Abstract
Estimating the small failure probability of highly reliable structures is often computationally expensive in reliability analysis. The adaptive kriging-based reliability analysis methods have been widely used to solve this issue. However, the kriging refinement phase of these methods may not achieve adequate efficiency due to a large candidate sample pool (CSP) size and unnecessary limit state function (LSF) evaluations. In this work, an efficient adaptive kriging refinement method (EAKRM) is proposed to alleviate the computational burden. First, a CSP generation strategy is developed using the radius sequence to gradually generate uniform samples along the direction vector until the failure region appears. Considering points with a high risk of misjudgment and located outside of CSP, a two-stage training point selection strategy is then proposed based on the learning function U to determine the most valuable training point. Finally, a correlation-based stopping criterion is presented by quantifying the consistency of the kriging predictive signs between two successive refinement processes. Three mathematical examples and three engineering examples are employed to illustrate the effectiveness of the proposed EAKRM.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 51475425), the Science and Technology Plan of Zhejiang Province (CN) (Grant No. 2021C01097), and the College Student’s Science and Technology Innovation Project of Zhejiang Province (CN) (Grant No. 2022R403B060).
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Shi, L., Xiang, Y., Pan, B. et al. An efficient adaptive kriging refinement method for reliability analysis with small failure probability. Struct Multidisc Optim 66, 222 (2023). https://doi.org/10.1007/s00158-023-03672-z
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DOI: https://doi.org/10.1007/s00158-023-03672-z