基于最小割集理论的可靠性计算精度提高方法

A Method for Improving Computational Accuracy of Reliability Based on the Theory of the Minimum Cut Set

针对功能函数存在非线性和多极值点的情况,提出将功能函数分段处理,利用最小割集的概念进行失效概率计算的新方法:运用多个二次功能函数分段取代复杂的原功能函数,使所有二次功能函数失效区的组合与原功能函数失效区尽可能一致,并用二阶可靠性方法计算各个二次功能函数的可靠性指数;利用最小割集的概念,得到用所有的二次功能函数失效区来表达原失效区的最小割集形式,并通过等效失效区替代二次功能函数失效区,可用等效失效区的最小割集形式表达原失效区;通过重新规定按一阶可靠性方法计算的可靠性指数,使之适用于失效区包含坐标原点的场合,实现多个等效失效区组合失效概率的近似计算,得到原失效区的近似概率。算例验证了方法是可行的,并可大幅度提高失效概率的计算精度。

According to the nonlinearity and the multiple extreme value points of performance function, it is dealt with piecewise and a new computing method of failure probability based on the minimum cut set is put forwards. Multiple quadratic performance functions are used to replace the original complicated performance function piecewise, and the combination of failure domains of these quadratic performance functions is as close as to the failure domain of original performance function. The reliability indexes of quadratic performance functions are calculated by second order reliability method. All the minimum cut sets to describe the original failure domain are obtained by using the failure domains of quadratic performance functions according to the concept of the minimum cut set. All the minimum cut sets of equivalent failure domains were obtained to express the original failure domain by substituting quadratic failure domains with equivalent failure domains. Reliability index calculated by first order reliability method is redefined so that it could be suitable to the case that the origin of coordinates is in failure domain. And then, the combination of failure probabilities of multiple equivalent failure domains could be computed and the approximate probability of the original failure domain could be obtained. The example shows that the method is feasible and the calculation accuracy of failure probability could be improved greatly.