摘要
在估计小失效概率时,基于主动学习Kriging(Active learning Kriging,ALK)模型的可靠性方法常常面临候选样本过多,计算耗时的问题。针对这一问题,引入改进的交叉熵自适应重要抽样(Improved cross-entropy adaptive important sampling,iCE-AIS),提出一种融合ALK模型与iCE-AIS的高效可靠性方法。该方法记为ALK-iCE-AIS。在ALK-iCE-AIS中,iCE-AIS根据Kriging模型的预测抽取重要样本,Kriging模型在iCE-AIS的重要样本中选取最优训练点。如此迭代,Kriging模型将越来越精确地预测失效域,由iCE-AIS估计的失效概率也愈加精确。鉴于传统的收敛标准比较保守,特在iCE-AIS的框架下进一步提出一种基于失效概率误差的收敛标准,以保证Kriging模型在达到目标精度要求后及时终止学习。从算例测试来看,ALK-iCE-AIS能够以较少的训练样本获得准确的失效概率估计值。
When estimating very small failure probability,the traditional methods based on active learning Kriging(ALK)model usually needs too many candidate points.This problem will cause the learning process to be very time-consuming.To address this problem,the improved cross-entropy adaptive important sampling(iCE-AIS)is introduced and a new reliability method fusing ALK model and iCE-AIS is proposed in this paper.The new method is termed as ALK-iCE-AIS.In ALK-iCE-AIS,the iCE-AIS generates important samples according to the prediction of Kriging model and the Kriging model chooses the next best training points from the importance samples of iCE-AIS.After several iterations,the Kriging model will be finely predicting the failure regions and accurate failure probability is obtained by iCE-AIS.Considering the conventional stopping criteria are too conservative,under the framework of iCE-AIS,a new stopping criterion based on failure probability error is proposed to ensure that the Kriging model can automatically stop the learning process after reaching the accuracy requirements.From the investigation of several examples,the ALK-iCE-AIS has excellent accuracy and efficiency:it can accurately estimate very small failure probability with a small number of training samples.
作者
杨旭锋
程鑫
刘泽清
YANG Xufeng;CHENG Xin;LIU Zeqing(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031)
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2024年第16期73-82,共10页
Journal of Mechanical Engineering
基金
中央高校基本科研业务费专项资金(2682022ZTPY079)
四川省科技计划重点研发(2021YFG0178)
国家自然科学基金(51705433)资助项目。
