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.

中文翻译：

---

高效3D机翼参数化和生成的深度生成模型

在空气动力学形状优化中，表示能力和设计空间的紧凑性极大地影响了收敛性和计算成本。先前的研究表明，使用深度生成模型对二维（2D）机翼进行参数化可实现较高的表示能力/紧凑性，这将大大有利于形状优化。在本文中，我们提出了一个深层生成模型，即自由形式变形生成对抗网络（FFD-GAN），该模型可为飞机机翼，涡轮叶片，车身，和船体。学习的模型将一组紧凑的设计变量映射到表示形状的3D表面点。通过将FFD层合并到生成模型中，我们可以确保生成的几何图形的表面光滑度和连续性。我们通过机翼形状设计实例演示FFD-GAN的性能。结果表明，FFD-GAN可以生成逼真的设计并形成合理的参数化。通过测试FFD-GAN的设计空间覆盖率，设计空间的可行性比以及其在设计优化中的性能，我们进一步证明了FFD-GAN的高表示紧凑性和容量。我们证明了在FFD-GAN随机生成的机翼中实现了超过94％的可行性比，而FFD和B样条仅实现了不到31％。我们还表明，与FFD和B样条参数化相比，FFD-GAN在机翼形状优化问题中导致更快的数量级收敛。