基于主动学习Kriging模型和子集模拟的可靠度分析  

Reliability analysis based on active learning Kriging model and subset simulation method

作　　者：黄晓旭[1,2] 陈建桥[1,2] 

机构地区：[1]华中科技大学力学系,武汉430074 [2]工程结构分析与安全评定湖北省重点实验室,武汉430074

出　　处：《应用力学学报》2016年第5期866-871,939,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11572134);国家重点基础研究发展计划(2011CB013800)

摘　　要：工程结构的功能函数大多数具有隐式非线性程度高的特点,且失效概率较小,需要复杂的有限元分析计算。针对工程实际中大量存在的小失效概率问题,本文提出了基于主动学习Kriging模型和子集模拟方法相结合的可靠度分析方法——AK-SS。AK-SS方法有子集模拟求解小失效概率和主动学习的Kriging模型代替真实功能函数的优势。该方法首先采用Kriging模型代替真实功能函数,通过主动学习方法逐步扩充实验设计点,逐步改善Kriging模型的精度;然后利用子集模拟方法的基本思路,通过引入合理的中间失效事件计算小失效概率。结果表明,AK-SS方法在保证结果精度的同时减少了功能函数的评估次数,对于工程实际中具有隐式功能函数的小失效概率计算问题具有较强的应用前景。With complex performance functions and time-demanding computation of structural responses, the estimation of small failure probabilities is a challenging problem in engineerings. To address this issue, an active learning method combining Kriging model(AK) and subset simulation(SS) is proposed in this paper. The efficiency of this new method relies upon the advantages of SS in evaluating small failure probabilities and the Kriging model with active learning and updating characteristic for approximating the true performance function. First, a Kriging model is utilized to approximate the true performance function and then this Kriging model is updated by adding new points into the design of experiment based on active learning methods. Then the small failure probability can be evaluated by the subset simulation method. The efficiency of the proposed new method is demonstrated through several examples. The results show that AK-SS can provide accurate solutions more efficiently, making it a promising approach for structural reliability analyses involving small failure probabilities, high-dimensional performance functions, and time-consuming simulation codes in practical engineerings.

关 键 词：功能函数 主动学习 KRIGING模型 子集模拟方法 小失效概率 

分 类 号：TU311.2[建筑科学—结构工程]