Please wait a minute...
Chinese Journal of Engineering Design  2025, Vol. 32 Issue (6): 735-744    DOI: 10.3785/j.issn.1006-754X.2025.05.130
Theory and Method of Mechanical Design     
Optimization design method for construction machinery structure based on adaptive Kriging surrogate model
Xin LIU(),Qingfeng WU,Wenguang YANG
College of Mechanical and Vehicle Engineering, Changsha University of Science and Technology, Changsha 410114, China
Download: HTML     PDF(2165KB)
Export: BibTeX | EndNote (RIS)      

Abstract  

In view of the characteristics of high nonlinearity and high computational complexity in the optimization design of construction machinery, as well as the demand for high-fidelity and low-cost simulation models, an optimization design method for construction machinery structure based on an adaptive Kriging surrogate model was proposed. Firstly, the design variable sample space of the construction machinery structure was partitioned using the Voronoi diagram method. The global sparsity index (GSI) of the sample points was defined to identify subspaces requiring node-adding, and global points were generated within these subspaces using the max-min criterion. Next, local node-adding subspaces were identified based on the potential optimal parameters, and local points were generated accordingly. Finally, by integrating a local refinement strategy, the generated global points, local points and potential optimal solutions were filtered and incorporated into the sample set to update the surrogate model, thereby improving the fitting accuracy of the surrogate model. It was applied to the surrogate model construction phase in the construction machinery structure optimization design to significantly shorten the computational time for traditional high-fidelity model simulation and improve the efficiency of the optimization design. The numerical example verifications and engineering application results demonstrated that, compared with the existing methods, the proposed method achieved faster convergence within an acceptable error range under the same node-adding number. In the lightweight design of the upper structure of the arm-type bucket wheel reclaimer and the front boom structure of the tower crane, after only one iteration, the maximum relative errors of the optimal solution were reduced to 0.09% and 0.59% respectively. The proposed method is feasible and effective in the structural optimization design of construction machinery.



Key wordsadaptive surrogate model      construction machinery structure      optimization design      Voronoi diagram      genetic algorithm     
Received: 09 April 2025      Published: 30 December 2025
CLC:  TH 122  
Cite this article:

Xin LIU,Qingfeng WU,Wenguang YANG. Optimization design method for construction machinery structure based on adaptive Kriging surrogate model. Chinese Journal of Engineering Design, 2025, 32(6): 735-744.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.05.130     OR     https://www.zjujournals.com/gcsjxb/Y2025/V32/I6/735


基于自适应Kriging代理模型的工程机械结构优化设计方法

针对工程机械优化设计问题呈现高非线性、高计算复杂度等特征及对高保真度、低成本仿真模型的需求,提出了一种基于自适应Kriging代理模型的工程机械结构优化设计方法。首先,采用泰森多边形(Voronoi diagram)方法划分工程机械结构设计变量样本空间,根据定义的样本点全局稀疏度指标(global sparsity index, GSI)找出需要加点的子空间,并根据最大最小准则在该子空间内生成全局点;其次,根据潜在最优参数定位局部加点子空间,在该子空间内产生局部点;最后,结合局部加密技术,将所得到的全局点、局部点和潜在最优解进行筛选后加入样本集以更新代理模型,从而提高代理模型的拟合精度,并将其运用于工程机械结构优化设计时代理模型的构建阶段,以大幅缩短传统高保真模型仿真时的计算时长,提升优化设计效率。数值算例验证和工程应用结果表明:与现有方法相比,在相同的加点数量下,采用所提出的方法能够使优化解更快地收敛至容许误差范围内;在臂式斗轮机上部结构和塔式起重机前臂架结构的轻量化设计中,经过1次迭代,最优解的最大相对误差分别降至0.09%和0.59%。该方法在工程机械结构优化设计中具有可行性和有效性。


关键词: 自适应代理模型,  工程机械结构,  优化设计,  泰森多边形,  遗传算法 
Fig.1 Example of two-dimensional Voronoi diagram
Fig.2 Flowchart of optimization design method for construction machinery structure based on adaptive Kriging surrogate model
方法迭代步新加入样本数量/个总样本数量/个最大相对误差/%
本文方法Step 101522.24
Step 231817.13
Step 33211.09
EI方法Step 101522.24
Step 211622.12
Step 311722.34
Step 411828.80
Step 511962.10
Step 612040.86
Step 712154.88
PI方法Step 101522.24
Step 211693.07
Step 311720.66
Step 411837.80
Step 511915.46
Step 612018.17
Step 712115.77
Table 1 Convergence performance under different node-adding methods in numerical example 1
Fig.3 Maximum relative error convergence curves under different node-adding methods in numerical example 1
函数

代理模型

近似值

真实值相对误差/%
X =(6.900 6 10.240 3 15.000 0 13.504 2)T
f(X)2.590 32.618 81.09
g1(X)71.167 770.617 10.78
g2(X)7.309 97.286 30.32
g3(X)34.916 534.729 30.54
Table 2 Optimization results of proposed method in numerical example 1
方法迭代步新加入样本数量/个总样本数量/个

