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Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments

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Abstract

Aiming at efficiently estimating the dynamic failure probability with multiple temporal and spatial parameters and analyzing the global reliability sensitivity of the dynamic problem, a method is presented on the moment estimation of the extreme value of the dynamic limit state function. Firstly, two strategies are proposed to estimate the dynamic failure probability. One strategy is combining sparse grid technique for the extreme value moments with the fourth-moment method for the dynamic failure probability. Another is combining dimensional reduction method for fractional extreme value moments and the maximum entropy for dynamic failure probability. In the proposed two strategies, the key step is how to determine the temporal and spatial parameters where the dynamic limit state function takes their minimum value. This issue is efficiently addressed by solving the differential equations satisfying the extreme value condition. Secondly, three-point estimation is used to evaluate the global dynamic reliability sensitivity by combining with the dynamic failure probability method. The significance and the effectiveness of the proposed methods for estimating the temporal and spatial multi-parameter dynamic reliability and global sensitivity indices are demonstrated with several examples.

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Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant 51475370) and the fundamental research funds for the central university (Grant 3102015 BJ (II) CG009).

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Authors and Affiliations

  1. School of Aeronautics, Northwestern Polytechnical University, P.O. Box 120, Xi’an City, 710072, Shaanxi Province, People’s Republic of China

    Yan Shi, Zhenzhou Lu, Kai Cheng & Yicheng Zhou

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  1. Yan Shi
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  2. Zhenzhou Lu
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  3. Kai Cheng
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  4. Yicheng Zhou
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Correspondence to Zhenzhou Lu.

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Shi, Y., Lu, Z., Cheng, K. et al. Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments. Struct Multidisc Optim 56, 117–129 (2017). https://doi.org/10.1007/s00158-017-1651-2

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