Optimization using surrogate models and partially converged computational fluid dynamics simulations

Forrester, Alexander I. J.; Bressloff, Neil W.; Keane, Andy J.

doi:10.1098/rspa.2006.1679

Cited by 159 publications

(124 citation statements)

References 31 publications

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“…If the correction process is simpler than f e , then we can expect predictions based on a large quantity of cheap data with a simple correction to be more accurate than predictions based on a small quantity of expensive data. This simple form of combining multi-fidelity analyses has be used by Leary et al [52] for finite element analyses using different mesh sizes and by Forrester et al [20] for combining CFD of varying levels of convergence.…”

Section: Multi-fidelity Analysismentioning

confidence: 99%

“…As when dealing with constrained surrogates, it is assumed that these models are independent (though it is also possible to build correlated models by using co-Kriging, as per section 3.7.2). The Gaussian processes have means y 1 (x) and y 2 (x) (from equation (20)), and variances s 2 1 (x) and s 2 2 (x) (from equation (22)). These values may then be used to construct a two dimensional Gaussian probability density function for the predicted responses of the form where it is made explicitly clear that y 1 (x), s 2 1 (x), y 2 (x) and s 2 2 (x) are all functions of the location at which an estimate is being sought.…”

Section: Multi-objective Expected Improvementmentioning

confidence: 99%

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Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,882

954

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The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.

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Section: Multi-fidelity Analysismentioning

confidence: 99%

Section: Multi-objective Expected Improvementmentioning

confidence: 99%

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,882

954

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show abstract

“…A correlation coefficient [73] r 2 is introduced to assess the accuracy of the kriging, GEK, and WGEK models for the sum-square functions of varying dimensions:…”

Section: High-dimensional Analytical Test Casementioning

confidence: 99%

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

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A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to ameliorate the "curse of dimensionality". The core idea is to build a series of submodels with much smaller correlation matrices and then sum them up with appropriate weight coefficients, aiming to avoid the prohibitive cost associated with decomposing the large correlation matrix of a gradient-enhanced kriging. A self-contained derivation of the proposed method is presented, and then it is verified by surrogate modeling test cases. The present method is integrated into a surrogatebased optimizer and tested for design optimizations. It is further demonstrated for inverse design of a transonic wing, parameterized with a number of design variables in the range from 36 to 108, using Reynolds-averaged Navier-Stokes flow and adjoint solvers. It is observed that, for the wing design with 36 and 54 variables, the weighted and conventional gradient-enhanced kriging are comparable, and both are much more efficient than kriging without using any gradient. For the wing design with 72 and 108 variables, the cost of training a gradient-enhanced kriging increases rapidly and becomes prohibitive. In contrast, the cost of training a weighted gradient-enhanced kriging is kept in an acceptable level, which makes it more practical for higher-dimensional problems.

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“…Techniques for achieving this are widely described in literature, e.g. by Forrester et al 12,13 and Jones et al 14 There is also a wide choice in global optimization algorithms, two promising techniques are genetic algorithms and particle swarm optimization, see e.g. Green and Cheng 15 and Venter and SobieszczanskiSobieski.…”

Section: Xml Iges …mentioning

confidence: 99%

Development and Implementation of Novel Parametrization Techniques for Multidisciplinary Design Initialization

Straathof¹,

Tooren²,

Voskuijl³

et al. 2010

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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A new parametrization method for aircraft shapes is presented to enhance shape optimization for aircraft design. This parametrization method was implemented in a tool that creates feasible initial solutions for multidisciplinary design optimization problems. The tool combines all aspects of the aerodynamic design process: parametrization, aerodynamic analysis and optimization. The novel parametrization method presented in this paper makes use of the Class-Shape-Refinement-Transformation (CSRT) method. This method employs a combination of Bernstein polynomials and B-splines to allow for both global and local control of the shape. Additionally, the use of B-splines makes it possible to efficiently handle volume constraints, which are very common in aircraft design. The parametrization method was coupled to two different aerodynamic analysis tools. The commercial panel method code VSAERO was used for the low-speed regime and an inhouse Euler code was used for transonic and supersonic flight conditions. Various different optimization schemes were investigated and compared. A number of test cases were performed. For the first set of test cases, a three-dimensional geometry was optimized for subsonic conditions, using VSAERO and various optimization algorithms. For the second set of test cases, an airfoil was optimized for transonic and supersonic conditions, using the in-house Euler solver and a gradient-based optimizer. From this work it can be concluded that a combination of stochastic and gradient-based optimization algorithms works best together with the CSRT method. Additionally, refining the shape using B-splines proved to be an efficient way of increasing the design freedom, while the design space remained smooth enough to employ gradient-based optimization.

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Optimization using surrogate models and partially converged computational fluid dynamics simulations

Cited by 159 publications

References 31 publications

Recent advances in surrogate-based optimization

Recent advances in surrogate-based optimization

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Development and Implementation of Novel Parametrization Techniques for Multidisciplinary Design Initialization

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