基于柯西不等式的结构可靠度取尾重要抽样法  

INTERCEPTING TAIL IMPORTANCE SAMPLING METHOD OF STRUCTURAL RELIABILITY BASED ON CAUCHY-INEQUALITY

作　　者：房艳峰[1] 高华喜[1] 

机构地区：[1]浙江海洋学院船舶与建筑工程学院,浙江舟山316004

出　　处：《工程力学》2013年第1期64-68,125,共6页Engineering Mechanics

基　　金：浙江省教育厅项目(Y201018955)

摘　　要：该文采用柯西不等式对结构可靠度计算中Monte Carlo重要抽样法的模拟方差进行了分析与评价,提出了中间概率的概念并推导出其与模拟方差的函数关系。在此基础上得出使方差达到极小值的抽样函数具体形式,并建立了属于重要抽样技术的圆环和半圆环取尾抽样方法。与其他方法不同的是其抽样函数与原变量分布函数的比值是一常数,其分布区域是以原点为中心以原点到极限状态面距离为半径的圆形外部空间,模拟结果的方差可以定量描述。理论分析和例题模拟结果都表明:圆环取尾抽样方法可使模拟结果的方差缩减到直接模拟的1/10,而半圆环取尾抽样方法能缩减到1/20。Cauchy-inequality is utilized to analyze and evaluate the variance of the simulation result of the Monte Carlo method with importance sampling technique involved. The concept of medium probability is introduced and the relationship between medium probability and simulation result variance is deduced. And based on this conclusion, the sampling function which will minimum the simulation result variance is figured, and cirque and semi-cirque intercepting tail importance sampling methods, as importance sampling techniques, are built. Especially, the ratio between the sampling function to the original distribution function is constant in the methods and the sampling points distribute in a spherical space, which take the origin as a center and the distance from the origin to the limit state surface as a radius. Furthermore, the quantitative description for the reduction of variance of simulation results can be obtained. The results of example and analysis indicate that the variance of simulation results by cirque and semi-cirque intercepting tail importance sampling methods can be reduced to one tenth and one twentieth of that by a direct method.

关 键 词：MONTE Carlo法 柯西不等式 中间概率 重要抽样方法 圆环取尾抽样方法 

分 类 号：TU311.4[建筑科学—结构工程]