On confidence intervals for failure probability estimates in Kriging-based reliability analysis
On confidence intervals for failure probability estimates in Kriging-based reliability analysis
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DOI：
10.1016/j.ress.2019.106758
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Zeyu Wang;A. Shafieezadeh
中科院分区：
文献类型：
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作者：
Zeyu Wang;A. Shafieezadeh
尽管最近的进步，自适应克里金为基础的可靠性分析复杂的极限状态，估计的准确性，现存的技术时，真正的故障概率是未知的仍然是一个重要的挑战。本研究通过开发失效概率估计的分析置信区间（CI）来解决这一差距。这是通过利用泊松二项分布的统计特性，在自适应克里格以及Lindeberg的中心极限定理的条件下，在一组候选设计样本中的预期数量的故障点，在这里促进。关于计算需求中涉及的计算CI，一个简单的情况下，克里金相关性被忽略，也来自。随后分析了五个不同的和不同的复杂性的例子所提出的CI的性能。结果表明，建议的CI与相关性考虑提供了最准确的区间。此外，而没有克里格相关估计的CI是不完全令人满意的自适应可靠性分析的早期阶段，它收敛到准确的界限在后期阶段。
Despite recent advancements in adaptive Kriging-based reliability analysis for complex limit states, estimation of the accuracy of extant techniques when the true failure probability is unknown remains an important challenge. The present study addresses this gap by developing analytical confidence intervals (CIs) for failure probability estimates. This is facilitated here by leveraging statistical properties of Poisson Binomial distribution for the expected number of failure points in the set of candidate design samples in adaptive Kriging as well as Lindeberg's condition for central limit theorem. Concerning computational demands involved in the computation of CIs, a simpler case where Kriging correlations are neglected is also derived. The performance of the proposed CIs is subsequently analyzed for five examples with different and varying complexities. Results indicate that the proposed CI with correlations considered offers the most accurate intervals. Additionally, whereas the CI estimated without Kriging correlation is not entirely satisfactory at early-stages of adaptive reliability analysis, it converges to accurate bounds at later stages.