针对极端事件估计的高斯主动学习算法

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中图分类号：TU311.41 文献标志码：A 文章编号：2096-6717（2025）04-0148-09

Gaussian active learning algorithm for extreme event estimation

YANG Haiting1a， YIN Weihao1a， HUANG Yanwen1a， YANG Cheng 1b ， HU Ruiqing （l School of Civil Enginering;1b.Land Trafic Geological Disaster Prevention Technology National Engineering Research Center，Southwest Jiaotong University， Chengdu 6lOo31，P.R.China; 2. China Railway First Survey and Design Institute Group Co.，Ltd.，Xi'an7l0O43，P.R.China）

Abstract： Some major key structures willface extreme events during their service life，which may be ignored due to their extremely low probability，but will result in serious losses if they occur.In order to accurately estimate the minimum probability of failure of complex structures，this paper presents a method that can balance the accuracy and cost of calculating the probability of extreme events.Using an active learning strategy based on a Gaussian surrogate metamodel，a search function is constructed that can efectively concentrate the training points on one side of the tail，and the function is beter at finding the maximum error region weighted by the distribution function and re-investing the new training points.To verify the efectivenessof the algorithm，the nonlinear analysis ofa structural crack is taken as an example.The relative error of the proposed algorithm is about 10% compared to MCS.The mean relative error of the estimated random variables is about 10% ， indicating that this method can obtain acceptable statistical results. Compared to the results ofAL-GP，the error expectation of the estimated random variables is reduced by 20% ，indicating that the uncertainty in 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.

Keywords： Gaussian surrogate model; reliability；active learning;extreme events

大型、复杂、关键的工程结构往往需要具备较高的可靠性，虽然这些结构都经历了规范可靠性设计，结构失效概率已经被控制在较小范围内，但在全寿命服役期内，仍然可能遭遇极为罕见的外部环境影响，例如，远超最大设计重现期的地震、极端气候灾害、非法超载或意外撞击、爆炸等[1-3]。（剩余12883字）