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.

翻译：可靠度更新是指将贝叶斯更新技术与结构可靠度分析相结合的一类问题，当涉及等值信息时，无法通过结构可靠度方法直接求解。现有方法通过引入辅助标准正态参数将等值信息转化为不等式信息。然而，这些方法因似然函数极值求解困难、后验失效概率变异系数过大以及不适用于信息持续更新的动态更新场景，导致计算效率显著降低。为克服上述局限，本文提出一种名为RU-SAIS（基于序贯自适应重要性抽样的可靠度更新）的创新方法，该方法融合序贯重要性抽样与K均值聚类技术，通过高斯混合模型构建一系列重要性抽样密度函数，并运用交叉熵方法对序列末位重要性抽样密度函数进行自适应修正。通过三个算例验证RU-SAIS的效能，结果表明：相较于子集模拟等现有方法，RU-SAIS能够获得更精确且鲁棒的后验失效概率估计值。