A cooperative radial basis function method for variable-fidelity surrogate modeling

Xu, Li; Gao, Wenkun; Gu, Liangxian; Gong, Chunlin; Jing, Zhao; Su, Hua

doi:10.1007/s00158-017-1704-6

Cited by 28 publications

(23 citation statements)

References 30 publications

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“…Co-Kriging (CK) model is widely used in the optimization design for complex products [1,2], for its advantage on reducing the computation cost in high-dimensional and strong nonlinear problem. In order to improve the prediction power of the CK model, the ordinary CK model needs to be improved, and the accuracy of the optimization design will be increased as well.…”

Section: Introductionmentioning

confidence: 99%

A Novel Combination Co-Kriging Model Based on Gaussian Random Process

Xie

Zeng

Song

et al. 2018

Mathematical Problems in Engineering

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Co-Kriging (CK) modeling provides an efficient way to predict responses of complicated engineering problems based on a set of sample data obtained by methods with varying degree of accuracy and computation cost. In this work, the Gaussian random process (GRP) is introduced to construct a novel combination CK model (CK-GRP) to improve the prediction accuracy of the conventional CK model, in which all the sample information provided by different correlation models is well utilized. The features of the new model are demonstrated and evaluated for a numerical case and an engineering application. It is shown that the CK-GRP model proposed in this work is effective and can be used to improve the prediction accuracy and robustness of the CK model.

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Section: Introductionmentioning

confidence: 99%

A Novel Combination Co-Kriging Model Based on Gaussian Random Process

Xie

Zeng

Song

et al. 2018

Mathematical Problems in Engineering

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“…There are three assessments to validate the accuracy of the RBF model: the root mean square error (RMSE RBF ), the maximum absolute error (MAX) and the correlation coefficient ( R 2 ) ( 20 ) . RMSE RBF is used to measure the global accuracy of the RBF model; MAX is employed to evaluate the local accuracy of the RBF model; R 2 can reflect the linear dependence between the predicted values of the RBF model and the actual values.…”

Section: Geometric Inverse Fitting Test and Resultsmentioning

confidence: 99%

Improved aerofoil parameterisation based on class/shape function transformation

Liu

2019

Aeronaut. j.

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A new aerofoil parameterisation method is put forward to represent an aerofoil by combining the leading edge modification class/shape function transformation (LEM CST) method and improved Hicks–Henne bump function’s method. The new class/shape function transformation (NEW CST) method has two additional basis functions comparing the original CST method. In order to confirm these two basis functions, the radial basis functions neural network (RBF) model is trained by some samples which are generated by the Latin hypercube design (LHD) method and Genetic Algorithm (GA) is proposed to achieve the basis functions of the NEW CST method. The NEW CST method has been evaluated in fitting precision of 1,545 aerofoils by comparison with the LEM CST method and the original CST method. And the improved ability of the NEW CST at the leading edge and trailing edge is verified by a series of complex aerofoil case studies within 1,545 aerofoils. The results indicate that the NEW CST method can represent the whole aerofoils and possesses the intuitive property as well as the original CST. Moreover, the number of control parameters (NCP) to parameterise aerofoils is the fewest among these three methods. Furthermore, when the NCP of the NEW CST and LEM CST is the same, the NEW CST method has the higher accuracy and smaller root mean square errors (RMSE) especially at the leading edge and trailing edge.

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“…In this work the optimal number of RBF centers ( ) is defined by minimizing a leave-one-out cross-validation (LOOCV) metric [28]. Leth(x) be a metamodel trained by all points but the -th point, then is defined as:…”

Section: A Stochastic Radial-basis Functionsmentioning

confidence: 99%

Adaptive N-Fidelity Metamodels for Noisy CFD Data

Wackers

Visonneau

Ficini

et al. 2020

Aiaa Aviation 2020 Forum

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An adaptive-fidelity approach to metamodeling from noisy data is presented for designspace exploration and design optimization. Computational fluid dynamics (CFD) simulations with different numerical accuracy (spatial discretization) provides metamodel training sets affected by unavoidable numerical noise. The-fidelity approximation is built by an additive correction of a low-fidelity metamodel with metamodels of differences (errors) between higherfidelity levels whose hierarchy needs to be provided. The approach encompasses two core metamodeling techniques, namely: i) stochastic radial-basis functions (SRBF) and ii) Gaussian process (GP). The adaptivity stems from the sequential training procedure and the auto-tuning capabilities of the metamodels. The method is demonstrated for an analytical test problem and a CFD-based optimization of a NACA airfoil, where the fidelity levels are defined by an adaptive grid refinement technique of a Reynolds-averaged Navier-Stokes (RANS) solver. The paper discusses: i) the effect of using more than two fidelity levels; ii) the use of least squares regression as opposed to exact interpolation; iii) the comparison between SRBF and GP; and iv) the use of two sampling approaches for GP. Results show that in presence of noise, the use of more than two fidelity levels improves the model accuracy with a significant reduction of the number of high-fidelity evaluations. Both least squares SRBF and GP provide promising results in dealing with noisy data.

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A cooperative radial basis function method for variable-fidelity surrogate modeling

Cited by 28 publications

References 30 publications

A Novel Combination Co-Kriging Model Based on Gaussian Random Process

A Novel Combination Co-Kriging Model Based on Gaussian Random Process

Improved aerofoil parameterisation based on class/shape function transformation

Adaptive N-Fidelity Metamodels for Noisy CFD Data

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