自适应多保真度Kriging模型辅助的一阶可靠性分析方法

doi:10.3901/JME.2025.18.344

机械工程学报 ›› 2025, Vol. 61 ›› Issue (18): 344-365.doi: 10.3901/JME.2025.18.344

• 交叉与前沿 • 上一篇

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自适应多保真度Kriging模型辅助的一阶可靠性分析方法

孟德彪^1,2, 杨恒飞^1,2, 杨世源³, 苏晓燕⁴, 朱顺鹏¹

1. 电子科技大学机械与电气工程学院成都 611731;
2. 电子科技大学广东电子信息工程学院东莞 523808;
3. 波尔图大学工程系波尔图 4150-564 葡萄牙;
4. 上海电力大学自动化工程学院上海 200090

收稿日期:2024-10-12 修回日期:2025-03-25 发布日期:2025-11-08
作者简介:孟德彪(通信作者)，男，1985年出生，博士，副教授，硕士研究生导师。主要研究方向为不确定性量化和可靠性评估、复杂系统建模、基于不确定性的设计优化。E-mail：dbmeng@uestc.edu.cn;杨恒飞，男，2000年出生。主要研究方向为可靠性分析、可靠性设计优化。E-mail：202321040145@std.uestc.edu.cn;杨世源，男，1998年出生，博士研究生。主要研究方向为可靠性分析、可靠性设计优化。E-mail：up202311575@edu.fe.up.pt;苏晓燕，女，1986年出生，博士，副教授。主要研究方向为信息融合、不确定信息处理、复杂系统关联分析、人因可靠性分析。E-mail：suxiaoyan@shiep.edu.cn;朱顺鹏，男，1983年出生，博士，教授，博士研究生导师。主要研究方向为结构完整性评定、失效物理可靠性分析、疲劳强度与可靠性设计、损伤容限与寿命预测。E-mail：zspeng2007@uestc.edu.cn
基金资助:
国家自然科学基金(12232004)、广东省基础与应用基础研究基金海上风电联合基金(2024A1515240025)和国家留学基金委(202406070025，202406070043)资助项目

Adaptive Multi-fidelity Kriging Model-assisted First-order Reliability Analysis Method

MENG Debiao^1,2, YANG Hengfei^1,2, YANG Shiyuan³, SU Xiaoyan⁴, ZHU Shunpeng¹

1. School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731;
2. Institute of Electronic and Information Engineering of UESTC in Guangdong, Dongguan 523808;
3. Faculty of Engineering, University of Porto, Porto 4150-564, Portugal;
4. School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090

Received:2024-10-12 Revised:2025-03-25 Published:2025-11-08

摘要/Abstract

摘要： 结构可靠性分析对于保障工程装备安全可靠运行至关重要。传统的一阶可靠性方法及其改进算法精度受限于极限状态函数的类型与梯度信息，往往无法适用于复杂工程案例。面对日益复杂的工程场景，虽然多保真度模型的建立策略被广泛研究，但在可靠性分析中，其应用潜力尚有待进一步开发。为此，发展一种自适应多保真度Kriging(Multi-fidelity Kriging，MF-Kriging)模型辅助的一阶可靠性分析方法。首先，通过增广拉格朗日函数将一阶可靠性分析问题转化为无约束优化问题，从而使其能够采用启发式优化算法求解。其次，通过融合多个数据源进行自适应MF-Kriging建模，以进一步降低可靠性分析的计算成本。基于该可靠性分析方法，任意自适应MF-Kriging建模策略不论是全局搜索或者是局部搜索均可嵌套使用。另外，考虑到一阶可靠性方法的重要步骤之一是精确定位设计验算点(Most probable point，MPP)，提出一种混合MF-Kriging建模策略。通过权衡全局搜索策略和基于迭代MPP邻域的局部搜索策略，平衡可靠性分析的局部精确度以及全局收敛性。最后，利用四个数学算例和三个工程案例对所提出方法进行了应用。结果表明，该可靠性分析方法在精度、效率和鲁棒性方面均具有显著优势。

关键词: 结构可靠性分析, 一阶可靠性方法, 多保真度Kriging模型, 启发式优化算法

Abstract: Structural reliability analysis is crucial for ensuring the safe and reliable operation of engineering equipment. The accuracy of traditional first-order reliability methods and their improved algorithms is limited by the type of limit state functions and gradient information，which may not be applicable to certain complex engineering cases. In the face of increasingly complex engineering scenarios，although the establishment strategies for multi-fidelity models have been widely studied，their application potential in reliability analysis remains to be further developed. Therefore，an adaptive Multi-Fidelity Kriging (MF-Kriging) model-assisted first-order reliability analysis method is proposed in this study. Firstly，the first-order reliability analysis problem is transformed into an unconstrained optimization problem through the augmented Lagrange function，enabling the use of heuristic optimization algorithms for its solution. Secondly，adaptive MF-Kriging modeling is employed by integrating multiple data sources to further reduce the computational cost of reliability analysis. Based on this reliability analysis method，any adaptive MF-Kriging modeling strategy，whether global or local search，can be nested. Additionally，considering that one of the important steps of the first-order reliability method is to accurately locate most probable point(MPP)，this study proposes a hybrid MF-Kriging modeling strategy. By balancing a global search strategy with a local search strategy based on iterative MPP neighborhood，it achieves a trade-off between local accuracy and global convergence in reliability analysis. Finally，the proposed method was applicated through four mathematical examples and three engineering cases. The results illustrate that the proposed method offers significant advantages in terms of accuracy，efficiency，and robustness.

Key words: structural reliability analysis, first-order reliability method, multi-fidelity Kriging model, heuristic optimization algorithms

中图分类号:

TB114

孟德彪, 杨恒飞, 杨世源, 苏晓燕, 朱顺鹏. 自适应多保真度Kriging模型辅助的一阶可靠性分析方法[J]. 机械工程学报, 2025, 61(18): 344-365.

MENG Debiao, YANG Hengfei, YANG Shiyuan, SU Xiaoyan, ZHU Shunpeng. Adaptive Multi-fidelity Kriging Model-assisted First-order Reliability Analysis Method[J]. Journal of Mechanical Engineering, 2025, 61(18): 344-365.

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自适应多保真度Kriging模型辅助的一阶可靠性分析方法

Adaptive Multi-fidelity Kriging Model-assisted First-order Reliability Analysis Method

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