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Local maximum-entropy based surrogate model and its application to structural reliability analysis

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Abstract

A novel surrogate model based on the Local Maximum-Entropy (LME) approximation is proposed in this paper. By varying the degrees of locality, the LME-based surrogate model is constructed according to the local behavior of the response function at the prediction points. The proposed method combines the advantages of both local and global approximation schemes. The robustness and effectiveness of the model are systematically investigated by comparing with the conventional surrogate models (such as Polynomial regression, Radial basis function, and Kriging model) in three types of test problems. In addition, the performance of the LME-based surrogate model is evaluated by an industry case of turbine disk reliability analysis (TDRA) involving random geometric parameters. In TDRA, two LME-based surrogate models are built including a 1st surrogate model employed in the sensitivity analysis to determine the key random variables and a 2nd surrogate model utilized in Monte-Carlo Simulations (MCS) to predict the Low Cycle Fatigue (LCF) life of turbine disks. Finally, a model-based Uncertainty Quantification (UQ) analysis is performed to rigorously quantify the uncertainties of the physical system and fidelity of surrogate model predictions simultaneously. Results show that the LME-based surrogate model can achieve a desirable level of accuracy and robustness with reduced number of sample points, which indicates the proposed method possess the potential for approximating highly nonlinear limit state functions and applicable for structural reliability analysis.

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Acknowledgements

This work is supported by the State Scholarship Fund of China (File No.201506020025), National Natural Science Foundation of China (File No.51275024) and Aviation Science Foundation of China (File No.2014ZB51). The authors are grateful for these supports.

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Authors and Affiliations

  1. School of Energy and Power Engineering, Beihang University, Beijing, 100191, China

    Jiang Fan, Huming Liao, Junheng Hu & Zhiying Chen

  2. Beijing Key Laboratory of Aero-Engine Structure and Strength, Beijing, 100191, China

    Jiang Fan

  3. Collaborative Innovation Center of Advanced Aero-Engine, Beijing, 100191, China

    Jiang Fan

  4. Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, 44106, USA

    Hao Wang & Bo Li

  5. Guangdong Institute of Aeronautics and Astronautics Equipment & Technology, Zhuhai, Guangdong, 519000, China

    Jian Lu

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  1. Jiang Fan
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Correspondence to Jian Lu or Bo Li.

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Fan, J., Liao, H., Wang, H. et al. Local maximum-entropy based surrogate model and its application to structural reliability analysis. Struct Multidisc Optim 57, 373–392 (2018). https://doi.org/10.1007/s00158-017-1760-y

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  • DOI: https://doi.org/10.1007/s00158-017-1760-y

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