多模式广义失效概率计算的数值模拟法及其工程应用

提出了安全与失效状态含有模糊信息时，广义失效概率计算的数值模拟，及相应的方差估算，并提出了对应的数值积分方法．当状态变量服从正态分布，且其对模糊安全域的隶属函数为正态型时，单个模式的广义失效概率具有精确解．首先利用这种特殊情况检验了所提数值模拟的精度，结果表明对于数值模拟法，随抽样次数的增加，估计值逐渐收敛于真实值．然后利用扩展原理和概率定理，提出两个及两个以上失效模式数广义失效概率的数值模拟计算方法以及相应的数值积分方法．对于工程结构问题，一般在删除次要失效模式之后，主要失效模式的数目不会太多，因此用该数值模拟与数值积分法可以得到精度较高的解．工程算例结果证明了此结论．另外还对所提的两种方法的适用范围做了讨论．

General Failure Probability Simulation and Application for Multi-Mode

A general failure probability simulation and deviation evaluation methods were presented for fuzzy safety state and fuzzy failure state. And the corresponding number integral method was si- multaneously established. AS the distribution of state variable and the membership of the state variable to the fuzzy safety set were normal, the general failure probability of the single failure mode had pre- cise analytic solution, which was used to verify the precision of the presented methods. The results show that the evaluation of the simulation method convergences to the analytic solution with the num- ber increase of the sampling. The above methods for the single failure mode was extended to the mul- ti-mode by the expansion and probability principles. The presented methods were applied to the engi- neering problem. For the number of significant mode is not too many, the high precision solution can be given by the presented number simulation and number integral methods, which is illustrated by the engineering examples. In addition, the application scope of the methods was discussed.