论文标题
空气动力应用的硕士形状表示
Grassmannian Shape Representations for Aerodynamic Applications
论文作者
论文摘要
机翼形状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的原则性考虑对形状设计问题的考虑与以数据驱动方法告知的现代计算技术相结合。对机翼形状的传统分析强调了对变形的基于流动的敏感性，该敏感性通常由仿射转换（旋转，缩放，剪切，翻译）表示。我们提出了形状的新颖表现形式，该形状将仿生式变形与格拉斯曼尼亚的子曼群上的一系列数据驱动的变形相结合。 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.
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.
