摘要
在结构可靠度计算中,利用重要抽样技术可以有效提高蒙特卡罗法的计算效率,其中抽样重心的确定是一个关键。当结构功能函数无法表达为随机变量的解析表达式而需借助有限元计算时,在传统响应面法的有限元数值试验中引入Neumann级数展开式,可以加速求出设计验算点。以设计验算点作为抽样重心进行重要抽样后,即可进一步采用蒙特卡罗法计算结构的失效概率。数值算例表明:所提出的基于Neumann展开响应面技术的重要抽样蒙特卡罗法具有较高的计算效率,同时又能保持很高的计算精度。
Importance sampling techniques can Monte-Carlo method in the calculation of structure effectively enhance the computation efficiency of the reliability. How to determine the sampling center is a key problem. When structure performance functions can not be explicitly expressed by random variables and need to be determined by finite element analysis, Neumann series expansion is incorporated into finite element numerical tests in the traditional response surface method. This can speed up the process for searching the design point, which is then used as the sampling center and importance sampling is conducted. Monte-Carlo method is further employed to obtain the failure probability. Numerical examples show the proposed method, the importance sampling Monte-Carlo method based on Neumann expansion response surface techniques, has high computation efficiency and maintains excellent computation accuracy.
出处
《工程力学》
EI
CSCD
北大核心
2009年第12期1-5,共5页
Engineering Mechanics
基金
华南理工大学亚热带建筑科学国家重点实验室资助项目(2008ZC21)
国家科技支撑计划子课题(2006BAJ01B07)
