东华大学学报（英文版）2025，Vol.42Issue(4)：409-416,8.DOI:10.19884/j.1672-5220.202408005
基于Kriging模型和球冠区域积分的结构可靠性分析方法
Structural Reliability Analysis Method Based on Kriging and Spherical Cap Area Integral
摘要
Abstract
In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher accuracy,the additional computation of the Hessian matrix leads to lower computational efficiency.Additionally,when the dimensionality of the random variables is high,the approximation formula of SORM can result in larger errors.To address these issues,a structural reliability analysis method based on Kriging and spherical cap area integral is proposed.Firstly,this method integrates FORM with the quasi-Newton algorithm Broyden-Fletcher-Goldfarb-Shanno(BFGS),trains the Kriging model by using sample points from the algorithm's iteration process,and combines the Kriging model with gradient information to approximate the Hessian matrix.Then,the failure surface is approximated as a rotating paraboloid,utilizing the spherical cap to replace the complex surface.For the n-dimensional case,the hyperspherical cap area expression is combined with the integral method to calculate the failure probability.Finally,the method is validated through three examples,demonstrating improved computational accuracy and efficiency compared to traditional methods.关键词
结构可靠性分析/拟牛顿算法/Kriging模型/球冠区域积分Key words
structural reliability analysis/quasi-Newton algorithm/Kriging model/spherical cap area integral分类
机械制造引用本文复制引用
张吉祥,陈振中,陈革,李晓科,赵鹏程,潘强华..基于Kriging模型和球冠区域积分的结构可靠性分析方法[J].东华大学学报（英文版）,2025,42(4):409-416,8.基金项目
National Natural Science Foundation of China(No.52375236) （No.52375236）
Fundamental Research Funds for the Central Universities,China(No.23D110316) （No.23D110316）
