针对结构可靠性分析中如何减小结构失效概率的问题,引入一种基于失效概率的全局灵敏度指标,通过分析指标,可判断基本变量的不确定性如何影响系统失效概率。求解全局灵敏度指标,在H—S方法基础上,提出一种改进估计量与重要抽样法相结合的方法,基本思想是用重要抽样法构造输入变量样本,寻找中间估计量,建立模型输出量和中间估计量;中间估计量和输入变量主效应、总效应之间的关系,然后求得变量基于失效概率全局灵敏度指标。由于所提方法继承了中间估计量的快速收敛性及重要抽样法高效搜索感兴趣区域样本的优点,因此在保证与标准Sobol方法计算结果同等精度的条件下,方法大大减少了对结构功能函数的计算次数,提高了效率,方便对精度和计算时间控制。最后,算例验证所提方法求解基于失效概率的全局灵敏度指标的准确性和高效性。
In order to analyze the effect of input variable on the failure probability of the system and reduce the failure probability, a failure probability based global sensitivity is investigated. Generally Monte carlo based method is widely used to solve the failure probability sensitivity measure, but its large computational cost can not be afforded, especially for the low failure probability in eomputationally engineering demanding problems. To overcome the disadvantage of MC method, an improved importance sampling method for global sensitivity measure of failure probability is proposed combining with H-S method. The main idea of the proposed method is firstly generating samples in interesting region by efficient importance sampling (IS) , then searching the proper estimator and establishing the relationship between failure probability based global sensitivity measure and the estimator, furthermore, obtaining the global sensitivity measure. Since the proposed method combines the fast convergence of H-S estimator and high efficient searching capability in interesting region of the IS. The proposed method is more efficient with enough accuracy, compared with the standard Sobol' method for the variance based on global sensitivity measure. Finally, two numerical examples and an engineering example are employed to demonstrate the reasonability of the proposed sensitivity measure and the efficiency of the proposed method.