利用序列自适应重要性采样处理等式信息的可靠性更新鲁棒方法
A robust method for reliability updating with equality information using sequential adaptive importance sampling
AI总结：
本文提出 RU-SAIS 方法，结合序列重要性采样、K-means 聚类和交叉熵方法，解决含等式信息的可靠性更新问题，实验表明其后验失效概率估计比子集模拟等方法更准确、更鲁棒。
摘要：
可靠性更新是指将贝叶斯更新技术与结构可靠性分析相结合的问题，当涉及等式信息时，无法直接用结构可靠性方法（SRMs）求解。现有最先进的方法通过引入辅助标准正态参数将等式信息转化为不等式信息。然而，这些方法由于难以找到似然函数的最大值、后验失效概率伴随的较大变异系数（COV），以及不适用于新信息不断出现的动态更新问题，导致计算效率下降。为克服这些局限性，本文提出了一种创新方法，称为 RU-SAIS（利用序列自适应重要性采样进行可靠性更新），该方法结合序列重要性采样和 K-means 聚类，利用高斯混合构造一系列重要采样密度（ISDs）。序列中最后一个 ISD 通过交叉熵方法进一步自适应修正。通过三个算例展示了 RU-SAIS 的性能。结果表明，与子集模拟等现有方法相比，RU-SAIS 对后验失效概率的估计更准确、更鲁棒。
英文摘要：
Reliability updating refers to a problem that integrates Bayesian updating technique with structural reliability analysis and cannot be directly solved by structural reliability methods (SRMs) when it involves equality information. The state-of-the-art approaches transform equality information into inequality information by introducing an auxiliary standard normal parameter. These methods, however, encounter the loss of computational efficiency due to the difficulty in finding the maximum of the likelihood function, the large coefficient of variation (COV) associated with the posterior failure probability and the inapplicability to dynamic updating problems where new information is constantly available. To overcome these limitations, this paper proposes an innovative method called RU-SAIS (reliability updating using sequential adaptive importance sampling), which combines elements of sequential importance sampling and K-means clustering to construct a series of important sampling densities (ISDs) using Gaussian mixture. The last ISD of the sequence is further adaptively modified through application of the cross entropy method. The performance of RU-SAIS is demonstrated by three examples. Results show that RU-SAIS achieves a more accurate and robust estimator of the posterior failure probability than the existing methods such as subset simulation.
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