结构可靠度模拟的方向重要抽样法

方向抽样法是结构可靠度Monte—Carlo模拟的方法之一。同其他的抽样方法一样，为提高抽样效率，需进行重要抽样。本文提出一种新的方向重要抽样法，该方法通过构造以验算点为球心的椭球，将以验算点为抽样中心的方向矢量变换为以原坐标系原点为中心的方向矢量，进而建立重要方向抽样的失效概率估计公式。在这种方法中，所构造的椭球半轴的长度为待定参数。分析表明，对于实际结构中的非闭合型极限状态方程，理论上应使与极限状态曲面正交的半轴的长度大于由一次二阶矩方法计算的可靠指标，本文建议取可靠指标值的1．1—1．2倍，其余半轴的长度可通过优化确定，本文采用了边模拟边优化的方法。算例分析表明，本文方法可以大大提高模拟的效率和精度，在随机变量数目较多时效果更为明显。

Structural reliability analysis by importance directional simulation

It is one of attractive method for Monte-Carlo simulation of structural reliability in sphere coordinate system. To improve the simulation efficiency and accuracy, important sampling is necessary. A new important directional sampling approach is developed in this paper. By means of an ellipsoid whose center is located at the design point on the limit state surface, the directional vectors sampled at the design point were transmitted into directional vectors centered at the origin. Thus the formula to estimate the failure probability was set up. It is shown that the length of half axle that orthogonal to the limit state surface at design point should be larger than the reliability index computed based on First-Order Second-Moment method. The length of remained half axles can be determined based on optimization procedure. For the purpose of simplicity, an identical value was suggested. Numerical examples indicate that the approach presented is simple and efficiency.