一种基于主动学习克里金模型的证据理论可靠性分析方法

doi:10.3901/JME.2024.02.356

机械工程学报 ›› 2024, Vol. 60 ›› Issue (2): 356-368.doi: 10.3901/JME.2024.02.356

• 交叉与前沿 • 上一篇

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一种基于主动学习克里金模型的证据理论可靠性分析方法

韦新鹏, 姚中洋, 宝文礼, 张哲, 姜潮

湖南大学汽车车身先进设计制造国家重点实验室长沙 410082

收稿日期:2023-01-25 修回日期:2023-08-17 出版日期:2024-01-20 发布日期:2024-04-09
通讯作者: 张哲(通信作者)，男，1988年出生，博士，副教授，硕士研究生导师。主要研究方向为可靠性评估与优化、结构先进设计。E-mail：zhangzhe@hnu.edu.c
作者简介:韦新鹏，男，1990年出生，博士，助理研究员。主要研究方向为可靠性分析与优化设计。E-mail：weixp@hnu.edu.cn
基金资助:
湖南省科技创新计划(2021RC2054)、中央高校基本科研业务费(531118010677)、国家自然科学基金(51725502)和基础科研(JCKY2020110C105)资助项目。

Evidence-theory-based Reliability Analysis Method Using Active-learning Kriging Model

WEI Xinpeng, YAO Zhongyang, BAO Wenli, ZHANG Zhe, JIANG Chao

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082

Received:2023-01-25 Revised:2023-08-17 Online:2024-01-20 Published:2024-04-09

摘要/Abstract

摘要： 提出一种基于主动学习克里金模型的证据理论可靠性分析方法，可高效高精度计算出结构失效的可信度与似真度。首先，对不确定变量空间进行离散，并使用拉丁超立方抽样方法生成克里金模型的初始训练样本；其次，推导基于克里金模型快速判断证据变量焦元类别(正焦元、负焦元或边界焦元)的方法及克里金模型的迭代停止条件；再次，根据焦元类别判断方法发展基于功能函数符号预测正确概率的学习函数，可自适应增加训练样本以提高克里金模型关键区域的精度；最后，在克里金模型并非全局精确的情况下判断焦元的类别，并计算出结构失效的可信度和似真度。数值算例显示，该方法能够高效准确地判断所有焦元的类别，进而计算出结构失效可信度和似真度的确切值。

关键词: 结构可靠性, 认知不确定性, 证据理论, 主动学习, 克里金模型

Abstract: An evidence-theory-based reliability analysis method using the active-learning Kriging model is proposed to effectively calculate the belief and plausibility of a structural failure. First, the input uncertainty space is discretized and the Latin hypercube sampling is employed to generate the initial training samples for the Kriging model. Then, an efficient method based on the Kriging model is developed to classify all focal elements (positive, negative or boundary elements). Also developed is the stopping criterion of the active learning procedure. Next, a learning function based on the probability of correctly predicting the sign of performance function is proposed to adaptively increase the training samples and refine the Kriging model in important domain. Finally, the Kriging model, which is usually not globally accurate, is used to classify all focal elements correctly and obtain the belief and plausibility of a structural failure. Numerical examples show that the proposed method can classify all the focal elements correctly and efficiently, thus obtaining exact belief and plausibility.

Key words: structural reliability, epistemic uncertainty, evidence theory, active learning, Kriging model

中图分类号:

TB114

韦新鹏, 姚中洋, 宝文礼, 张哲, 姜潮. 一种基于主动学习克里金模型的证据理论可靠性分析方法[J]. 机械工程学报, 2024, 60(2): 356-368.

WEI Xinpeng, YAO Zhongyang, BAO Wenli, ZHANG Zhe, JIANG Chao. Evidence-theory-based Reliability Analysis Method Using Active-learning Kriging Model[J]. Journal of Mechanical Engineering, 2024, 60(2): 356-368.

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一种基于主动学习克里金模型的证据理论可靠性分析方法

Evidence-theory-based Reliability Analysis Method Using Active-learning Kriging Model

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