Influence of Shape Parameterization on a Benchmark Aerodynamic Optimization Problem

Masters, Dominic; Poole, Daniel J; Taylor, Nigel J.; Rendall, Thomas; Allen, Christian B

doi:10.2514/1.c034006

Cited by 29 publications

(36 citation statements)

References 24 publications

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“…This advantage was emphasised by Braibant and Fleury when advocating the use of B-Splines for shape optimisation [5]. However the reduction in dimensionality inevitably corresponds to a reduction in the available design space and therefore attainable optimum; as such, the choice of parameterisation fidelity becomes important and this is investigated extensively by Masters et al for several different parameterisation methods [25,26]. High fidelity parameterisations often exhibit poor optimisation performance due to degraded design space conditioning or the generation of non-smooth shapes [26][27][28] as shape control locality approaches that of mesh-point control.…”

Section: Shape Parameterisationmentioning

confidence: 99%

“…The poor performance of B-Splines at high fidelity matches that observed by Reuther and Jameson [27] and again by Castonguay et al [28] who subsequently showed that this effect is eliminated when used with sensitivity filtering. Masters et al [26] found that increasing the order of B-Splines, which increases the support and smoothness of the basis, was also able to alleviate some of the convergence issues.…”

Section: A Motivationmentioning

confidence: 99%

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Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Kedward

Allen

Rendall

2019

AIAA Scitech 2019 Forum

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Without addressing shape smoothness, gradient-based optimisation methods naturally amplify high-frequency shape components which can lead to poor convergence of the optimisation problem and a convergence rate exhibiting dependency on the fidelity of shape-control. Recent work by the authors demonstrated that this problem arises due to the discrete shape problem being ill-posed by naturally including geometries that are invalid both in physicality (shape) and discretisation (mesh), and a new shape control methodology has been developed which addresses this explicitly. The new approach uses two-dimensional control to recover shaperelevant displacements and surface gradient constraints to ensure smooth and valid iterates. The shape gradient constraints, approximating a C 2 continuity condition, are derived for two local shape control methods: discrete grid point control and cubic B-Splines. The local control methods provide high-fidelity control whereas the surface constraints exclude non-physical shapes from the design space making the shape problem well-posed. As a result, high-fidelity shape optimisation is possible at a reasonable computational cost. In this paper, further results are presented for the aerodynamic optimisation of two standard test cases defined by the AIAA aerodynamic design optimisation discussion group. A value of 7 drag counts is achieved on the inviscid case and 66 drag counts on the viscous case; to the authors' knowledge these are the lowest results published for either case.

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Section: Shape Parameterisationmentioning

confidence: 99%

Section: A Motivationmentioning

confidence: 99%

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Kedward

Allen

Rendall

2019

AIAA Scitech 2019 Forum

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show abstract

“…So, Kulfan (9) proposed the leading-edge modification (LEM) to the CST method. Though the LEM CST method adds a control parameter in comparison with the original CST method, it improves the geometric accuracy for aerofoils and also reduces the order of the Bernstein polynomial (3,17) . Five properties including completeness, orthogonality, flawlessness, economy and intuitiveness (2,18) are specified to evaluate the merits and demerits of the aerofoil parameterisation.…”

Section: Combination Of Cst and Hicks-henne Bump Functionmentioning

confidence: 99%

Improved aerofoil parameterisation based on class/shape function transformation

Liu

2019

Aeronaut. j.

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A new aerofoil parameterisation method is put forward to represent an aerofoil by combining the leading edge modification class/shape function transformation (LEM CST) method and improved Hicks–Henne bump function’s method. The new class/shape function transformation (NEW CST) method has two additional basis functions comparing the original CST method. In order to confirm these two basis functions, the radial basis functions neural network (RBF) model is trained by some samples which are generated by the Latin hypercube design (LHD) method and Genetic Algorithm (GA) is proposed to achieve the basis functions of the NEW CST method. The NEW CST method has been evaluated in fitting precision of 1,545 aerofoils by comparison with the LEM CST method and the original CST method. And the improved ability of the NEW CST at the leading edge and trailing edge is verified by a series of complex aerofoil case studies within 1,545 aerofoils. The results indicate that the NEW CST method can represent the whole aerofoils and possesses the intuitive property as well as the original CST. Moreover, the number of control parameters (NCP) to parameterise aerofoils is the fewest among these three methods. Furthermore, when the NCP of the NEW CST and LEM CST is the same, the NEW CST method has the higher accuracy and smaller root mean square errors (RMSE) especially at the leading edge and trailing edge.

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“…Constrained smooth mesh-point movement can also be used to control the evolution of the geometry [42]. Many of these parameterisation are directly compared inside a single ASO framework, in geometric and aerodynamic terms, in [43] and [44] respectively. Conventional parameterisation methods in ASO are only capable of shape parameterisation.…”

Section: Aerodynamic Shape Optimisationmentioning

confidence: 99%

“…In ASO gradient based optimisation is most common, it offers fast and reliable convergence. SNOPT [46] is a widely used Sequential Quadratic Programming (SQP) code used in the ASO community [4,15,44,[47][48][49]. The adjoint method, developed by Pironneau [50] and popularised in ASO by Jameson [51], was a major breakthrough in the field of optimisation.…”

Section: Aerodynamic Shape Optimisationmentioning

confidence: 99%

Structural Topology Optimisation with R-Snakes Volume of Solid

Taylor

Payot

Allen

et al. 2019

AIAA Scitech 2019 Forum

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A topologically flexible parameterisation method developed for aerodynamic optimisation is tested on a variety of 2 dimensional structural topology problems. The background to the restricted snakes volume of solid (RSVS) is explained. A topology optimisation framework is develloped using FreeFem++ as a linear elastic solver and differential evolution as the agent based optimiser. Validation of the analysis is presented as well as mesh convergence and impact studies. The work here is significant such that if a parameterisation method is capable of both aerodynamic and structural optimisation, the potential for multidisciplinary analysis arises. Structural topology optimisation of volume constrained agent-based optimisation, minimising deflection, has been run on four common benchmark cases; two short cantilever beams and two longer centrally loaded (MBB) beams. Results were compared to SIMP calculations made following using Sigmund's 99 line topology optimisation code [1]. RSVS solutions scored objective functions comparable to those found via SIMP in all cases with differences ranging from +40% to-5%. In the long run the combined capability of the RSVS in aerodynamics and structures offers the potential of the development of a general aero-structural topology optimisation framework using a single set of design variables.

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Influence of Shape Parameterization on a Benchmark Aerodynamic Optimization Problem

Cited by 29 publications

References 24 publications

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Improved aerofoil parameterisation based on class/shape function transformation

Structural Topology Optimisation with R-Snakes Volume of Solid

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