中文摘要：

针对工程实际中由于信息量不足而难以准确确定基本随机变量分布参数的情况,采用模糊数来描述分布参数,建立了模糊分布参数情况下的可靠性特征值分析模型,并研究了模型的求解方法。首先采用通用数字模拟法对模型进行了求解,该方法的优点是概念简单易于实现,并且其结果随模拟样本的增加而收敛于真值,但该方法的效率很低。为提高模型求解的效率,基于已有的三点估计建立了模型求解的单重和双重矩估计方法。在给出了所建模型求解方法的实现过程后,通过数值算例、工程算例来说明模型的合理性以及所提求解方法的精度和效率。相对于通用数字模拟方法来说,单重矩方法和双重矩方法具有较高的效率,而且矩方法比较简单,计算过程中不需要迭代和求导,可以方便的应用于分布参数为模糊数时的可靠性模型的求解。

英文摘要：

In case that available information is not sufficient to determine distribution parameters,fuzzy numbers can be used to describe the distribution parameters.For fuzzy distribution parameters,a new reliability measure model is established on characteristic value analysis,and the solutions of the model are proposed.Firstly,universal numerical simulation is introduced to estimate the new reliability measure.The universal numerical simulation is simple in concept and easy in implementation,and its solution converges to the real value.However,the efficiency of this method is low.In order to improve the efficiency,a single loop moment method and a double loop moment method are presented to estimate the new reliability measure based on the available three-point estimation.After the detailed implementations are described for the presented solutions of the model,several numerical and engineering samples are used to demonstrate the rationality of the model,the efficiency and the precision of the presented solutions.Comparing with the universal numerical simulation,the single loop moment method and the double one possess higher efficiency for solving the new reliability measures,and moment based methods are easily to be implemented,in which neither iteration nor gradient is required,so they can be conveniently applied to the reliability analysis involving fuzzy distribution parameters.