Multi-level gradient-based methods and parametrisation in aerodynamic shape design

Martinelli, Massimiliano; Beux, F.

doi:10.3166/remn.17.169-197

Cited by 7 publications

(7 citation statements)

References 34 publications

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“…This approach is akin to a multi-grid method for parameterisation and was first used in an aerodynamic optimisation setting by Beux and Dervieux [18]. It has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [19,20,21,22], Bèzier surface FFD [23,24,25,26], RBFs [27] and B-Splines with a knot insertion algorithm [28,29]. In general, they have shown that implementation of progressive nested parameterisations can improve the convergence rate, robustness and final solution of an optimisation procedure.…”

Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Department of Aerospace Engineering, University of BristolThis work presents a shape parameterisation method based on multi-resolutional subdivision curves and investigates its application to aerodynamic optimisation. Subdivision curves are defined as the limit curve of a recursive application of a subdivision rule, which provides an intrinsically hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This is used to construct a progressive aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then periodically increased in resolution through the optimisation. This brings the benefits of a low dimensional design space (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the progressive refinement technique is tested on a variety of optimisation problems. For each problem a range of 'static' (non-progressive) subdivision schemes (equivalent to cubic B-splines) are also used as a control group. For all the optimisation cases the progressive schemes perform comparably or better than the static methods, often providing a significant computational advantage, and in many cases allowing a solution to be found when the static method would otherwise finish prematurely in a local optimum.

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Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

show abstract

“…This approach was first used in an aerodynamic optimisation setting by Beux and Dervieux 18 and has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [19][20][21][22] , Bèzier surface FFD [23][24][25][26] , RBFs 27 and B-splines with a knot insertion algorithm 28,29 . In general, it was shown that implementation of multi-level nested parameterisations can improve the convergence rate, robustness and final solution of an optimisation procedure.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Masters

Taylor²,

Rendall

et al. 2017

AIAA Journal

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Subdivision curves are defined as the limit of a recursive application of a subdivision rule to an initial set of control points. This intrinsically provides a hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This work presents a shape parameterisation method based on this principle and investigates its application to aerodynamic optimisation. The subdivision curves are used to construct a multi-level aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then be periodically increased in resolution throughout. This brings the benefits of a low fidelity optimisation (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the multi-level subdivision parameterisation is tested on a variety of optimisation problems and compared to a control group of single-level subdivision schemes. For all the optimisation cases the multi-level schemes provided robust and reliable results in contrast to the single-level methods that often experienced difficulties with large numbers of design variables. As a result of this the multi-level methods exploited the high-dimensional design spaces better and consequently produced better overall results.

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“…increasing the number of design variables) occurs at regular intervals during the optimization process, but it is hard to identify a clear signal for this procedure. Some authors 1,3 argue that when the number of design variables is small, a small number of optimization iterations is enough and full convergence is unnecessary, since these optimization cycles are only intermediate steps. However others 32,33 point out that the optimizations at the first few cycles should be driven sufficiently close to the optimal shape that the current shape can provide a good start for subsequent optimizations.…”

Section: Optimization Proceduresmentioning

confidence: 99%

“…One well recognized problem in aerodynamic shape optimization is attributed to an excessive number of design variables. A number of authors [1][2][3] have pointed out that the presence of a large number of design variables results in poor performance for most existing optimization algorithms. Thus, it is essential to include a limited number of critical design variables in an optimization, and the challenge of choosing design variables is faced by a designer.…”

Section: Introductionmentioning

confidence: 99%

An Evolutionary Geometry Parametrization for Aerodynamic Shape Optimization

Han

Zingg

2011

20th AIAA Computational Fluid Dynamics Conference

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An evolutionary geometry parametrization is presented for aerodynamic shape optimization. The geometry parametrization technique is constructed by integrating the traditional B-spline approach with a knot insertion procedure. It is capable of defining a sequence of nested parametrizations with the number of design variables being gradually enlarged. The optimization coupled with this technique is carried out sequentially from the basic parametrization to more refined parametrizations, as long as the geometry can be continuously improved. Due to the nature of the B-spline formulation, feasible parametrization refinements are not unique. Guidelines based on sensitivity analysis and geometric constraints are developed to assist the automation. The proposed process is applied to several optimization examples to demonstrate its effectiveness.

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Multi-level gradient-based methods and parametrisation in aerodynamic shape design

Abstract: ABSTRACT. The present study focuses on multi-level approaches in the context

Cited by 7 publications

References 34 publications

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

An Evolutionary Geometry Parametrization for Aerodynamic Shape Optimization

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