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工程力学  2013 

基于柯西不等式的结构可靠度取尾重要抽样法

DOI: 10.6052/j.issn.1000-4750.2011.06.0374

Keywords: 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

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Abstract:

该文采用柯西不等式对结构可靠度计算中MonteCarlo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。

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