences exist in the importance and correlation of POD bases derived from different geometric forms, with those from closed curves providing better reconstruction efficiency for geometric parameters.