Generating various airfoils with required lift coefficients by combining NACA and Joukowski airfoils using conditional variational autoencoders

Abstract

The aim of inverse design problem in mechanical design is to obtain shapes that satisfy the required design specifications. It is also desired to obtain varieties of shapes, but finding multiple shapes in a short computation time is difficult using the conventional methods. This paper proposes the use of the conditional variational autoencoders (CVAE) with normal distribution, denoted by N-CVAE, along with the von Mises–Fischer distribution, denoted by S-CVAE, to find multiple solutions for the inverse design problems. Both the CVAE models embed shapes into a latent space. The S-CVAE enables the separation of data in the latent space, whereas the N-CVAE embeds the data in a narrow space. These different features are used for various tasks in this study. In the first task, the dataset consists of only one type of data. Here, S-CVAE outperforms N-CVAE because it can easily separate the data. In the second task, the dataset consists of two different types of airfoils. It is desired to combine two types and to generate new types of data. N-CVAE is useful in this task since it embeds different shapes in the same latent area, due to which, the model outputs intermediate shapes of different types. The shape-generation capability of S-CVAE and N-CVAE are experimentally compared in this study.