Abstract Bayesian updating offers a powerful tool for probabilistic calibration and uncertainty quantification of models as new observations become available. By reformulating Bayesian updating into a structural reliability problem via introducing an auxiliary random variable, the state-of-the-art Bayesian updating with structural reliability method (BUS) has showcased large potential to achieve higher accuracy and efficiency compared with conventional approaches based on Markov Chain Monte Carlo simulations. However, BUS faces a number of limitations. The transformed reliability problem often involves a very rare event especially when the number of observations increases. This along with the fact that conventional reliability analysis techniques are not efficient, and often not capable of accurately estimating the probability of rare events, unavoidably lead to a very large number of evaluations of the likelihood function and simultaneously insufficient accuracy of the derived posterior distributions. To overcome these limitations, we propose Simple Rejection Sampling with Multiple Auxiliary Random Variables (SRS-MARV), where the limit state function in BUS is decomposed into a system reliability problem with multiple limit state functions. The main advantage of this approach is that the acceptance rate of each decomposed limit state function is significantly improved, which facilitates effective integration of adaptive Kriging-based reliability analysis into SRS-MARV. Moreover, a new stopping criterion is proposed for efficient, adaptive training of the Kriging model. The proposed method called BUAK is shown to be highly computationally efficient and accurate based on results of comprehensive investigations for three diverse benchmark problems. Compared to the state-of-the-art methods, BUAK substantially reduces the computational demand by one to three orders of magnitude, therefore, facilitating the application of Bayesian updating to computationally very intensive models.

中文翻译：

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使用元模型的高效贝叶斯更新：一种基于自适应克里金法的方法

摘要 贝叶斯更新为模型的概率校准和不确定性量化提供了一个强大的工具，因为新的观察结果可用。通过引入辅助随机变量将贝叶斯更新重新转化为结构可靠性问题，与基于马尔可夫的传统方法相比，结构可靠性方法 (BUS) 的最新贝叶斯更新展示了实现更高准确性和效率的巨大潜力链式蒙特卡罗模拟。但是，BUS 面临许多限制。转换后的可靠性问题通常涉及非常罕见的事件，尤其是当观察次数增加时。再加上传统的可靠性分析技术效率不高，通常无法准确估计罕见事件的概率，不可避免地导致对似然函数的大量评估，同时导出的后验分布的准确性不足。为了克服这些限制，我们提出了具有多个辅助随机变量的简单拒绝采样 (SRS-MARV)，其中 BUS 中的极限状态函数被分解为具有多个极限状态函数的系统可靠性问题。这种方法的主要优点是显着提高了每个分解的极限状态函数的接受率，有利于将基于自适应克里金法的可靠性分析有效地集成到 SRS-MARV 中。此外，还提出了一种新的停止标准，用于高效、自适应地训练克里金模型。基于对三个不同基准问题的综合调查结果，所提出的称为 BUAK 的方法被证明具有很高的计算效率和准确性。与最先进的方法相比，BUAK 将计算需求大幅减少了一到三个数量级，因此，有助于将贝叶斯更新应用于计算密集型模型。