Airfoil parameterization method based on latent diffusion model

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 Transformation (CST), Autoencoder (AE), and Denoising Diffusion Implicit Model (DDIM). The geometric quality of the airfoils generated by the proposed method is analyzed. Then, the effect of different latent dimensions on the distribution of the samples is examined. Next, the fitting accuracy and the representational capability of LDM is compared with those of 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 the 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, the LDM demonstrates faster convergence and shorter optimization time. The optimized airfoil exhibits better aerodynamic performance and a more stable optimization process. 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.