基于两阶段主动学习Kriging模型的广义概率区间混合可靠性分析  

Generalized Probability and Interval Hybrid Reliability Analysis Based on Two-stage Active Learning Kriging Model

作　　者：余萌晨 龙湘云[1] YU Mengchen;LONG Xiangyun(State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha 410082)

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082

出　　处：《机械工程学报》2022年第6期274-288,共15页Journal of Mechanical Engineering

基　　金：国家自然科学基金(11802088,52175134);国家自然科学基金创新研究群体(51621004);基础科研(JCKY2020110C105)资助项目。

摘　　要：提出一种基于双阶段主动学习Kriging模型的广义概率区间混合可靠性分析方法(TALK-HRA)。该TALK-HRA方法可有效处理包含概率与区间模型、区间概率模型及其组合在内的多种混合模型。首先,建立第一阶段主动学习Kriging模型以选择有可能跨越极限状态面的高风险点,从而准确预测功能函数符号,并为给定区间参数下的失效概率计算奠定基础。其次,构造第二阶段的Kriging模型以学习最大或最小失效概率附近的区域,从而寻找失效概率的边界。再次,提出的TALK-HRA方法被应用到随机-模糊混合可靠性分析中。最后,通过五个算例验证该方法的有效性。结果表明,该方法不仅可以准确高效地计算多种概率区间混合模型下的可靠度,而且能应用于具有高非线性和多峰极限状态面的“黑箱”问题的可靠性分析。A generalized hybrid reliability analysis(HRA) method under probability and interval uncertainties by a two-stage active learning Kriging(TALK) model is proposed.The proposed TALK-HRA method can effectively deal with the probability and interval model,interval-probability model,as well as their combination.A first-stage active learning Kriging model is first established to locally select the high-risk points that may cross the limit state surface so as to predict the separator determining sign of performance functions accurately,and it lays the foundation for the calculation of the failure probability under the given interval.Then,a second-stage Kriging model is further constructed by approximating the region of interest around the maximal or minimal failure probability to calculate the upper and lower bounds of the failure probability.The possible application to random-fuzzy reliability analysis is also discussed.Finally,five numerical examples are investigated to demonstrate the validity of the proposed method.The results show that the proposed method can not only calculate the reliability of multiple types of probability interval hybrid models accurately and efficiently,but also be well applicable to the HRA of ‘black box’ problems with high nonlinearity as well as multi-peak limit state surface.

关 键 词：主动学习Kriging模型 概率和区间不确定性 混合可靠性分析 模糊随机可靠性 

分 类 号：TB114.3[理学—概率论与数理统计]