Traditional airfoil parametric technique has significant limitation in modern aerodynamic optimization design.There is a strong demand for developing a parametric method with good intuitiveness, flexibility and representative accuracy. In this paper, two parametric generative schemes based on deep learning methods are proposed to represent the complicate design space under specific constraints. 1. Soft-constrained scheme: The CVAE-based model trains geometric constraints as part of the network and can provide constrained airfoil synthesis; 2. Hard-constrained scheme: The VAE-based model serves to generate diverse airfoils, while an FFD-based technique projects the generated airfoils to the final airfoils satisfying the given constraints. The statistical results show that the reconstructed airfoils are accurate and smooth without extra filters. The soft constrained scheme tend to synthesize and explore airfoils efficiently and effectively, concentrating to the reference airfoil in both geometry space and objective space. The constraints will loose for a little bit because the inherent property of the model. The hard constrained scheme tend to generate and explore airfoils in a wider range for both geometry space and objective space, and the distribution in objective space is closer to normal distribution. The synthesized airfoils through this scheme strictly conform with constraints, though the projection may produce some odd airfoil shapes.

翻译：1. 软控制办法:以CVAE为基础的模型将几何限制作为网络的一部分,并能够提供有节制的空气循环合成;2. 严格控制的办法:以VAE为基础的模型能够产生多种空气循环,而以FFFD为基础的技术则能够产生和探索更宽的空气循环,以满足既定的制约条件;统计结果显示,经过重建的空气 foil是准确和顺畅的,没有额外的过滤器;软限制办法倾向于高效和有效地合成和探索空气流油,侧重于在几何空间和客观空间的参考空气流。由于该模型的固有特性,这些限制将略为松动。