Modification of the Class-Shape-Transformation Parameterization Based on Radial Basis Functions

Abstract

To improve the capacity for utilizing a higher number of design variables and handling complex geometries in the class-shape-transformation parameterization method, this paper introduces an alternative for the shape function that employs radial basis functions to interpolate the deformations of the control points throughout the entire shape function. Two representative airfoils are parameterized first, and the results indicate that the presented method can avoid the ill-conditioning problem encountered when using high-order Bernstein polynomials in the traditional method. Moreover, it is more effective in parameterizing complex geometries. A comprehensive test on a database containing 1433 airfoils reveals that the presented method can cover a larger design space with an increase in the number of design variables. The presented method is further employed and validated in two typical aerodynamic shape optimization tasks: an airfoil inverse design and a benchmark problem for drag minimization in transonic viscous flow. The results suggest that the presented method has potential advantages in gaining better optimized results when more design variables are employed.