An Evolutionary Geometry Parametrization for Aerodynamic Shape Optimization

Han, Xiaocong; Zingg, David W.

doi:10.2514/6.2011-3536

Cited by 6 publications

(8 citation statements)

References 33 publications

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“…Recently, adaptive or refinement-based parametrization have been developed to improve the efficiency of shape optimization algorithms [30,31,32,33]. Zingg et al [34] show that gradient-based optimization is more efficient than gradient-free optimization in aerodynamics.…”

Section: Sole Design Frameworkmentioning

confidence: 99%

Design of optimized soft soles for humanoid robots

Magistris

Miossec

Escande

et al. 2017

Robotics and Autonomous Systems

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We describe a methodology to design foot soles for a humanoid robot given walking gait parameters (i.e. given centerof-mass and zero-moment-point trajectories). In order to obtain an optimized compliant sole, we devised a shape optimization framework which takes -among other inputs, an initial rough (simplified) shape of the sole and refines it through successive optimization steps under additional constraints and a cost function. The shape is optimized based on the simulation of the sole deformation during an entire walking step, taking time dependent input of the walking pattern generator into account. Our shape optimization framework is able to minimize the impact of the foot with the ground during the heel-strike phase and to limit foot rotation in case of perturbations. Indeed, low foot rotation enforces a vertical posture and secures the balance of the humanoid robot. Moreover, weight restriction (formulated as a constraint on the sole volume) is added to our optimization problem.

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Section: Sole Design Frameworkmentioning

confidence: 99%

Design of optimized soft soles for humanoid robots

Magistris

Miossec

Escande

et al. 2017

Robotics and Autonomous Systems

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show abstract

“…uniformly spaced, averaged from independent parameters or by applying more complicated formulations. Han proposes a formula which ensures that B‐spline passes through the two edges of the trailing end and the leading edge (middle of vector sequence). In a cubic B‐spline, the resulting knot sequence method produces a triple knot in the leading edge area and thus the inconvenience of producing a discontinuity in B‐spline first derivative at the leading edge.…”

Section: Airfoil Variables Using B‐splinesmentioning

confidence: 99%

“…As it is a usual practice to employ around 13 control points, the considered candidates are 9, 11, 13, 15, 17 and 19. To be coherent with knot vector equation, the number of control points must be odd. They are named cp9, …,cp19 . Independent parameterization.…”

Section: Airfoil Variables Using B‐splinesmentioning

confidence: 99%

“…In contrast, few design variables may be insufficient to explore all the relevant candidate geometries. This problem has been specifically dealt with in aircraft wing design …”

Section: Introductionmentioning

confidence: 99%

“…Traditionally, piecewise polynomial B‐spline functions are a widely adopted solution to represent blade geometry . Non‐uniform rational B‐splines (NURBS) and particularly B‐splines provide a unified mathematical basis for representing shapes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global sensitivity analysis of the blade geometry variables on the wind turbine performance

2017

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The need for implementing efficient blade designs gains relevance as wind turbine developments require longer blades. The design of blade geometry, traditionally divided in 2D airfoils and spanwise distributions, is usually addressed as an optimization problem. A correct identification of the design variables is crucial to avoid unnecessary computational cost or insufficient exploration of the design space. This paper deals with the identification of the design variables that affect the wind turbine performance.First, the number of design variables for an accurate airfoil representation is resolved. A methodology, based on statistical hypothesis testing applied to the airfoil approximation errors, is presented to assess the accuracy of types of B-splines.Second, the study is extended to chord and twist distributions besides airfoil geometry with the purpose of assessing the sensitive blade variables in the wind turbine performance. Global sensitivity analysis as multi-variable linear regressions and variance-based methods are used. Latin hypercube sampling is applied to generate efficient inputs. MATLAB-based code is developed to obtain outputs: annual energy production, maximum blade tip deflection, overall sound power level and blade mass.As result of the study, a list of non-affecting variables is deduced. These variables can be avoided in the optimization without loss of gain in the performance. The method is a powerful tool to analyse in a preliminary phase a design problem involving a high amount of variables and complex physical relations by means of combining different multi-disciplinar calculation codes and performing statistical treatments.

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A Dynamic Parametrization Scheme for Shape Optimization Using Quasi-Newton Methods

Hwang

Martins

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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A variable parametrization scheme is developed and demonstrated for shape optimization using quasi-Newton methods. The scheme performs adaptive parametrization refinement while preserving the approximate Hessian of the shape optimization problem and enables free-form shape design using quasi-Newton optimization methods. Using a Bspline parametrization, the scheme is validated using a 1-D shape approximation problem and is shown to improve efficiency and optimal solution quality compared to the traditional quasi-Newton method. The scheme is also applied to a 3-D test problem, demonstrating the feasibility of free-form shape optimization using parametrization refinement and a method for partially constraining the degrees of freedom.

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An Evolutionary Geometry Parametrization for Aerodynamic Shape Optimization

Cited by 6 publications

References 33 publications

Design of optimized soft soles for humanoid robots

Design of optimized soft soles for humanoid robots

Global sensitivity analysis of the blade geometry variables on the wind turbine performance

A Dynamic Parametrization Scheme for Shape Optimization Using Quasi-Newton Methods

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