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Time-dependent reliability analysis method based on ARBIS and Kriging surrogate model

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Abstract

Based on the existed idea of adaptive radial-based important sampling (ARBIS) method, a new method solving time-dependent reliability problems is proposed in this paper. This method is more widely used than the existed method combining importance sampling (IS) with time-dependent adaptive Kriging surrogate (AK) model, which is not only suitable for time-dependent reliability problems with single design point, but also for multiple design points, high nonlinearity, and multiple failure modes, especially for small failure probability problems. This method combines ARBIS with time-dependent AK model. First, at each sample point, the AK model of the performance function with regard to time t is established in the inner layer, and its minimum value is calculated as the performance function value of the outer layer to established time-independent AK model. Then, the optimal radius of the β-sphere is obtained with an efficient adaptive scheme. Excluding a β-sphere from the sample pool, there is no need to calculate the performance function value of the samples inside the β-sphere, which greatly improves the estimation efficiency of structural reliability analysis. Finally, three numerical examples are given to show the estimation efficiency, accuracy, and robustness of this method.

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Abbreviations

ARBIS:

Adaptive radial-based important sampling

PDF:

Probability density function

MCS:

Monte Carlo simulation

IS:

Important sampling

AK:

Adaptive Kriging surrogate

AK-MCS:

Active learning method combining Kriging model and MCS

AK-IS:

The reliability method combining AK and IS

AK-ARBIS:

Improved AK-MCS based on the adaptive radial-based importance sampling for small failure probability

ALK-Pfst:

Active learning method based on the Kriging model for the profust reliability analysis

MAIS:

Multimodal adaptive important sampling

MPP:

Most probable point

LSS:

Limit state surface

TCR:

Truncated candidate region

EMO-MMO:

Evolutionary multimodal optimization algorithm and multi-objective optimization

ALK-EMO-IS:

Active learning method combining Kriging model and evolutionary multimodal optimization algorithm and important sampling

EOLE:

Expansion optimal linear estimation model

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Acknowledgements

Authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant No.11902259, No.52175149), Innovation Foundation for the Postdoctoral Talents (Grant No. BX20190285), and Basic Research Fund of Central University (Grant No. G2020KY05406)

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710129, People’s Republic of China

    Huan Liu, Xindang He, Pan Wang, Zhenzhou Lu & Zhufeng Yue

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  1. Huan Liu
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  2. Xindang He
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Correspondence to Xindang He.

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Liu, H., He, X., Wang, P. et al. Time-dependent reliability analysis method based on ARBIS and Kriging surrogate model. Engineering with Computers 39, 2035–2048 (2023). https://doi.org/10.1007/s00366-021-01570-w

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