Optimized Nonuniform Rational B-Spline Geometrical Representation for Aerodynamic Design of Wings

Lepine, Jerome; Guibault, François; Trépanier, Jean‐Yves; Pépin, François

doi:10.2514/2.1206

Cited by 81 publications

(8 citation statements)

References 15 publications

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“…Common parameterization for aerodynamic shapes includes splines (e.g., B-spline and Bézier curves) [47][48][49], free-form deformation (FFD) [25,26], class-shape transformations (CST) [50,51], PARSEC [52,53], and Bézier-PARSEC [54].…”

Section: B Shape Parameterizationmentioning

confidence: 99%

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Airfoil Design Parameterization and Optimization using Bézier Generative Adversarial Networks

Chen¹,

Chiu²,

Fuge³

2020

Preprint

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Global optimization of aerodynamic shapes usually requires a large number of expensive computational fluid dynamics simulations because of the high dimensionality of the design space. One approach to combat this problem is to reduce the design space dimension by obtaining a new representation. This requires a parametric function that compactly and sufficiently describes useful variation in shapes. We propose a deep generative model, Bézier-GAN, to parameterize aerodynamic designs by learning from shape variations in an existing database. The resulted new parameterization can accelerate design optimization convergence by improving the representation compactness while maintaining sufficient representation capacity. We use the airfoil design as an example to demonstrate the idea and analyze Bézier-GAN's representation capacity and compactness. Results show that Bézier-GAN both (1) learns smooth

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Section: B Shape Parameterizationmentioning

confidence: 99%

“…Specifically, we interpolate 192 points over each airfoil with the concentration of these points along the B-spline curve based on the curvature [47]. The preprocessed data are visualized at the top of Fig.…”

Section: A Dataset and Preprocessingmentioning

confidence: 99%

Airfoil Design Parameterization and Optimization using Bézier Generative Adversarial Networks

Chen¹,

Chiu²,

Fuge³

2020

Preprint

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“…Both the upper and lower surfaces are represented as separate NURBS curves that have been optimized to fit the original airfoil as per the method of Lépine et al [31]. The NURBS curves, control polygon, and original airfoil are presented in Fig.…”

Section: A Nonuniform Rational B-splines-based Parameterizationmentioning

confidence: 99%

Efficient Multipoint Aerodynamic Design Optimization Via Cokriging

Toal

Keane

2011

Journal of Aircraft

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Multipoint objective functions are often employed within aerodynamic optimizations to prevent a reduction in offdesign performance. However, this typically results in the need for a significant number of simulations at a variety of design conditions to calculate the objective function. The following paper attempts to address this problem through the application of a multilevel cokriging model within the optimization process. A large number of single-point design simulations are augmented by a smaller number of multipoint simulations. The technique is shown to result in surrogate models as effective as those produced using a traditional multipoint process when optimizing a transonic airfoil but with a reduction in the total number of simulations.between expensive and cheap data K = total number of design conditions n = total number of sample points p = hyperparameter governing smoothness R = correlation matrix r = correlations between known and unknown points w = design point weighting X = matrix of design points x = vector of design variables y = vector of objective function values Zx = Gaussian process = hyperparameter governing correlation = regression constant = mean = scaling parameter 2 = variance = concentrated log likelihood Subscripts c = cheap data d = difference between cheap and expensive data e = expensive data

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“…not too close to the leading and the trailing edge (since it clearly leads to an unrealistic wing section). The angle of incidence can also be taken as a fourth design parameter, and will be studied in the next cases, since it influences the aerodynamic performance of the airfoils (Lépine et al, 2001). In the present case, the angle of attack is fixed because its influence dominates that of the other parameters (e, m and p).…”

Section: Drag and Lift Matchingmentioning

confidence: 99%

The sensitivity equation method in fluid mechanics

Pelletier

Hay

Étienne

et al. 2008

TECM

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We present the sensitivity Equation Method (SEM) as a complementary tool to adjoint based optimisation methods. Flow sensitivities exist independently of a design problem and can be used in several non-optimization ways: characterization of complex flows, fast evaluation of flows on nearby geometries, and input data uncertainties cascade through the CFD code to yield uncertainty estimates of the flow field. The Navier-Stokes and sensitivity equationssensitivity are solved by an adaptive finite element method.

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Optimized Nonuniform Rational B-Spline Geometrical Representation for Aerodynamic Design of Wings

Cited by 81 publications

References 15 publications

Airfoil Design Parameterization and Optimization using Bézier Generative Adversarial Networks

Airfoil Design Parameterization and Optimization using Bézier Generative Adversarial Networks

Efficient Multipoint Aerodynamic Design Optimization Via Cokriging

The sensitivity equation method in fluid mechanics

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