【作者】 刘骁骁； 马引刚； 任兴民；

【Author】 Liu Xiao-Xiao;Ma Yin-Gang;Ren Xing-Min;Department of Engineering Mechanics,Northwestren Ploytechnical Univisity;

【机构】 西北工业大学力学与土木建筑学院；

【摘要】 混合可靠性分析(HRA)中现有的主动学习Kriging(ALK)算法不能够处理小概率事件[1-3]。此外,当存在大量的不确定性,ALK-HRA算法会降低数值有效性。为了克服以上算法存在的缺陷,将ALK方法与重要性抽样(IS)相结合,提出所谓的ALK-IS算法并应用在HRA中。然而,同时包含随机变量和区间/凸集变量的HRA方法不能够处理复杂的多源不确定性问题。因此,提出了同时包含随机变量和多维平行六面体变量的更为一般的HRA框架(MGHRA),并紧密的和ALK-IS相结合。在联合不确定性分析框架中多维平行六面体能够描述区间变量的相关和独立性。所提方法称为ALK-MGHRA-IS,该方法仅需少量的函数调用就可精确地获得小失效概率的上下界。为了使所提方法能够更为高效,引入基于KKT条件的全局优化算法减轻搜索极值的负担。三个算例和一个实际工程应用展示了所提方法的精确性和有效性。更多还原

【Abstract】 The existing active learning Kriging(ALK) algorithm [1-3] in hybrid reliability analysis(HRA) is found not suitable for estimating small failure probabilities. Moreover,ALK-HRA reduces its numerical efficiency when the number of uncertain variables increases. To overcome the above defects,an original method called ALK-IS for ALK-based Importance Sampling can be developed in HRA. However,HRA with both random and interval/ellipsoid variables cannot deal with complex "multi-source uncertainty" problems. As a consequence,a more general HRA(MGHRA) with both random and parallelepiped convex variables is presented and closely combined with ALK-IS. A multidimensional parallelepiped convex model is used to describe independent and correlated interval variables in a unified framework. The proposed approach is termed as ALK-MGHRA-IS,which can accurately obtain the bounds of small failure probabilities with only a few function calls. To make ALK-MGHRA-IS more efficient,an optimization method based on Karush–Kuhn–Tucker conditions(KKT) is introduce to relieve the burden of searching the extreme values. Four numerical examples are investigated to demonstrate the efficiency and accuracy of the proposed method.更多还原