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An efficient method for estimating time-dependent global reliability sensitivity

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Abstract

Time-dependent global reliability sensitivity can quantify the effect of input variables in their whole distribution ranges on the time-dependent failure probability. To efficiently estimate it to help researchers control the time-dependent failure probability, a novel method is proposed. The proposed method transforms the estimation of unconditional-conditional time-dependent failure probabilities into that of the unconditional-conditional probability density functions (PDFs) of the minimum of time-dependent performance function. Firstly, the minimum of time-dependent performance function is evaluated by adaptive Kriging, and its unconditional-conditional fractional moments are estimated by multiplicative dimensional reduction method (M-DRM). Then, the maximum entropy (MaxEnt) constrained by these fractional moments is used to estimate the unconditional-conditional PDFs, on which the unconditional-conditional time-dependent failure probabilities can be obtained. Finally, the one-dimensional Gaussian quadrature is applied to estimate the time-dependent global reliability sensitivity indices. Due to the high efficiency of adaptive Kriging for estimating the minimum of time-dependent performance function, the avoidance of dimensional curse by M-DRM, and the high efficiency of MaxEnt constrained by fractional moments for estimating PDF, the proposed method can reduce the computational cost dramatically.

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Acknowledgments

The manuscript is approved by all authors for publication. We would like to declare that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part.

Funding

This work was supported by the National Natural Science Foundation of China (Grant no. NSFC 51775439 and NSFC 11902254) and National Science and Technology Major Project (Grant no. 2017-IV-0009-0046).

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Correspondence to Zhenzhou Lu.

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The MATLAB codes used to generate the results are available in the supplementary material.

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Responsible Editor: Byeng D Youn

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Ling, C., Lu, Z., Zhang, X. et al. An efficient method for estimating time-dependent global reliability sensitivity. Struct Multidisc Optim 62, 851–871 (2020). https://doi.org/10.1007/s00158-020-02541-3

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  • DOI: https://doi.org/10.1007/s00158-020-02541-3

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