考虑基本变量模糊与随机性的广义自适应重要抽样法

Adaptive Importance Sampling Algorithm for Fuzzy-Random failure Probability

基于模糊随机广义可靠性分析向随机可靠性分析的转换,提出了模糊随机广义失效概率计算的自适应重要抽样法,该方法利用模拟退火智能优化,在模拟的过程中逐步逼近模糊随机广义设计点,并在模拟过程中自适应地构造重要抽样函数,从而使得模糊随机失效概率的计算效率和精度大为提高。与传统的重要抽样法相比,本文方法无需首先求解失效模式的设计点。对非线性失效区和复杂等价概率密度函数,由于模拟退火智能优化在寻找设计点时比诸如一次二阶矩法(FOSM)更为有效,因而所提方法适合非线性失效区和复杂等价概率密度函数情况下的广义可靠性分析。另外,随着重要抽样密度函数逐步向最优值的自动调整,抽取的样本数逐渐增大,使后续构建的重要抽样函数更能体现对广义失效概率贡献的重要程度,并使失效概率的计算更加准确。文中算例证明了所提方法的合理性。

An adaptive importance sampling algorithm is presented to evaluate fuzzy-random general failure probability,where a simulated annealing optimization is employed to seek the fuzzy-random design point—the Most Probable Failure Point(MPFP) in the failure region.The efficiency of the simulated annealing is more than that of the first order and second moment for seeking the MPFP,this method is especially suitable for the failure probability computation with the highly non-linear failure region and the complicated equivalent joint probability density function.The contribution of the set of importance sampling functions to the fuzzy-random failure probability is represented by the designed simulation number to lead to more accurate computation.The illustrations verify the feasibility and efficiency of the proposed method.