摘要
基于Gisranov定理,提出一种估计稳态高斯白噪声激励的结构动力学系统首穿失效概率的重要样本法.文章重点是构造控制函数,控制函数促使随机响应尽量集中在样本空间中最易导致首次穿越发生的部分.利用设计点构造控制函数,在线性系统场合,结合时不变系统的结构可靠性理论,通过解有约束的优化问题得到设计点;在非线性系统场合,利用Heonsang Koo提出的设计点激励,通过镜像法得到设计点.最后给出例子,将所提方法与原始蒙特卡罗法相比较,模拟结果显示方法的正确性与有效性.
Based on the Girsanov transformation, this paper develops a method for estimating the first excursion probability of dynamical systems with stationary gauss white noise. The focus is to construct control function that concentrates on the samples paths in the ＂most important part＂ of the sample space, to achieve the purpose of variance reduction. The paper uses design point to construct control function. For linear systems, the present approach combines with the time-invariant structure reliability theory to get design points by solving the problem of the optimization. For non-linear systems, the paper uses mirror-images method to get design points. Finally the paper gives two examples. The results show the method of this paper to be correct and effective by comparing with the primitive Monte Carlo method.
出处
《力学学报》
EI
CSCD
北大核心
2012年第3期648-652,共5页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(10872165
10932009
11172233)~~
关键词
首穿失效概率
重要抽样法
设计点激励
镜像法
first excursion probability, importance sampling, design-point excitation, mirror-image method
