Grassmannian Shape Representations for Aerodynamic Applications

Published

February 28, 2022

Author(s)

Olga Doronina, Zachary J. Grey, Andrew Glaws

Abstract

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.

Citation

ADAM AAAI 2022

Pub Weblink

https://openreview.net/forum?id=1RRU6ud9YC

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Keywords

Shape representation, Grassmannian, Principal Geodesic Analysis, data-driven deformations, blade representation

Citation

Doronina, O. , Grey, Z. and Glaws, A. (2022), Grassmannian Shape Representations for Aerodynamic Applications, ADAM AAAI 2022, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=933695, https://openreview.net/forum?id=1RRU6ud9YC (Accessed October 8, 2025)