一些重大关键结构在服役期间会面临一些极端事件，它们由于概率极低而可能被忽视，但如果发生会导致严重的损失。为了准确估计复杂结构的极小失效概率，提出一个能平衡极端事件发生概率计算精度和成本的方法。通过基于高斯代理模型的主动学习策略，构建能够将训练点有效集中在单侧尾部的搜索函数，该函数更善于寻找分布函数加权后的误差最大区域，并重新投入新增训练点。为了验证算法的有效性，本文以结构开裂的非线性分析为算例，将本算法结果与MCS比较，所估计的随机变量的均值相对误差在10%左右，表明本方法能得到可接受的统计量结果；与AL-GP的结果进行对比，所估计的随机变量的误差期望降低了20%，表明在尾部的不确定性能更快降低。通过算例证明了本算法对尾部的敏感性更高，适用于有潜在尾部风险的分布计算。

Some major critical key structures will face extreme events during their service that may be overlooked disregarded due to their extremely low probability, but will result in serious losses if they occur. To accurately estimate the minimal failure probability of complex structures, this paper presents a method that can balance the accuracy and cost of calculating the probability of extreme events. By using an active learning strategy based on Gaussian surrogate metamodel, a search function is constructed that can effectively concentrate the training points on unilateral of the tail, and the function is better at finding the maximum error region weighted by the distribution function and re-investing the new training points. In order to verify the effectiveness of the algorithm, the nonlinear analysis of structural cracking is taken as an example. The relative error of the proposed algorithm is about 10% compared with MCS. The mean relative error of the estimated random variables is about 10%, indicating that this method can obtain acceptable statistical results. Compared with the results of AL-GP, the error expectation of the estimated random variables is reduced by 20%, indicating that the uncertainty at the tail can be reduced faster. The example proves that the algorithm is more sensitive to the tail and is suitable for the distribution calculation with potential tail risk.

国家重点研发计划（2019YFD1101005,2019YFD1101001,2021YFB2600501）、四川省自然科学基金（2022NSFSC0458）、四川省自然科学基金资助项目(2022NSFSC0458)和中铁第一勘察设计院集团有限公司科研开发项目（院科20-53,院科20-21,CR2321718）,国家自然科学基金项目（面上项目，重点项目，重大项目）