用于翼型编码与合成的带几何约束的参数化生成方案
Parametric Generative Schemes with Geometric Constraints for Encoding and Synthesizing Airfoils
AI总结：
针对传统翼型参数化技术难以兼顾直观性、灵活性与精度的问题，本文提出软约束（CVAE直接训练约束）和硬约束（VAE生成加FFD投影）两种深度学习生成方案，后者在严格满足约束的同时兼具多样性，可提升优化设计效率。
摘要：
现代气动优化对具备高度直观性、灵活性和表征精度的参数化方法有强烈需求，而传统翼型参数化技术无法完全满足这一需求。本文提出两种基于深度学习的生成方案，可在满足特定约束的同时有效捕捉设计空间的复杂性。1. 软约束方案：一种基于条件变分自编码器（Conditional Variational Autoencoder, CVAE）的模型，将几何约束直接作为网络的一部分进行训练。2. 硬约束方案：一种基于变分自编码器（VAE）的模型用于生成多样化翼型，同时采用基于自由变形（FFD）的技术将生成的翼型投影到给定约束上。统计结果显示，重建的翼型既准确又平滑，无需额外滤波器。软约束方案生成的翼型与预期几何约束存在微小偏差，但仍能在几何空间和目标空间中收敛至参考翼型，不过存在一定程度的分布偏差。相比之下，硬约束方案生成的翼型具有更广泛的几何多样性，同时严格遵循几何约束。其在目标空间中的对应分布也更加多样，在参考点周围呈各向同性均匀分布，无显著偏差。这些提出的翼型参数化方法能够突破目标空间中训练数据的边界，为随机采样提供更高质量的样本，并提升优化设计的效率。
英文摘要：
The modern aerodynamic optimization has a strong demand for parametric methods with high levels of intuitiveness, flexibility, and representative accuracy, which cannot be fully achieved through traditional airfoil parametric techniques. In this paper, two deep learning-based generative schemes are proposed to effectively capture the complexity of the design space while satisfying specific constraints. 1. Soft-constrained scheme: a Conditional Variational Autoencoder (CVAE)-based model to train geometric constraints as part of the network directly. 2. Hard-constrained scheme: a VAE-based model to generate diverse airfoils and an FFD-based technique to project the generated airfoils onto the given constraints. According to the statistical results, the reconstructed airfoils are both accurate and smooth, without any need for additional filters. The soft-constrained scheme generates airfoils that exhibit slight deviations from the expected geometric constraints, yet still converge to the reference airfoil in both geometry space and objective space with some degree of distribution bias. In contrast, the hard-constrained scheme produces airfoils with a wider range of geometric diversity while strictly adhering to the geometric constraints. The corresponding distribution in the objective space is also more diverse, with isotropic uniformity around the reference point and no significant bias. These proposed airfoil parametric methods can break through the boundaries of training data in the objective space, providing higher quality samples for random sampling and improving the efficiency of optimization design.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
