摘 要：为缓解气动外形优化设计中的“维数灾难”问题，提高参数化方法的表示能力和气动优化效率，本文基于类别/形状函数变换方法(CST)、自编码器(AE)以及去噪扩散隐式模型(DDIM)，提出了一种基于潜在扩散模型的翼型参数化方法(Latent Diffusion Model, LDM)。随后，分析了该方法生成翼型样本的几何质量，研究了该方法不同潜在维度对样本分布的影响，对比了该方法与CST-AE、PCA、FFD、CST四种参数化方法的翼型拟合精度和表示能力，并开展翼型气动优化设计以验证其性能。结果表明，LDM方法可以生成光滑、有效的翼型样本，与其他参数化方法相比，该方法对翼型具有较精确的描述能力与较强的表示能力。此外，该方法在翼型气动优化过程中具有较快的收敛速度与较短的优化耗时，优化结果较好且优化过程更为稳定。未来，该方法具有拓展至翼段、短舱、风扇等复杂外形气动优化设计过程的潜力。

Abstract: To alleviate the curse of dimensionality problem in aerodynamic shape optimization and improve the representation capability as well as optimization efficiency of parameterization method, this paper proposes a new airfoil parameterization method named Latent Diffusion Model(LDM), which combines Class Shape Transfor-mation(CST), Autoencoder (AE), and Denoising Diffusion Implicit Model (DDIM). The geometric quality of the air-foils generated by the proposed method is first analyzed. Then, the effect of different latent dimensions on the dis-tribution of the samples is examined. Next, the fitting accuracy along with the representational capability of LDM is compared with four different parameterization methods: CST-AE, Principal Component Analysis(PCA), Free Form Deformation(FFD), and CST. Finally, airfoil aerodynamic optimization is conducted to verify the performance of the LDM method. The results show that LDM can generate smooth and acceptable airfoil samples. Compared with other parameterization methods, this method offers a more accurate description and stronger representation capability for airfoils. Additionally, LDM demonstrates faster convergence and shorter optimization times. The opti-mized airfoils exhibits better aerodynamic performance and a more stable optimization processes. In the future, this method has the potential to be extended to aerodynamic optimization for more complex shapes, such as wing segments, nacelles and fans.