A Novel Metric-Based Geometric Parameterization Approach with Performance Filtration

In the approach of metric-based geometric parameterization, the concept of database filtration and proper orthogonal decomposition manipulation quantitatively enhances the generation of new geometric parameters so that the problem-oriented information is reflected in aerodynamic design. Compared with the conventional approach that applies only geometric filtration, this paper incorporates performance filtration so that the problem-oriented information is no longer limited to geometric constraints, thereby enabling the guidance of optimization direction in a more informed manner. This paper focuses on the pressure distribution of samples and their relationship with geometric variations. A variational autoencoder is employed to extract the dominant features of the aerodynamic potentials that an initial geometry can attain in optimization. The authors believe that the aerodynamic potential is reflected in how the pressure distribution differs from that of the initial geometry. Then, samples have to meet the performance filtration criterion based on pressure distribution proposed by designers according to their aerodynamic understanding of the optimization problem. Finally, the remaining collection of qualified samples generates new geometric parameters via proper orthogonal decomposition. The conventional and new approaches were validated in a two-dimensional airfoil case of drag coefficient optimization; the lift-to-drag ratio improved by 17.07% using the traditional method, and by 38.20% using the new approach. The pressure distribution shows that the performance filtration approach produces more supercritical properties than the geometric filtration approach. This implies that the performance filtration approach can capture more intricate details related to the aerodynamic performance of the airfoil.