基于子集抽样的模糊失效概率分析新方法

NOVEL METHOD OF FUZZY FAILURE PROBABILITY ANALYSIS ON THE BASIS OF SUBSET SAMPLING

针对结构失效和安全状态具有模糊性的失效概率分析问题,提出一种基于子集抽样的新方法。所提方法首先将模糊失效域离散为功能函数变化较小的若干子集,然后利用马尔可夫链Monte Carlo法求得各子集上不考虑状态模糊性的随机失效概率,最后利用各子集中功能函数对模糊失效域的隶属度与相应随机失效概率乘积的和,求得模糊失效概率。文中用简单算例和工程算例比较所提方法与Monte Carlo法的效率和精度,结果表明,文中方法在保证计算精度的条件下,具有更高的计算效率。

For fuzzy failure probability evaluation of structure with fuzzy failure and fuzzy safety state, a novel method is presented on the basis of subset sampling. Firstly, the fuzzy failure region is separated as some subsets, in which the value of performance function keeps a constant approximately and membership of the performance function to the fuzzy failure state keeps a constant approximately as well. Secondly, Markov Chain based Monte Carlo method is employed to calculate the random failure probability of each subset, lastly, the products of the random failure probability and the corresponding approximate constant membership value at each subset to the fuzzy failure state are added to obtain the fuzzy failure probability. Comparing to Monte Carlo method, the efficiency of the presented method is improved greatly while the precision of the fuzzy failure probability evaluation is acceptable.