An airfoil geometric-feature extraction and discrepant data fusion learning method

The perception of geometric-features of airfoils is the basis in aerodynamic area for performance prediction, parameterization, aircraft inverse design, etc. There are three approaches to percept the geometric shape of airfoils, namely manual design of airfoil geometry parameters, polynomial definition and deep learning. The first two methods directly define geometric-features or polynomials of airfoil curves, but the number of extracted features is limited. Deep learning algorithms can extract a large number of potential features (called latent features). However, the features extracted by deep learning lack explicit geometrical meaning. Motivated by the advantages of polynomial definition and deep learning, we propose a geometric-feature extraction method (named Bézier-based feature extraction, BFE) for airfoils, which consists of two parts: manifold metric feature extraction and geometric-feature fusion encoder (GF encoder). Manifold metric feature extraction, with the help of the Bézier curve, captures manifold metrics (a sort of geometric-features) from tangent space of airfoil curves, and the GF-encoder combines airfoil coordinate data and manifold metrics together to form novel fused geometric-features. To validate the feasibility of the fused geometric-features, two experiments based on the public UIUC airfoil dataset are conducted. Experiment I is used to extract manifold metrics of airfoils and export the fused geometric-features. Experiment II, based on the Multi-task learning (MTL), is used to fuse the discrepant data (i.e., the fused geometric-features and the flight conditions) to predict the aerodynamic performance of airfoils. The results show that the BFE can generate more smooth and realistic airfoils than Auto-Encoder, and the fused geometric-features extracted by BFE can be used to reduce the prediction errors of C L and C D .