A geometry-based deep learning feature extraction method for airfoils

Abstract

The geometry of airfoils, crucial in predicting aerodynamic coefficients, can be perceived by three existing methods: manual definition of geometry parameters, polynomial and deep learning. The first two methods are capable of directly obtaining geometry-features or polynomial coefficients from airfoil coordinates, but they are insufficient to extract latent features. Current deep learning techniques are capable of extracting latent features from only Euclidean space. However, it has been proven that curves of airfoils are exists in Riemannian space. Inspired by deep learning and polynomial (especially the Bézier polynomial) and deep learning, we propose a Geometry-based Feature Extraction method (GFE) to extract airfoil geometry-features from both Euclidean space and Riemannian space. By utilizing Bézier curve, GFE can extract geometry-features (i.e., manifold metrics) of airfoils in Riemannian space. Through an internal auto-encoder, GFE encodes airfoil coordinates and manifold metrics to generate a novel feature representation. The UIUC airfoil dataset is employed to test the feasibility of GFE. Experimental results show that smooth and realistic airfoils can be rebuilt based on the geometry-features extracted by GFE, and the average MSE of rebuilt airfoils is 38.66% lower than those rebuilt by existing auto-encoders.