摘要
针对主动学习Kriging(Active Learning Kriging,ALK)模型在评估小失效概率时遇到的候选样本过多、计算耗时的问题,提出了一种结合ALK模型与子集模拟(Subset Simulation,SS)的双阶段代理模型方法——ALK⁃SS2。首先在第1阶段基于构建的极限状态函数代理模型,采用较少数量的SS最后一层样本作为候选样本完成极限状态面的粗略近似,然后在第2阶段选择更大样本量的SS最后一层样本来细化第1阶段的极限状态函数代理模型,以获得更高的精度。此外,考虑到传统ALK模型的收敛准则太过于保守,在ALK⁃SS2评估的失效概率基础上,提出了一种更高效的基于失效概率误差的收敛标准,进一步提高了该方法的效率。通过4个算例的测试以及同类方法的对比,证明其具有较高的计算精度和计算效率,适用于处理小失效概率问题和耗时的隐式功能函数问题。
When estimating very small failure probability,the methods based on active learning Kriging(ALK)model usually need too many candidate points and time⁃consuming calculation.To address this problem,this paper proposes a two⁃stage surrogate model method,ALK⁃SS2,which combines the ALK model and subset simulation(SS).Firstly,based on the constructed surrogate model in the first stage,the method uses a small number of SS last layer samples as candidate samples to complete the rough approximation of the limit state surface,and then in the second stage,it selects the SS last layer samples with a larger sample size to refine the surrogate model in the first stage,so as to obtain higher accuracy.In addition,considering the conventional stopping criteria are too conservative,based on the failure probability evaluated by ALK⁃SS2,a new stopping criterion based on failure probability error is proposed,which further improves the efficiency of the method.From the investigation of four examples and the comparison with relative methods,it is proved that the proposed method has high calculation accuracy and efficiency,and is suitable for dealing with small failure probability problems and time⁃consuming implicit function problems.
作者
刘泽清
程鑫
杨旭锋
LIU ZeQing;CHENG Xin;YANG XuFeng(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,China)
出处
《机械强度》
CAS
CSCD
北大核心
2024年第1期96-106,共11页
Journal of Mechanical Strength
基金
中央高校基本科研业务费专项资金(2682022ZTPY079)
四川省科技计划项目重点研发项目(2021YFG0178)
国家自然科学基金项目(51705433)资助。
