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

扫码分享

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.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.2024.05.249

http://www.cjmenet.com.cn/CN/Y2024/V60/I5/249

参考文献

[1] 魏昕，吴义忠，陈立平. 基于径向基函数的DIRECT全局优化方法[J]. 华中科技大学学报，2012，40(5)：6-9. WEI Xin，WU Yizhong，CHEN Liping. DIRECT global optimization method using radial basis functions[J]. Journal of Huazhong University of Science and Technology，2012，40(5)：6-9.
[2] 崔宝珍，孔维娜，马恺. 多项式响应面代理模型在立柱结构优化中的应用[J]. 机械设计，2017，34(4)：44-48. CUI Baozhen，KONG Weina，MA Kai. Application of polynomial response surface surrogate model in the large column structure optimization[J]. Journal of Machine Design，2017，34(4)：44-48.
[3] 李铁柱，李光耀，陈涛，等. 基于Kriging近似模型的汽车乘员约束系统稳健性设计[J]. 机械工程学报，2010，46(22)：123-129. LI Tiezhu，LI Guangyao，CHEN Tao，et al. Robustness design of occupant restraint system based on Kriging model[J]. Journal of Mechanical Engineering，2010，46(22)：123-129.
[4] 李恩颖，王琥，李光耀. 基于支持向量机回归的材料参数反求方法[J]. 机械工程学报，2012，48(6)：90-95. LI Enying，WANG Hu，LI Guangyao. Material parameter inverse technique based on support vector regression[J]. Journal of Mechanical Engineering，2012，48(6)：90-95.
[5] 韩忠华. Kriging模型及代理优化算法研究进展[J]. 航空学报，2016，37(11)：3197-3225. HAN Zhonghua. Kriging surrogate model and its application to design optimization：a review of recent progress[J]. Acta Aeronautica et Astronautica Sinica，2016，37(11)：3197-3225.
[6] FORRESTER A，KEANE A. Recent advances in surrogate-based optimization[J]. Progress in Aerospace Sciences，2009，45(1)：50-79.
[7] 彭磊，刘莉，龙腾. 基于动态径向基函数代理模型的优化策略[J]. 机械工程学报，2011，47(7)：164-170. PENG Lei，LIU Li，LONG Teng. Optimization strategy using dynamic radial basis function metamodel[J]. Journal of Mechanical Design，2011，47(7)：164-170.
[8] 龙腾，郭晓松，彭磊，等. 基于信赖域的动态径向基函数代理模型优化策略[J]. 机械工程学报，2014，50(7)：184-190. LONG Teng，GUO Xiaosong，PENG Lei ，et al. Optimization strategy using dynamic radial basis function metamodel based on trust region[J]. Journal of Mechanical Engineering，2014，50()：184-190.
[9] CHOWDHURY R，RAO B，PRASAD A. High dimensional model representation for structural reliability analysis[J]. Communications in Numerical Methods in Engineering，2009，25(4)：301-337.
[10] WU Xiaojing，PENG Xuhao，CHEN Weisheng，et al. A developed surrogate-based optimization framework combining HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems[J]. Structural and Multidisciplinary Optimization，2019，60(2)：663-680.
[11] 汤龙，李光耀，王琥. Kriging-HDMR非线性近似模型方法[J]. 力学学报，2011，43(4)：780-784. TANG Long，LI Guangyao，WANG Hu. Kriging-HDMR metemodeling technique for nonlinear problems[J]. Chinese Journal of Theoretical and Applied Mechanics，2011，43(4)：780-784.
[12] 黄志远，邱浩波，蔡习文. IDIRECT-HDMR高维近似模型方法及工程应用[J]. 机械制造与自动化，2015，44(3)：100-103. HUANG Zhiyuan，QIU Haobo，CAI Xiwen. IDIRECT-HDMR approximation model for high dimensional problems and engineering application[J]. Machine Building & Automation，2015，44(3)：100-103.
[13] WANG Hu，TANG Long，LI Guangyao. Adaptive MLS-HDMR metamodeling techniques for high dimensional problems[J]. Expert Systems with Applications，2011，38(11)：14117-14126.
[14] SHAN Songqing，WANG G. Metamodeling for high dimensional simulation-based design problems[J]. Journal of Mechanical Design，2010，132(5)：051009.
[15] CAI Xiwen，GAO Liang，LI Xinyu. Efficient generalized surrogate-assisted evolutionary algorithm for high-dimensional expensive problems[J]. IEEE Transactions on Evolutionary Computation，2020，24(2)：365-379.
[16] LIU Jie，CAI Heng，JIANG Chao，et al. An interval inverse method based on high dimensional model representation and affine arithmetic[J]. Applied Mathematical Modelling，2018，63：732-743.
[17] YUE Xinxin，ZHANG Jian，GONG Weijie，et al. An adaptive PCE-HDMR metamodeling approach for high-dimensional problems[J]. Structural and Multidisciplinary Optimization，2021，64(1)：141-162.
[18] LIU Jie，ZHAO Yue，LEI Fei，et al. Net-HDMR metamodeling method for high-dimensional problems[J]. Journal of Mechanical Design，2023，145(9)：1-25.
[19] RABITZ H，ALIS O. General foundations of high-dimensional model representations[J]. Journal of Mathematical Chemistry，1999，25(2)：197-233.
[20] HUANG Zhiyuan，QIU Haobo，ZHAO Ming，et al. An adaptive SVR-HDMR model for approximating high dimensional problems[J]. Engineering Computations，2015，32(3)：643-667.
[21] WANG Qian，FANG Hongbing. An adaptive high‐dimensional model representation method for reliability analysis of geotechnical engineering problems[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2020，44(12)：1705-1723.
[22] ZHANG Qi，WU Yizhong，LU Li，et al. An adaptive Dendrite-HDMR metamodeling technique for high-dimensional problems[J]. Journal of Mechanical Design，2022，144(8)：081701.
[23] JONES D，PERTTUNEN C，STUCKMAN B. Lipschitzian optimization without the Lipschitz constant[J]. Journal of Optimization Theory and Applications，1993，79(1)：157-181.
[24] 汤龙. 多参数非线性优化方法关键技术研究及应用[D].长沙：湖南大学，2013. TANG Long. The key of research and application of multi-parameter nonlinear optimization[D].Changsha：Hunan University，2013.
[25] MENG Zeng，ZHANG Zhuohui，ZHANG Dequan，et al. An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization[J]. Computer Methods in Applied Mechanics and Engineering，2019，357：112570.
[26] MENG Zeng，ZHANG Zhuohui，LI Gang，et al. An active weight learning method for efficient reliability assessment with small failure probability[J]. Structural and Multidisciplinary Optimization，2019，61(3)：1157-1170.
[27] LOPHAVEN S，NIELSEN H，SONDERGAARD J. DACE：a matlab kriging toolbox[M]. Lyngby：IMM，Informatics and Mathematical Modelling，The Technical University of Denmark，2002.
[28] WANG G，SHAN Songqing. Review of metamodeling techniques in support of engineering design optimization[J]. Journal of Mechanical Design，2007，129(4)：370-380.
[29] JIN R，CHEN W，SIMPSON T W. Comparative studies of metamodelling techniques under multiple modelling criteria[J]. Structural and Multidisciplinary Optimization，2001，23(1)：1-13.
[30] 周炜. 飞机自动化装配工业机器人精度补偿方法与实验研究[D]. 南京：南京航空航天大学，2012. ZHOU Wei. Compensation Method of industrial robot accuracy and experimental research for aircraft automated assembly[D]. Nanjing：Nanjing University of Aeronautics and Astronautics，2012.
[31] ZHANG Dequan，SHEN Shuohuo，WU Jinhui，et al. Kinematic trajectory accuracy reliability analysis for industrial robots considering intercorrelations among multi-point positioning errors[J]. Reliability Engineering & System Safety，2023，229：108808.
[32] ZHANG Dequan，HAN Zhonghao，WANG Fang，et al. Proficiency of statistical moment-based methods for analysis of positional accuracy reliability of industrial robots[J]. International Journal of Mechanics and Materials in Design，2021，17(2)：403-418.

