Efficient Optimization Design Method Using Kriging Model

Jeong, Shinkyu; Murayama, Mitsuhiro; Yamamoto, Kazuomi

doi:10.2514/1.6386

Cited by 426 publications

(138 citation statements)

References 8 publications

(5 reference statements)

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“…The representative surrogate models are polynomial response surface model (PRSM) [13,14], kriging [15,16], radial-basis functions (RBFs) [17,18], artificial neural network (ANN) [19,20], support-vector regression (SVR) [21,22], multivariate interpolation [23], polynomial chaos expansion [24,25], etc. Among them, kriging gets popularity in the fields of aerodynamic design optimization [26][27][28][29][30] and structural and multidisciplinary optimization [8] because it can represent nonlinear and multidimensional functions and has a unique feature of offering a mean-squared-error estimation. A surrogate model is a cheap-toevaluate approximation model built through the sampled data, which are obtained by evaluating a limited number of sample points in the parameter space via expensive analysis code.…”

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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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confidence: 99%

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

et al. 2017

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“…This criterion represents a balancing between exploitation and exploration, which has proven to be efficient at least for low-dimensional problems, 6,[28][29][30] when the number of variables does not exceed ten. It maximizes the probability of improving the function over the current best known sample given a model and its standard error.…”

Section: A Combination Of Three Sampling Criteriamentioning

confidence: 99%

Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers

et al. 2010

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This paper deals with aerodynamic shape optimization using a high fidelity solver. Due to the computational cost needed to solve the Reynolds-averaged Navier-Stokes equations, the performance of the shape must be improved using very few objective function evaluations despite the high number of design variables. In our framework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensively computes the sensitivities of the functions with respect to design variables to build the gradient of the objective function. As usual aerodynamic functions show numerous local optima when the shape varies, a more global optimizer is expected to be beneficial. Consequently, a Kriging based optimizer is set up and described. It uses an original sampling refinement process which adds up to three points per iteration by using a balancing between function minimization and error minimization. In order to efficiently apply this algorithm to high-dimensional problems, the same sampling process is reused to form a Cokriging (gradient-enhanced model) based optimizer. A comparative study is then described on two drag minimization problems depending on six and forty-five design variables. This study was conducted using an original set of performance criteria characterizing the strength and weakness of each optimizer in terms of improvement, cost, exploration and exploitation.

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“…While Kriging is commonly applied in geostatistics and fluid dynamics [3,4], the method is only recently recognized in biotechnology [5,6]. The empirical part of Kriging analyzes first how the covariance of given measurement data depends on the distance of the respective measurement points.…”

Section: Introductionmentioning

confidence: 99%

Kriging with trend functions nonlinear in their parameters: Theory and application in enzyme kinetics

Freier

Wiechert

Lieres

2017

Engineering in Life Sciences

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Kriging is an interpolation method commonly applied in empirical modeling for approximating functional relationships between impact factors and system response. The interpolation is based on a statistical analysis of given data and can optionally include a priori defined trend functions. However, Kriging can so far only be used with trend functions that are linear with respect to the parameters. In this contribution, we present an extension of the Kriging approach for handling trend functions that are nonlinear in their parameters. Our approach is based on Taylor linearization combined with an iterative parameter estimation procedure whose solution is practically computed via a root finding problem. We demonstrate our novel approach with measurement data from the application field of biocatalysis.

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Efficient Optimization Design Method Using Kriging Model

Cited by 426 publications

References 8 publications

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

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

Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers

Kriging with trend functions nonlinear in their parameters: Theory and application in enzyme kinetics

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