In aerodynamic shape optimization, the convergence and computational cost are greatly affected by the representation capacity and compactness of the design space. Previous research has demonstrated that using a deep generative model to parameterize two-dimensional (2D) airfoils achieves high representation capacity/compactness, which significantly benefits shape optimization. In this paper, we propose a deep generative model, Free-Form Deformation Generative Adversarial Networks (FFD-GAN), that provides an efficient parameterization for three-dimensional (3D) aerodynamic/hydrodynamic shapes like aircraft wings, turbine blades, car bodies, and hulls. The learned model maps a compact set of design variables to 3D surface points representing the shape. We ensure the surface smoothness and continuity of generated geometries by incorporating an FFD layer into the generative model. We demonstrate FFD-GAN's performance using a wing shape design example. The results show that FFD-GAN can generate realistic designs and form a reasonable parameterization. We further demonstrate FFD-GAN's high representation compactness and capacity by testing its design space coverage, the feasibility ratio of the design space, and its performance in design optimization. We demonstrate that over 94% feasibility ratio is achieved among wings randomly generated by the FFD-GAN, while FFD and B-spline only achieve less than 31%. We also show that the FFD-GAN leads to an order of magnitude faster convergence in a wing shape optimization problem, compared to the FFD and the B-spline parameterizations.

本研究提出了一种名为“Free-Form Deformation Generative Adversarial Networks (FFD-GAN)”的深度生成模型，可用于三维空气动力学/水力学形状优化，例如机翼、涡轮叶片、汽车车身和船体。该模型通过一组紧凑的设计变量映射到表示形状的三维表面点，具有高表征容量/紧凑度，并能够加速形状优化。

高效三维翼型参数化与生成的深度生成模型