A Manifold-Based Airfoil Geometric-Feature Extraction and Discrepant Data Fusion Learning Method

The geometrical shape of airfoils and the corresponding flight conditions are crucial factors for aerodynamic coefficient prediction. The obtained geometric-features of airfoils in most existing approaches (e.g., geometrical parameter extraction, polynomial description, and deep learning) are in Euclidean space. State-of-the-art studies have shown that the curves or surfaces of an airfoil form a manifold in Riemannian space. Therefore, the features extracted by existing methods are not sufficient to reflect the geometric-features of airfoils. Meanwhile, flight conditions and geometric-features are greatly discrepant with different types. The discrepancy between these two factors must be considered and evaluated to improve the aerodynamic coefficient accuracy. Motivated by the advantages of manifold theory and multitask learning (MTL), we propose a manifold-based airfoil geometric-feature extraction and discrepant data fusion learning method (MDF) to extract geometric-features of airfoils in Riemannian space (we call them manifold-features) and further fuse the manifold-features with flight conditions to predict aerodynamic coefficients. Experimental results show that our method can extract geometric-features of airfoils more accurately than existing methods, that the average mean square error (MSE) of airfoils rebuilt based on geometric-features is reduced by 41.30%, and that while keeping the same prediction accuracy level for the lift coefficient $C_{L}$, the MSE of the drag coefficient $C_{D}$ predicted by MDF is further reduced by 54.56%.