摘要
提出了高斯白噪声激励的线性及非线性结构动力学系统的首次穿越失效概率的估计方法.对于线性结构动力学系统,失效区域被分解为互斥的基本失效域之和,每个基本失效域可用其设计点完全描述,并以正态分布代替卡方分布估计失效概率中的参数.对于非线性结构动力学系统,基于Rice穿越理论,将非线性方程转化为与之具有相同平均上穿率的线性化方程,然后利用文中方法对等效线性化方程估计首穿失效概率.最后给出了线性及非线性结构动力学系统的数值例子,并将所提方法与蒙特卡罗法及重要样本法相比较,模拟结果显示了方法的正确性与有效性.
The first passage problems of linear and nonlinear dynamical systems excited by Gauss white noise are considered. For linear dynamical system, the failure domain can be described as a union of mutually exclusive events, and every event is completely described by a local design point. The paper uses standard Gaussian distribution instead of chi-square distribution to estimate the parameter of first passage probability. For nonlinear dynamical system, the equivalent linear system is carried out based on the out-crossing theory. The linearization principle is that nonlinear and linear systems have the same up-crossing rate for a specified threshold. Finally the paper gives two examples. The results show that the method of the paper suggested is correct and effective by comparing with the Monte Carlo method.
出处
《力学学报》
EI
CSCD
北大核心
2013年第3期421-425,共5页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10932009
11172233)
长安大学中央高校专项基金(CHD2011JC019)资助项目~~
关键词
结构可靠性
首穿失效概率
区域分解
等效线性化
structural reliability, first passage probability, domain decomposition, equivalent linearization
