ESC: an efficient error-based stopping criterion for kriging-based reliability analysis methods
ESC: an efficient error-based stopping criterion for kriging-based reliability analysis methods
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DOI：
10.1007/s00158-018-2150-9
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发表时间：
2018-11
影响因子：
3.9
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
数值模型的日益复杂性和相关的计算需求对经典的可靠性分析方法提出了挑战。基于代理模型的可靠性分析技术，特别是那些使用克里金元模型，最近获得了相当大的关注，因为它们能够实现高精度和计算效率。然而，现有的停止标准，这是用来终止代理模型的训练，不直接涉及估计的故障概率的错误。这种限制可能导致高计算需求，因为不必要地调用昂贵的性能函数（例如，涉及有限元模型）或由于训练过程的过早终止而可能不准确地估计故障概率。在这里，我们提出了基于错误的停止标准（ESC）来解决这些限制。首先，它表明，总的错误符号估计的候选设计样本的性能函数的克里金，S，遵循泊松二项分布。随后，这一发现是用来估计的下限和上限ofS为一个给定的置信水平的候选设计样本集克里金分类为安全和不安全的。根据泊松二项分布的概率特性，推导出了失效概率估计误差的上界。建议的上限实现在基于克里格的可靠性分析方法作为停止标准。在这里使用五个基准可靠性分析问题的效率和鲁棒性的ESC进行了研究。结果表明，该方法实现了设定的精度目标，并大大减少了计算需求，在某些情况下超过50%。
The ever-increasing complexity of numerical models and associated computational demands have challenged classical reliability analysis methods. Surrogate model-based reliability analysis techniques, and in particular those using kriging meta-model, have gained considerable attention recently for their ability to achieve high accuracy and computational efficiency. However, existing stopping criteria, which are used to terminate the training of surrogate models, do not directly relate to the error in estimated failure probabilities. This limitation can lead to high computational demands because of unnecessary calls to costly performance functions (e.g., involving finite element models) or potentially inaccurate estimates of failure probability due to premature termination of the training process. Here, we propose the error-based stopping criterion (ESC) to address these limitations. First, it is shown that the total number of wrong sign estimation of the performance function for candidate design samples by kriging,S, follows a Poisson binomial distribution. This finding is subsequently used to estimate the lower and upper bounds ofSfor a given confidence level for sets of candidate design samples classified by kriging as safe and unsafe. An upper bound of error of the estimated failure probability is subsequently derived according to the probabilistic properties of Poisson binomial distribution. The proposed upper bound is implemented in the kriging-based reliability analysis method as the stopping criterion. The efficiency and robustness ofESCare investigated here using five benchmark reliability analysis problems. Results indicate that the proposed method achieves the set accuracy target and substantially reduces the computational demand, in some cases by over 50%.