Kriging-高维代理模型建模方法研究与改进

doi:10.3901/JME.2024.05.249

机械工程学报 ›› 2024, Vol. 60 ›› Issue (5): 249-263.doi: 10.3901/JME.2024.05.249

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Kriging-高维代理模型建模方法研究与改进

孟原^1,2,3, 史宝军^1,2,3, 张德权^1,2,3

1. 河北工业大学省部共建电工装备可靠性与智能化国家重点实验室天津 300401;
2. 河北工业大学先进智能防护装备技术教育部重点实验室天津 300401;
3. 河北工业大学机械工程学院天津 300401

收稿日期:2023-03-02 修回日期:2023-12-10 出版日期:2024-03-05 发布日期:2024-05-30
通讯作者: 史宝军，男，1963年出生，博士，教授，博士研究生导师，泰山学者。主要研究方向为工程设计和装备可靠性、智能机器人、振动与冲击、CAD/CAE轻量化。E-mail2018029@hebut.edu.cn；shibj2003@126.com
作者简介:孟原，男，1995年出生，博士研究生。主要研究方向为工程设计和装备可靠性。E-mail202011201004@stu.hebut.edu.cn；张德权，男，1990年出生，博士，教授，硕士研究生导师。主要研究方向为工程设计和装备可靠性。E-maildequan.zhang@hebut.edu.cn
基金资助:
国家自然科学基金(U20A20201, 52275244)和河北省省级科技计划(225676163GH)项目资助。

Research and Improvement of Kriging-HDMR Modeling Method

MENG Yuan^1,2,3, SHI Baojun^1,2,3, ZHANG Dequan^1,2,3

1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300401;
2. Key Laboratory of Advanced Intelligent Protective Equipment Technology of Ministry of Education, Hebei University of Technology, Tianjin 300401;
3. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401

Received:2023-03-02 Revised:2023-12-10 Online:2024-03-05 Published:2024-05-30

摘要/Abstract

摘要： 传统代理模型技术在处理高维问题时，由于变量维数增加使得建模所需样本数量呈指数型增长，将导致计算成本显著提高。为了构建适用于高维问题的代理模型，在DIRECT优化算法基础上，改进其初始样本点位置，实现初始样本集的扩充，并将克里金(Kriging)建模方法与高维代理模型(High-dimensional model representation, HDMR)相结合，这样可避免建立的模型陷入局部最优，提出一种改进的Kriging-HDMR建模方法。iKriging-HDMR建模方法利用高维代理模型的优点，将高维问题的响应函数等效为一系列低维函数的叠加，发挥iKriging-HDMR建模方法的优势以减少建模过程所需样本点个数，提出一种新的收敛条件，从而减小代理模型的局部误差以保证建立的代理模型具有较高的精度。通过数值算例和机器人工程应用，验证了提出方法的有效性。结果表明，所提出的iKriging-HDMR建模方法可显著减少建模所需样本点数量，具有很好的计算精度和效率。

关键词: 高维代理模型, Kriging, DIRECT采样, 试验设计, 工业机器人

Abstract: When dealing with high-dimensional problems in traditional representation model technology, the number of sample points required for modeling increases exponentially due to the increase in variable dimension, which will lead to a significant increase in computational cost. In order to build a representation model suitable for high-dimensional problems, based on the DIRECT optimization algorithm, the initial sample point position is improved, the initial sample set is expanded, and the Kriging modeling method and high-dimensional model representation (HDMR), which can avoid the established model from falling into local optimality, and proposes an improved Kriging-HDMR (iKriging-HDMR) modeling method. The iKriging-HDMR modeling method uses the advantages of HDMR to equate the response function of the high-dimensional problem to a series of low-dimensional function superpositions, taking advantage of the iKriging-HDMR modeling method to reduce the number of sample points required in the modeling process number. A new convergence condition is proposed to reduce the local error of the agent model to ensure that the established agent model has high accuracy. The effectiveness of the proposed method is verified by numerical examples and robot engineering applications. The results show that the proposed iKriging-HDMR modeling method can significantly reduce the number of sample points required for modeling, and has good calculation accuracy and efficiency.

Key words: high dimensional model representation, Kriging, DIRECT sampling, design of experiment, industrial robot

中图分类号:

TP242

孟原, 史宝军, 张德权. Kriging-高维代理模型建模方法研究与改进[J]. 机械工程学报, 2024, 60(5): 249-263.

MENG Yuan, SHI Baojun, ZHANG Dequan. Research and Improvement of Kriging-HDMR Modeling Method[J]. Journal of Mechanical Engineering, 2024, 60(5): 249-263.

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Kriging-高维代理模型建模方法研究与改进

Research and Improvement of Kriging-HDMR Modeling Method

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