Variable-complexity response surface approximations for wing structural weight in HSCT design

Kaufman, Matthew; Balabanov, Vladimir; Burgee, Susan L.; Giunta, Anthony A.; Grossman, Bernard; Haftka, Raphael T.; Mason, William H.; Watson, Layne T.

doi:10.1007/bf00350530

Cited by 78 publications

(22 citation statements)

References 20 publications

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“…As with other bilevel MDO architectures, the postoptimality analysis is necessary to ensure convergence to an optimal design of the original monolithic problem. We also note the work of Kaufman et al [197] and Hosder et al [198], who use structural optimization as an inner loop in aircraft design optimization with a surrogate model replacing the post-optimality sensitivity equations.…”

Section: J Asymmetric Subspace Optimization (Aso)mentioning

confidence: 96%

Multidisciplinary Design Optimization: A Survey of Architectures

2013

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Multidisciplinary design optimization (MDO) is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of MDO, various methods (architectures) have been developed and applied to solve MDO problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitates the understanding of the various architectures, and how they relate to each other.A classification of the MDO architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both a theoretical and experimental perspective. For each architecture, several applications to the solution of engineering design problems are cited. The result is a comprehensive but straightforward introduction to MDO for non-specialists, and a reference detailing all current MDO architectures for specialists.

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Section: J Asymmetric Subspace Optimization (Aso)mentioning

confidence: 96%

Multidisciplinary Design Optimization: A Survey of Architectures

2013

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“…Kaufman et al 7 proposed that an unreasonable design, x, should be moved so that it resides on the edge of the reasonable design space:…”

Section: Reasonable Design Spacementioning

confidence: 99%

“…Reducing the size of the region may sometimes be the only way of improving the accuracy. Kaufman et al 7 proposed a method to constrain the region of interest to a part of the design space containing only designs judged reasonable in terms of cost and constraint function values. This may be preferable to reducing the design space arbitrarily by imposing simple move limits.…”

Section: Introductionmentioning

confidence: 99%

Response surface approximations for structural optimization

Roux¹,

Stander²,

Haftka³

1998

Int. J. Numer. Meth. Engng.

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Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to ÿnd the region of interest containing the optimal design, and techniques for ÿnding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the 'best' regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-e ective. In a further attempt to improve e ciency, di erent regression models were investigated. The results indicate that the use of the two methods investigated does not signiÿcantly improve the results. Finding an accurate global approximation is challenging, and su cient accuracy could only be achieved in the example problems by considering a smaller region of the design space. ? 1998 John Wiley & Sons, Ltd.

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“…The variable-fidelity modelling concept was employed by various researchers such as Haftka [1], Hutchinson et al [2], Kaufmann et al [3] and Alexandrov et al [4][5][6][7][8] for solving design optimisation problems. In general, VFMs (sometimes these are referred to as multi-fidelity models) combine 2.…”

Section: Introductionmentioning

confidence: 99%

A variable‐fidelity aerodynamic model using proper orthogonal decomposition

Mifsud

MacManus

Shaw

2016

Numerical Methods in Fluids

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Summary A variable‐fidelity aerodynamic model based on proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions at different parameters is presented in this article. The ensemble of CFD solutions consists of two subsets of numerical solutions or snapshots computed at two different nominal orders of accuracy or discretization. These two subsets are referred to as the low‐fidelity and high‐fidelity solutions or data, whereby the low fidelity corresponds with computations made at the lower nominal order of accuracy or coarser discretization. In this model, the relatively inexpensive low‐fidelity data and the more accurate but expensive high‐fidelity data are considered altogether to devise an efficient prediction methodology involving as few high‐fidelity analyses as possible, while obtaining the desired level of detail and accuracy. The POD of this set of variable‐fidelity data produces an optimal linear set of orthogonal basis vectors that best describe the ensemble of numerical solutions altogether. These solutions are projected onto this set of basis vectors to provide a finite set of scalar coefficients that represent either the low‐fidelity or high‐fidelity solutions. Subsequently, a global response surface is constructed through this set of projection coefficients for each basis vector, which allows predictions to be made at parameter combinations not in the original set of observations. This approach is used to predict supersonic flow over a slender configuration using Navier–Stokes solutions that are computed at two different levels of nominal accuracy as the low‐fidelity and high‐fidelity solutions. The numerical examples show that the proposed model is efficient and sufficiently accurate. Copyright © 2016 John Wiley & Sons, Ltd.

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Variable-complexity response surface approximations for wing structural weight in HSCT design

Abstract: ii Acknowledgements

Cited by 78 publications

References 20 publications

Multidisciplinary Design Optimization: A Survey of Architectures

Multidisciplinary Design Optimization: A Survey of Architectures

Response surface approximations for structural optimization

A variable‐fidelity aerodynamic model using proper orthogonal decomposition

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