结构可靠性分析的拟蒙特卡罗方法

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。

Quasi-Monte Carlo Method for Structural Reliability Analysis

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 efficiency 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 applicatio...