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

Abstract

By coupling the low-fidelity (LF) model with the high-fidelity (HF) samples, the variable-fidelity model (VFM) offers an efficient way to overcome the expensive computing challenge in multidisciplinary design optimization (MDO). In this paper, a cooperative radial basis function (Co-RBF) method for the VFM is proposed by modifying the basis function of RBF. The RBF method is constructed on the HF samples, while the Co-RBF method incorporates the entire information of the LF model with the HF samples. In Co-RBF, the LF model is regard as a basis function of Co-RBF and the HF samples are utilized to compute the Co-RBF model coefficients. Two numerical functions and three engineering problems are adopted to verify the proposed Co-RBF method. The predictive results of Co-RBF are compared with those of RBF and Co-Kriging, which show that the Co-RBF method improves the efficiency, accuracy and robustness of the existing VFMs.

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Acknowledgements

The authors gratefully appreciate the support by Fundamental Research Funds for the Central Universities (Grant No. G2016KY0302), National Natural Science Foundation of China (Grant No. 51505385, No. 11572134), and also thank Dr. Hua Su and Dr. Chunna Li for the helpful discussion about the Co-RBF method. Moreover, thanks Dr. Zhao Jing and the anonymous reviewers for their efforts and constructive advice to improve the study.

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Correspondence to Xu Li.

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Li, X., Gao, W., Gu, L. et al. A cooperative radial basis function method for variable-fidelity surrogate modeling. Struct Multidisc Optim 56, 1077–1092 (2017). https://doi.org/10.1007/s00158-017-1704-6

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Keywords

  • VFM
  • Surrogate model
  • RBF
  • Co-RBF
  • Co-Kriging