模糊随机可靠性分析的迭代子集模拟法

FUZZY RANDOM RELIABILITY ANALYSIS BY ITERATION BASED SUBSET SIMULATION

针对同时存在随机基本变量和模糊基本变量的结构可靠性分析,提出一种模糊可靠度隶属函数求解的迭代子集模拟法。在模糊变量的某个给定的隶属度水平上,所提方法通过迭代策略求解使功能函数取极值的模糊基本变量的取值点及相应的收敛后的最可能失效点(也称设计点),再运用子集模拟法在缩减的随机变量空间内求得可靠度的上、下界,最后在每个隶属度水平上执行该分析过程,即可求得模糊可靠度的隶属函数。相比模糊随机可靠性分析的直接Monte Carlo法,所提方法在保证结果精度的同时大大减小了计算量,而且该方法对变量的分布形式、变量维数、极限状态方程的表达形式及非线性程度均没有限制,适用范围十分广泛。所提方法的优点在算例中得到验证。

For reliability analysis of structure with random variables as well as fuzzy ones, a new iteration based subset simulation （SubSim） is presented for obtaining the membership function of fuzzy reliability. Using iterating strategy, the values of the fuzzy variables which make the performance function take extreme values are firstly obtained at the given membership level, and the eorresponding convergent most probable points （usually named as design points） are also obtained simultaneously. Then SubSim is employed to obtain the bounds of the reliability in the reduced random variables space. At last, this analysis procedure is performed at each membership level and the membership function of fuzzy reliability can be obtained. Compared with the direct Monte Carlo simulation, the presented method largely reduces computational cost without a loss of accuracy. This method also has a comprehensive applicability because it has no limit on the variables＇ dimension and distribution, the type and nonlinearity of the limit-state function. The advantages of the presented method are demonstrated by several examples.