Restricted snakes volume of solid (RSVS): A parameterisation method for topology optimisation of external aerodynamics

Payot, Alexandre D.; Rendall, Thomas; Allen, Christian B

doi:10.1016/j.compfluid.2019.02.008

Cited by 10 publications

(5 citation statements)

References 51 publications

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“…This test case, the drag minimisation of a fixed-area biplane profile at Mach 2.0, originally derives from a result presented by Busemann at the 5th Volta conference on high speed flows [44] showing that wave drag can be cancelled using a biplane configuration. More recently, this test problem has been applied uniquely to the investigation of aerodynamic topology optimisation [28,45] where the number of aerodynamic bodies and the presence of discrete features are represented in a unified parameterisation. Formally, the case is defined as minimising the inviscid drag at Mach 2.00 and 0 degree incidence subject to the constraint on total internal volume:…”

Section: A Test Case 1: Viscous Aerofoil Drag Reductionmentioning

confidence: 99%

Generic Modal Design Variables for Efficient Aerodynamic Optimization

et al. 2023

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Orthogonal modes are an effective method for aerodynamic shape optimization due to their excellent design space compactness; however, all existing methods are generated from a database of representative geometry. Moreover, application to high-fidelity design spaces is not possible because high-frequency shape components are insufficiently bounded, leading to nonsmooth and oscillatory geometries. In this work, a new generic methodology for generating orthogonal shape modes is presented based on a purely geometric derivation, eliminating the need for geometric training data. The new method is a further development of the gradient-limiting method developed previously for constraining the design space in a geometrically meaningful way to reduce the effective degrees of freedom and improve optimization convergence rate and final result. Here, the gradient-limiting methodology is reformulated by transforming the constraints directly onto design variables to produce orthogonal shape modes with equivalent constraints for ensuring smooth and valid iterates. The new generic methodology requires no training data, can be applied to arbitrary topologies using different boundary conditions, and naturally includes translational modes as part of the orthogonal basis. When applied to two standard aerodynamic test cases, the new method has superior performance compared to library-derived modes. Importantly, the optimization convergence rate is independent of the number of design variables, and the optimized objective at high design fidelities is greatly improved by avoiding local minima corresponding to spurious geometries. A nonstandard test case is demonstrated, for which traditional library modes are not useable due to nontrivial topology, and it is shown to benefit from the high-fidelity design space and translational mode made possible with the novel methodology.

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Section: A Test Case 1: Viscous Aerofoil Drag Reductionmentioning

confidence: 99%

Generic Modal Design Variables for Efficient Aerodynamic Optimization

et al. 2023

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“…B-spline surfaces [20] Bezier surfaces [21] Volume splines: Bezier [22], B-spline [23], NURBS [3], Radial basis function [24] Hicks-Henne [25] CSTs [26] Fictitious loads [27] Singular value decomposition [28] Partial differential equation [29] Volume of solid active contour [30,31] Multilevel optimization Successive optimizations are performed where shape control is refined after each stage. Subdivision [32,33] B-spline/Bezier knot insertion [34] Radial basis function [35] Sensitivity filtering Mesh vertices are used for shape control, and surface sensitivities are filtered to remove high-frequency components.…”

Section: Shape Parameterizationmentioning

confidence: 99%

“…For example, the partial differential equation (PDE) approach by Bloor and Wilson [29] solves a fourth-order PDE where the boundary conditions are defined by the design variables. More recently, the restricted snake volume of solid method of Payot et al [30,31] defines shapes as the minimal surface enclosing specified volume fractions on a background grid. In this approach the volume fractions of the background grid cells are the design variables that, in combination with the restricted snakes active contour method, are able to produce shapes of arbitrary topology.…”

