结构混合可靠度计算的自适应重要性抽样方法

针对直接蒙特卡罗方法在高维非线性结构混合可靠度模拟中稳定性差和效率低的问题，将马尔可夫链自适应重要性抽样技术引入混合可靠度计算过程．经实验确定了马尔可夫链转移概率分布，可快速获得近似服从最优重要性抽样函数的系列状态点．根据状态点的一阶原点矩和二阶中心矩来确定所采用的重要性抽样函数；对区间变量进行等距划分，并计算以区间变量为自变量的可靠度平均值，可得到混合可靠度值；通过算例对本方法、非自适应重要性抽样法和直接蒙特卡罗法进行了对比，表明了本方法稳定高效的优势，为结构混合可靠度计算提供了新途径．

Adaptive importance sampling scheme simulate structural hybrid reliability

To improve the efficiency and stability of the direct Monte Carlo method,the adaptive importance sampling method by Markov Chain was introduced to the hybrid reliability analysis.The improved Markov chain simulation technique was proposed to gain the importance samples in the failure domain.These samples′ stationary distribution is the optimal importance sampling function.So the first and second moments of the optimal importance sampling function were obtained.Thus the chosen sampling function can be determined.By equidistant partition of the interval parameters,the average value of the random reliability is the structural hybrid reliability.The proposed method was compared with the other two previous methods through a numerical example.Results show that the proposed method has good performance in efficiency and stability.