同时考虑基本变量和失效域模糊性的广义失效概率数字计算方法

针对基本变量和失效域均具有模糊性的广义可靠性分析问题,提出了一种基于模拟退火优化的高效数字计算方法。在数字模拟的过程中,由模拟退火优化的Metropolis准则逐渐优化提取样本的重要抽样密度函数。由于基本变量和失效状态均含有模糊不确定性,因此所提算法在构造重要抽样函数时考虑了两个因素的影响,其一是基本变量的等价联合概率密度函数,其二是状态变量对模糊失效域的隶属函数,从而使得对广义失效概率贡献大的样本出现的概率较大,提高了抽样效率和计算精度。所提算法在模拟退火逐渐寻优的过程中,充分利用了过程中的信息,进一步提高了计算的效率,算例的结果也表明本文所提方法是合理可行的。

A Numerical Algorithm for General Failure Probability with Fuzzy Basic Variables and Fuzzy States

For general reliability analysis with fuzzy basic variables and fuzzy failure domain,an improved numerical simulation algorithm is presented on the basis of simulated annealing optimization.During the simulation procedure,the importance sampling function,from which the samples for evaluation of the general failure probability are taken,is gradually optimized by Metropolis rule in the simulated annealing method.Due to fuzziness both in the basic variables and in failure domain,two factors,i.e.,the equivalent joint probability density function of the basic variables and the membership of the state variable to the fuzzy failure domain,are taken into consideration in the construction of the importance sampling function.From the optimized importance sampling function,the samples contributing significantly to the general failure probability can be taken out with high probability.Hence the sampling efficiency and the precision of simulation are improved.In the present method,the information of the simulation obtained from the gradual optimization of importance sampling is sufficiently utilized,which improved the sampling efficiency further.Illustrations are used to explain the rationality and feasibility.