Section: Shape Parameterizationmentioning

confidence: 99%

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimization

2020

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Local shape control methods, such as B-spline surfaces, are well-conditioned such that they allow high-fidelity design optimization; however, this comes at the cost of degraded optimization convergence rate as control fidelity is refined due to the resulting exponential increase in the size of the design space. Moreover, optimizations in higherfidelity design spaces become ill-posed due to high-frequency shape components being insufficiently bounded; this can lead to nonsmooth and oscillatory geometries that are invalid in both physicality (shape) and discretization (mesh). This issue is addressed here by developing a geometrically meaningful constraint to reduce the effective degrees of freedom and improve the design space, thereby improving optimization convergence rate and final result. A new approach to shape control is presented using coordinate control (x;z) to recover shape-relevant displacements and surface gradient constraints to ensure smooth and valid iterates. The new formulation transforms constraints directly onto design variables, and these bound the out-of-plane variations to ensure smooth shapes as well as the in-plane variations for mesh validity. Shape gradient constraints approximating a C 2 continuity condition are derived and demonstrated on a challenging test case: inviscid transonic drag minimization of a symmetric NACA0012 airfoil. Significantly, the regularized shape problem is shown to have an optimization convergence rate independent of both shape control fidelity and numerical mesh resolution, while still making use of increased control fidelity to achieve improved results. Consequently, a value of 1.6 drag counts is achieved on the test case, the lowest value achieved by any method.

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“…Continuous shape functions are used to describe geometry such that the number of design variables is much less than the number of mesh nodes B-Spline surfaces [20] Bezier surfaces [21] Volume splines: Bezier [22], B-Spline [23], NURBS [3], RBF[24] Hicks-Henne [25] CSTs [26] Fictitious loads [27] SVD [28] Partial differential equation [29] Volume of solid active contour [30,31] Multilevel optimisation Successive optimisations are performed where shape control is refined after each stage Subdivision [32,33] B-Spline/Bezier knot insertion [34] RBF [35] Sensitivity filtering Mesh vertices are used for shape control and surface sensitivities are filtered to remove high frequency components…”

Section: Shape Parameterisationmentioning

confidence: 99%

“…For example, the partial differential equation (PDE) approach by Bloor and Wilson [29] solves a fourth-order PDE where the boundary conditions are defined by the design variables. More recently, the restricted snake volume of solid (RSVS) method of Payot et al [30,31] defines shapes as the minimal surface enclosing specified volume fractions on a background grid. In this approach the volume fractions of the background grid cells are the design variables which, in combination with the restricted snakes active contour method, are able to produce shapes of arbitrary topology.…”

Section: Shape Parameterisationmentioning

confidence: 99%

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimisation

Kedward

Allen

Rendall

2018

2018 Applied Aerodynamics Conference

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Local shape control methods, such as B-Spline surfaces, are well-conditioned such that they allow high-fidelity design optimisation, however this comes at the cost of degraded optimisation convergence rate as control fidelity is refined due to the resulting exponential increase in the size of the design space. Moreover, optimisations in higher-fidelity design spaces become illposed due to high frequency shape components being insufficiently bounded; this can lead to non-smooth and oscillatory geometries that are invalid both in physicality (shape) and discretisation (mesh). This issue is addressed here by developing a geometrically-meaningful constraint to reduce the effective degrees of freedom and improve the design space thereby improving optimisation convergence rate and final result. A new approach to shape control is presented using coordinate control (x, z) to recover shape-relevant displacements and surface gradient constraints to ensure smooth and valid iterates. The new formulation transforms constraints directly onto design variables, and these bound the out-of-plane variations to ensure smooth shapes as well as the in-plane variations for mesh validity. Shape gradient constraints approximating a C 2 continuity condition are derived and demonstrated on a challenging test case: inviscid transonic drag minimisation of a symmetric NACA0012 aerofoil. Significantly the regularised shape problem is shown to have an optimisation convergence rate independent of both shape control fidelity and numerical mesh resolution, while still making use of increased control fidelity to achieve improved results. Consequently, a value of 1.6 drag counts is achieved on the test case, the lowest value achieved by any method.

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Restricted snakes volume of solid (RSVS): A parameterisation method for topology optimisation of external aerodynamics

Cited by 10 publications

References 51 publications

Generic Modal Design Variables for Efficient Aerodynamic Optimization

Generic Modal Design Variables for Efficient Aerodynamic Optimization

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimization

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimisation

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