Kriging-高维代理模型建模方法研究与改进

Research and Improvement of Kriging-HDMR Modeling Method

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	郭万金, 利乾辉, 徐明坤, 侯旭栋, 刘孝恒, 曹雏清, 赵立军. 高抗干扰性的无力传感器工业机器人外力估计方法[J]. 机械工程学报, 2026, 62(3): 366-383.
[2]	马强, 刘从臻, 赵鹏斌, 王鹏, 李爱强. 复合工况轮胎滚动阻力分析及优化设计[J]. 机械工程学报, 2025, 61(9): 437-448.
[3]	田威, 李鹏程, 缪云飞, 廖文和, 董松, 孟丹. 大型复材薄壁构件工业机器人高精度原位铣边加工新方法[J]. 机械工程学报, 2025, 61(7): 120-133.
[4]	李睿智, 陈悦敏, 闫纪红. 面向轨迹动态感知与自主决策的工业机器人数字孪生建模方法研究[J]. 机械工程学报, 2025, 61(7): 269-283.
[5]	王凯, 范小宁, 余畅, 吕召国. 基于动态Kriging模型的起重机金属结构可靠性解耦优化方法[J]. 机械工程学报, 2025, 61(2): 384-394.
[6]	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.
[7]	王嘉, 葛曼哲, 王子铭, 张露予, 王崇帅. 服役工况下基于电流信号的工业机器人谐波减速器故障建模[J]. 机械工程学报, 2025, 61(18): 366-377.
[8]	吕鸿昊, 诸正杰, 程宇航, 何平, 汪若菡, 陈富国, 杨华勇, 杨赓, 董娜. 工业机器人主动安全作业方法与应用[J]. 机械工程学报, 2025, 61(15): 174-184.
[9]	程洪鑫, 李璐祎, 周长聪. 基于Kriging模型和代理抽样的分布参数不确定性灵敏度分析方法[J]. 机械工程学报, 2024, 60(8): 370-383.
[10]	刘达新, 王科, 刘振宇, 许嘉通, 谭建荣. 基于数据融合与知识推理的机器人装配单元数字孪生建模方法研究[J]. 机械工程学报, 2024, 60(5): 36-50.
[11]	吕利叶, 鲁玉军, 王硕, 刘印, 李昆鹏, 宋学官. 代理模型技术及其应用：现状与展望[J]. 机械工程学报, 2024, 60(3): 254-281.
[12]	王嘉, 姜露露, 陶友瑞, 韩旭. 交变载荷下基于电流信号的机电系统可靠性建模与评估[J]. 机械工程学报, 2024, 60(22): 437-446.
[13]	谢峰, 李红杨, 甄圣超, 魏华伟. 基于带通滤波二阶动量观测器的机器人碰撞检测[J]. 机械工程学报, 2024, 60(21): 99-111.
[14]	梁亮, 吴成东, 刘世昌. 基于关节损耗约束的工业机器人最优轨迹规划算法研究[J]. 机械工程学报, 2024, 60(19): 11-19.
[15]	于振, 刘海林, 裘祖荣, 安琪. 基于IGCF-IBSCF算法和BCF-IBPSO-NESN算法的工业机器人末端执行器位姿重复性检测[J]. 机械工程学报, 2024, 60(19): 71-87.