用于空气动力学的格拉斯曼形状表示法
Grassmannian Shape Representations for Aerodynamic Applications
摘要：
翼型设计是工程和制造中的经典问题。我们的动机是将基于物理学原理的形状设计问题的考虑与数据驱动方法所告知的现代计算技术相结合。翼型形状的传统分析强调基于流动的变形敏感性，其通常可以通过仿射变换（旋转、缩放、剪切、平移）来表示。我们提出了一种新的表示的形状，从一组丰富的数据驱动的变形的格拉斯曼子流形的仿射风格的变形。Grassmannian表示法由物理相关翼型的数据库提供信息，提供（i）一组丰富的新的2D翼型变形，这些变形以前未在数据中捕获，（ii）改进的低维参数域，用于通知设计/制造的推理统计，以及（iii）一致的3D叶片表示法和标称形状序列上的扰动。
英文摘要：
Airfoil shape design is a classical problem in engineering and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, translation). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.
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