基于Kriging模型梯度解析解的改进一次二阶矩方法  

An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model

作　　者：李宝玉[1,2] 张磊刚[2] 裘群海[2] 余雄庆 LI Baoyu;ZHANG Leigang;QIU Qunhai;YU Xiongqing(College of Aerospace Engineering ,Nanjing University of Aeronautics and Astronautics. Nanjing 210016 , China;China Academy of Launch Vehicle Technology. Beijing 100076 , China)

机构地区：[1]南京航空航天大学航空宇航学院,南京210016 [2]中国运载火箭技术研究院,北京100076

出　　处：《航空学报》2019年第5期150-157,共8页Acta Aeronautica et Astronautica Sinica

基　　金：军委装备发展部"十三五"装备发展领域基金(6140244010216HT15001)~~

摘　　要：改进一次二阶矩(AFOSM)法是一种基于功能函数梯度的结构可靠性分析方法,鉴于其对隐式函数的梯度较难求解,提出了一种基于Kriging模型梯度解析解的AFOSM方法,利用Kriging代理模型的解析表达式推导得到功能函数对输入变量的梯度解析解,为AFOSM中设计点的确定提供高精度的梯度信息。通过Kriging与AFOSM的结合,很好地解决了基于有限元模型的隐式情况下梯度计算量相当大、可靠性分析难的问题。数值与工程算例验证了所提Kriging梯度解析解的较高精确性,同时验证了所提基于Kriging解析解的AFOSM结构可靠性分析方法的正确性与较高精度。The Advanced First Order and Second Moment(AFOSM)method is a structural reliability analysis method based on the gradient information of performance function.Since the gradient information of the implicit function is difficult to solve,an AFOSM method based on the gradient analytical solution of Kriging surrogate model is proposed,using the analytical expression of Kriging surrogate model to obtain gradient information of the performance function with respect to input variables,and providing a high-precision gradient information for the computation of the design point in the AFOSM method.By combining Kriging and AFOSM,the problem of gradient calculation and reliability analysis in the implicit situation based on the finite element model can be better solved.Numerical and engineering examples are introduced to verify the high precision of the proposed gradient solution based on Kriging;besides,the accuracy and precision of the proposed Kriging analytical solution based AFOSM reliability analysis method are also verified.

关 键 词：结构可靠性 Kriging代理模型 梯度解析解 改进一次二阶矩 失效概率 

分 类 号：V19[航空宇航科学与技术—人机与环境工程] TB114.3[理学—概率论与数理统计]