分布参数为随机变量情况下可靠性灵敏度求解的方向抽样法

Directional Sampling Based Reliability Sensitivity Analysis with Random Distribution Parameter

针对工程中随机变量分布参数存在不确定性的情况,定义分布参数为区间内的随机变量情况下的可靠性灵敏度,并建立可靠性灵敏度求解的方向抽样法。在所建立的方向抽样法中,Monte Carlo法被用来模拟分布参数的样本,而对于每个分布参数样本点,方向抽样法被用来进行可靠性灵敏度分析,最后在整个分布参数空间上对可靠性灵敏度积分,以获得分布参数为区间内随机变量情况下的可靠性灵敏度的估计值,并对所推导的可靠性灵敏度估计值进行方差分析。通过算例比较方向抽样法与双重Monte Carlo数字模拟法,分析结果验证了方向抽样方法是可行和有效的。

For random variable involving uncertain distribution parameter commonly existing in engineering,the uncertain distribution parameter is assumed as uniformly distributing in an interval,on which a new reliability sensitivity is defined and its solution is given by use of the directional sampling method.In the given directional sampling method for solving the new reliability sensitivity,Monte Carlo method is used to simulate the samples of the interval distribution parameter,and the directional sampling is employed to analyze the reliability sensitivity corresponding to the distribution parameter sample.Finally,the estimations of the reliability sensitivity can be calculated by integral on the whole distribution parameter space,the variances of the reliability sensitivity estimations by directional sampling method are derived approximately.Directional sampling based method is compared with double Monte Carlo based method by illustrations,and the results show that the directional sampling method is feasible and effective.