Multilevel Simulation and Numerical Optimization of Complex Engineering Designs

Schwabacher, Mark; Gelsey, Andrew

doi:10.2514/2.2336

Cited by 8 publications

(4 citation statements)

References 17 publications

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“…While the GBMS label was first coined by Chernukhin and Zingg, variations on this idea are present in the literature under a number of di↵erent names. [25][26][27][28][29] Chernukhin and Zingg developed specialized linear constraints which ensure the generated samples can be easily tailored to produce feasible geometries within the geometric bounds desired by the user. In our previous work 15 we expanded on this method, utilizing FFD geometry control to generalize these constraints to a geometry-independent form, producing an algorithm that can be applied to any geometry or class of problem.…”

Section: A Gradient-based Multistart Algorithmmentioning

confidence: 99%

Correction: A Parametric Study of Multimodality in Aerodynamic Shape Optimization of Wings

Streuber

Zingg

2018

2018 Multidisciplinary Analysis and Optimization Conference

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A parametric study of multimodality in wing optimization is undertaken utilizing a gradient-based multistart method. The lift-constrained drag minimization of a wing is performed using between 17 and 33 initial geometries in subsonic and transonic viscous flows with varying degrees of freedom and under a variety of constraints. In nearly every examined case, including the ADODG CRM case, multimodality of some degree is found. The cross-sectional optimization of a wing is found to be unimodal to somewhat multimodal in both subsonic and transonic flows, depending on which degrees of freedom are permitted. Permitting large-scale planform deformations and non-planar geometries is shown to produce clear and significant multimodality in all examined cases. Requiring straight leading and trailing edges can significantly reduce, but not fully eliminate, multimodality. Other examined constraints, such as linear taper, linear twist, minimum thickness, and minimum pitching moment are shown to have lesser e↵ects on multimodality. Multimodality is ultimately found to be an inherent characteristic of most wing optimization design spaces, and it is concluded that gradient-based optimization based on a single initial geometry may not be su cient to ensure global optimality even in tightly constrained practical problems.

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Section: A Gradient-based Multistart Algorithmmentioning

confidence: 99%

Correction: A Parametric Study of Multimodality in Aerodynamic Shape Optimization of Wings

Streuber

Zingg

2018

2018 Multidisciplinary Analysis and Optimization Conference

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“…While the GBMS label is relatively new, equivalent methods have been used in the literature under other names. [12][13][14][15][16] In many of these works attention is paid to the idea of the feasible region in the design space. "Feasible" in this context goes beyond the more common definition used in most optimization applications, that is, a design for which all constraints have been satisfied.…”

Section: A Gradient Based Multistart Algorithm -Basicsmentioning

confidence: 99%

Investigation of Multimodality in Aerodynamic Shape Optimization Based on the Reynolds Averaged Navier-Stokes Equations

Streuber

Zingg

2017

35th AIAA Applied Aerodynamics Conference

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This paper presents an improvement to a multi-start method for gradient based exploration of moderately multimodal design spaces in aerodynamic shape optimization problems. Free form deformation geometry control is used in conjunction with a gradient-based multistart algorithm to generalize cascading linear constraints for a sampler algorithm into a geometry-independent form. This permits large, high-quality, feasible samples of the design space to be generated and optimized quickly and e ciently. This algorithm is then used to explore multimodality in viscous aerodynamic shape optimization problems, including wings in transonic and subsonic flow, as well as a transonic blended wing-body design. Both wing cases are found to be multimodal, while the blended wing-body case is believed to be unimodal based on available evidence. A brief investigation of the e↵ect that three degrees of freedom -twist, taper, and sectional control -have on multimodality in the viscous optimization of the common research model wing is undertaken. This investigation finds little evidence of multimodality related to twist and section control, while the addition of taper design variables leads to clear indications of multimodality.

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“…On another hand, to deal with complex engineering design optimisation, different multi-level or multi-scale approaches, in which the whole problem is decomposed in several simpler sub-problems to be solved in a predetermined sequence, have been developed (see e.g. (Migdalas et al, 1997;Schwabacher et al, 1998)). Each optimisation sub-problem can differ according to objective function, constraints, design space and/or optimisation algorithm allowing a better treatment of complex systems (multidisciplinary design, multiple local optima, large-scale system, multi-objective optimisation...).…”

Section: Introduction To Multi-level Approaches In Aerodynamic Shape Designmentioning

confidence: 99%

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

Martinelli

Beux

2008

TECM

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The present study focuses on multi-level approaches in the context of discrete gradient-based methods for aerodynamic shape design. More precisely, the minimisation is done alternatively on different control subspaces according to multigrid-like cycles, providing at each sub-level a particular gradient preconditioning. Starting from an existing multi-level gradient-based formulation associated to shape grid-points coordinates, a possible generalisation to more compact shape representations is proposed through the construction of adequate sets of embedded shape sub-parametrisations. The behaviour of the new formulation is illustrated on different 2D inverse problems for inviscid flows.

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Multilevel Simulation and Numerical Optimization of Complex Engineering Designs

Cited by 8 publications

References 17 publications

Correction: A Parametric Study of Multimodality in Aerodynamic Shape Optimization of Wings

Correction: A Parametric Study of Multimodality in Aerodynamic Shape Optimization of Wings

Investigation of Multimodality in Aerodynamic Shape Optimization Based on the Reynolds Averaged Navier-Stokes Equations

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

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