小失效概率和多失效模式相关的结构可靠性分析方法  

Structural reliability analysis for a small failure probability problem under multiple failure modes

作　　者：钱华明 黄土地 黄洪钟 刘宇[1,2] 黄鹏 QIAN HuaMing;HUANG TuDi;HUANG HongZhong;LIU Yu;HUANG Peng(School of Mechanical and Electrical Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China;Center for System Reliability and Safety,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]电子科技大学机械与电气工程学院,成都611731 [2]电子科技大学系统可靠性与安全性研究中心,成都611731

出　　处：《中国科学：物理学、力学、天文学》2022年第2期54-64,共11页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家重点研发计划(编号:2017YFB1301300)资助项目。

摘　　要：本文针对结构可靠性问题中普遍存在的小失效概率和多种失效模式的情形,提出一种联合多维响应高斯过程模型(Multiple Response Gaussian Process,MRGP)和子集模拟(Subset Simulation,SS)的结构可靠性分析新方法MRGP-SS.针对结构功能函数难以获取显式表达式及多种失效模式之间可能存在相关性的问题,采用MRGP模型构建多失效模式下功能函数的代理模型,并结合主动学习策略,对代理模型进行更新迭代,直至满足一定精度条件.针对小失效概率导致构建功能函数代理模型效率低的问题,采用SS方法来评估结构的失效概率,从而获得更小的变异系数,以提升MRGP构建代理模型的效率.将提出的MRGP-SS方法应用到案例分析中,并结合蒙特卡洛仿真,验证了本文方法的有效性.This paper proposes a new structural reliability analysis method for a small failure probability problem under multiple failure modes by combining the multiple response Gaussian process(MRGP) and subset simulation(SS). First, as the structural performance function cannot be analytically formulated and the correlation may exist between multiple failure modes, the MRGP model is adopted to construct the surrogate model of the performance function. Simultaneously, the MRGP model is updated by the active learning strategy until the predicted accuracy is satisfied. Then, due to the small failure probability problem brings a huge computational cost and even causes the infeasibility of constructing the surrogate model of performance function, the SS method is used to assess the structural failure probability and thus a smaller coefficient of variation(COV) can be obtained with a significant improvement of the computational efficiency.Finally, the proposed MRGP-SS method is applied into several examples and the Monte Carlo simulation(MCS) is also performed to demonstrate the effectiveness of the proposed method.

关 键 词：多维响应高斯过程 子集模拟 主动学习策略 多失效模式 小失效概率 可靠性分析 

分 类 号：TB114.3[理学—概率论与数理统计]