摘要
由于蒙特卡罗(MC)方法具有程序结构简单,收敛速度与问题维数无关等优点,故其在结构可靠性分析中得到了广泛应用。但是对于小失效概率等问题,计算效率低这一主要缺点限制了该方法的应用范围。为了解决MC方法存在的问题,通过引进单位超立方体中不同的低偏差点集代替伪随机数序列,并结合了重要抽样技术建立了结构可靠性分析的拟蒙特卡罗(QMC)方法。该方法不但可以大幅度减少抽样点数目,还能够得到确定性的估计值,避免传统MC方法只能得到概率意义下误差的缺陷。通过数值算例可以看出本文方法具有较高的计算精度和效率,因此适用于结构可靠性分析问题。
The Monte Carlo （MC） method has wide application in structural reliability problems not only for its simple program structure but also for the fact that its rate of convergence is completely independent of the number of dimensions of the problem under study. But, this method demonstrates poor computational efficien- cy in evaluating problems of small failure probability or problems that require a large amount of costly finite element analysis in each sampling cycle, and this disadvantage limits its application in structural reliability analy- sis. To overcome the deficiencies of the MC method, this article introduces and investigates various low-dis- crepancy sequences instead of pseudo random numbers to develop a quasi-Monte Carlo （QMC） method for esti mating the failure probability by combining these sequences with importance sampling. The proposed method exhibits advantages over the MC method in particular in that it is more accurate with the same number of sam- ples and that it produces a deterministic estimate of errors. The accuracy and efficiency of the proposed method are shown by numerical examples. Therefore, the QMC method would seem to qualify as a comprehensive tool in structural reliability analysis.
出处
《航空学报》
EI
CAS
CSCD
北大核心
2009年第4期666-671,共6页
Acta Aeronautica et Astronautica Sinica
关键词
可靠性
拟蒙特卡罗方法
误差估计
确定性点集
低偏差抽样
reliability
quasi-Monte Carlo methods
error estimate
deterministic point set
low discrepancy sampling
