Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization

Abstract

When carrying out design searches, traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables. This is particularly true when only a small number of simulations are combined with a parameterization that results in a large number of variables of seemingly equal importance. Here, the authors present a variable reduction technique that employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process. Unlike traditional screening techniques, the presented method operates at the geometric level instead of the variable level. The filtering process uses the designs that result from a geometry parameterization instead of the variables that control the parameterization. The method is shown to perform well in the optimization of a two-dimensional airfoil for the minimization of drag-to-lift ratio, producing designs better than those resulting from traditional krigingbased surrogate model optimization and with a significant reduction in surrogate tuning cost.

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

“…New aerofoil shapes can then be constructed as a linear combination of these modes where the fidelity of the construction is determined by the number of modes used. This technique was first employed by Toal et al [34] then by Ghoman et al [35] and Poole et al [36]. Ghoman et al [35] used a series of supercritical aerofoils to derive the modes and showed that other supercritical aerofoils could efficiently be reconstructed.…”

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

“…Consequently the choice of shape parameterisation method can have a significant impact on the effectiveness and efficiency of the overall procedure [3]. Many different methods have been used within an aerodynamic optimisation framework, from standard geometric curve definitions such as B-Splines [4] or NURBS [5] to aerospace-specific methods such as CST [6,7], Hicks-Henne bump functions [8,9] or PARSEC [9,10] to Free-Form Deformation [11,12,13,14], proper orthogonal decomposition [2,15,16] or the discrete method [17]. A whole variety of options are available, however all are subject to the 'curse of dimensionality'.…”

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

“…Consequently the choice of shape parameterisation method can have a significant impact on the effectiveness and efficiency of the overall procedure 3 . Many different methods have been used within an aerodynamic optimisation framework, from standard geometric curve definitions such as B-splines 4 or NURBS 5 to aerospace-specific methods such as CST 6,7 , HicksHenne bump functions 8,9 or PARSEC 9,10 to Free-Form Deformation [11][12][13][14] , proper orthogonal decomposition 2,15,16 or the discrete method 17 . All of these approaches are subject to the 'curse of dimensionality'; in the context of aerodynamic optimisation this refers to the problems associated with increasing the number of design variables used in the optimisation procedure.…”