多模式自适应重要抽样法及其应用  

AN ADAPTIVE IMPORTANCE SAMPLING ALGORITHM AND ITS APPLICATION FOR MULTIPLE FAILURE MODES

作　　者：吕震宙[1] 刘成立[1] 傅霖[1] 

机构地区：[1]西北工业大学航空学院,120信箱西安710072

出　　处：《力学学报》2006年第5期705-711,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10572117);新世纪优秀人才支持计划(NCET-05-0868)资助项目.~~

摘　　要：针对多模式的可靠性分析,研究了其失效概率计算的自适应重要抽样法,该方法用模拟退火算法来自动调整每个失效模式的重要抽样函数,使其逐渐趋近于估计方差最小的重要抽样函数．对于多个模式系统失效概率的计算,采用混合加权自适应重要抽样的方法,反映了每个失效模式对系统失效概率的贡献；对于系统失效模式所含基本变量不全相同的情况,提出了扩展自适应重要抽样法,来统一所有失效模式中的基本变量,从而使得混合自适应重要抽样,可以方便地求解变量不全相同时的系统失效概率．对估计值方差和变异系数的计算公式进行了推导．验证算例结果,充分说明方法的合理性与可行性．For failure probability of a system with multiple failure modes, an adaptive importance sampling algorithm is developed. The importance sampling function for each failure mode is found and optimized by means of the simulated annealing method. During the optimization of the importance sampling function, the variance of the failure probability evaluation is reduced. For the system with multiple failure modes, a weighted mixed importance sampling function is proposed, in which the contribution of each failure mode to the system failure probability is represented appropriately. When not all basic variables are included in the limit state equation of some failure modes, an extended algorithm is presented to unify the basic variables in all failure modes, hence the weighted mixed importance sampling can be implemented successfully in the case. The variances and the coefficients of variation are derived for the failure probability evaluation. The feasibility and the validity of the presented method are illustrated by numerical and engineering examples.

关 键 词：重要抽样 随机性 模糊性 多模式 广义失效概率 

分 类 号：TB114.2[理学—运筹学与控制论]