Fuzzy random reliability analysis by iteration based subset simulation

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 corresponding 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.