高维性能因子系统结构可靠性的主动学习分析方法  

Active learning analysis method for structural reliability of systems with high dimensional performance factors

作　　者：李炳毅 贾祥 张鑫航 李博文 LI Bing-yi;JIA Xiang;ZHANG Xin-hang;LI Bo-wen(College of Systems Engineering,National University of Defense Technology,Changsha 410073,China;College of Science,National University of Defense Technology,Changsha 410073,China;State Key Laboratory of Astronautic Dynamics,Xián 710043,China)

机构地区：[1]国防科技大学系统工程学院,长沙410073 [2]国防科技大学理学院,长沙410073 [3]宇航动力学国家重点实验室,西安710043

出　　处：《控制与决策》2024年第12期4160-4170,共11页Control and Decision

基　　金：国家自然科学基金项目(72271238,71801219);湖南省自然科学基金项目(2021JJ20050);国防科技大学研究生科研创新项目(XJCX2023055)。

摘　　要：在系统的结构可靠性分析中,针对主动学习克里金(active learning Kriging, AK)方法中学习函数涵盖信息不全面、终止准则过于保守,导致在高维因子系统的求解中加点过多带来高昂成本、效率较低的问题,提出一种高维性能因子系统结构可靠性的主动学习分析方法.首先,基于初始样本构建Kriging模型,基于一种新的学习函数寻点并更新模型,该函数能够同时考虑极限状态面附近、方差所度量的不确定性大小以及候选点本身的概率密度情况,使得增加的学习点更具代表性;然后,使用预测值的最大相对误差作为加点终止准则;接着,估计系统的失效概率;最后,在3个数值函数算例验证的基础上,针对一个8维曲柄滑块机械结构中连杆的失稳问题进行研究.实验结果表明:与已有常见的学习函数相比,所提出方法在保证预测精度的条件下,减少了加点数量,能够实现准确、高效的可靠性分析.In the structural reliability analysis of the system,the learning function in the active learning Kriging(AK)method does not cover comprehensive information and the termination criterion is too conservative,resulting in too many points added in the solution process of the high-dimensional factor system.To solve the problems of high cost and low efficiency,an active learning analysis method for the structural reliability of systems with high-dimensional performance factors is proposed.First,the Kriging model is constructed based on the initial samples,and a new learning function is proposed,which considers the uncertainty measured near the limit state surface,the variance,and the probability density of the candidate points themselves,making the added learning points more representative and updating the model.Then,the maximum relative error of the predicted value is used as the termination criterion,and the failure probability of the system is estimated.Finally,based on the verification of three numerical function examples,the proposed method is applied in an instability problem of the connecting rod in an 8-dimensional crank slider mechanical structure.The experimental results show that the proposed method reduces the number of addition points while ensuring the prediction accuracy,and can achieve accurate and efficient reliability analysis compared with the typical learning functions.

关 键 词：可靠性分析 主动学习克里金 学习函数 终止准则 失效概率 

分 类 号：TB114.3[理学—概率论与数理统计]