最大相对

误差/%

本文方法Step 101591.86
Step 231833.35
Step 332112.87
Step 43246.74
EI方法Step 101591.86
Step 2116122.79
Step 311796.51
Step 4118103.45
Step 511951.30
Step 612060.62
Step 71217.63
Step 8122100.17
Step 912391.90
Step 101248.77%
PI方法Step 101591.86
Step 211670.02
Step 3117150.01
Step 411839.75
Step 511949.35
Step 612040.34
Step 712177.75
Step 812241.64
Step 912383.66
Step 101244 643.46
Table 3 Convergence performance under different node-adding methods in numerical example 2
Fig.4 Maximum relative error convergence curves under different node-adding methods in numerical example 2
函数代理模型近似值真实值相对误差/%
X =(9.316 8.032 10.000)T
f(X)10.197910.15940.38
g1(X)-1.7478-1.63756.74
g2(X)-87.3676-87.67300.35
g3(X)-32.9077-33.73482.45
Table 4 Optimization results of proposed method in numerical example 2
Fig.5 Finite element model of upper structure of arm-type bucket wheel reclaimer
迭代步新加入样本数量/个

总样本

数量/个

最大相对

误差/%

Step 10156.02
Step 23180.09
Table 5 Iteration steps and their maximum errors of proposed method in engineering example 1
Fig.6 Mass convergence curve of upper structure of arm-type bucket wheel reclaimer
函数

代理模型

近似值

真实值

相对

误差/%

X =(101.328 7 mm 102.6471 mm 12.1096 mm 10.1796 mm) T
M(X)/kg94 183.846 894 1740.01
D(X)/mm17.073 017.0720.01
P(X)/MPa169.901 2170.050.09
Table 6 Optimization results of proposed method in engineering example 1
Fig.7 Finite element model of front boom structure of tower crane
迭代步新加入样本数量/个

总样本

数量/个

最大相对

误差/%

Step 10153.07
Step 23180.59
Table 7 Iteration steps and their maximum errors of proposed method in engineering example 2
Fig.8 Mass convergence curve of front boom structure of tower crane
函数

代理模型

近似值

真实值

相对

误差/%

X =(8.207 8 mm 9.719 5 mm 8.014 9 mm 9.705 3 mm) T
M(X)/kg11 941.2611 979.000.32
D(X)/mm199.86201.050.59
P(X)/MPa20.5420.590.26
Table 8 Optimization results of proposed method in engineering example 2
[[1]]   刘鑫, 张远洋. 基于混合模型汽车结构耐撞性的可靠性优化设计[J]. 长沙理工大学学报(自然科学版), 2021, 18(1): 95-101.
LIU X, ZHANG Y Y. Reliability-based design optimization for vehicle structural crashworthiness based on hybrid model[J]. Journal of Changsha University of Science & Technology (Natural Science), 2021, 18(1): 95-101.
[[2]]   王红涛, 竺晓程, 杜朝辉. 基于Kriging代理模型的改进EGO算法研究[J]. 工程设计学报, 2009, 16(4): 266-270, 302.
WANG H T, ZHU X C, DU Z H. Research on improved EGO algorithm based on Kriging surrogate model[J]. Chinese Journal of Engineering Design, 2009, 16(4): 266-270, 302.
[[3]]   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. doi:10.7527/S1000-6893.2016.0083
HAN Z H. 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.
doi: 10.7527/S1000-6893.2016.0083
[[4]]   陈一馨,陈再续,刘永生,等.基于改进深度代理模型的挖掘机铲斗结构优化设计[J/OL]. 吉林大学学报 (工学版). (2024-06-29) [2025-03-31]. .
CHEN Y X, CHEN Z X, LIU Y S, et al. Structural optimization design of excavator bucket based on improved depth surrogate model[J/OL]. Journal of Jilin University (Engineering and Technology Edition). (2024-06-29) [2025-03-31]. .
[[5]]   李浩, 王颖, 马耀帅, 等. 基于Kriging模型的大型立式磨机选粉机结构优化设计研究[J]. 工程设计学报, 2024, 31(6): 801-809.
LI H, WANG Y, MA Y S, et al. Research on structural optimization design for powder separator of large vertical mill based on Kriging model[J]. Chinese Journal of Engineering Design, 2024, 31(6): 801-809.
[[6]]   黄文建, 刘放, 李晨晖, 等. 基于代理模型的柔性机械臂区间不确定性分析[J]. 计算力学学报, 2024, 41(6): 1005-1011.
HUANG W J, LIU F, LI C H, et al. Interval uncertainty analysis of flexible manipulator based on surrogate model[J]. Chinese Journal of Computational Mechanics, 2024, 41(6): 1005-1011.
[[7]]   刘鑫, 毛勇勇. 基于代理模型更新管理策略的汽车乘员约束系统优化设计[J]. 长沙理工大学学报(自然科学版), 2024, 21(6): 87-95.
LIU X, MAO Y Y. Optimization design of vehicle occupant restraint system based on surrogate model update management strategy[J]. Journal of Changsha University of Science & Technology (Natural Science), 2024, 21(6): 87-95.
[[8]]   王波, HAECHANG G, 白俊强, 等. 基于Stochastic Kriging模型的不确定性序贯试验设计方法[J]. 工程设计学报, 2016, 23(6): 530-536.
WANG B, HAECHANG G, BAI J Q, et al. The uncertainty-based sequential design of experiment method based on Stochastic Kriging metamodel[J]. Chinese Journal of Engineering Design, 2016, 23(6): 530-536.
[[9]]   GU L. A comparison of polynomial based regression models in vehicle safety analysis[C]//International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York: American Society of Mechanical Engineers, 2001, 80227: 509-514.
[[10]]   LI B, SHIU B W, LAU K J. Fixture configuration design for sheet metal laser welding with a two-stage response surface methodology[C]//International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York: American Society of Mechanical Engineers, 2001, 80234: 801-808.
[[11]]   JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4): 455-492.
[[12]]   戴志远, 李田, 张卫华, 等. 基于混合加点Kriging代理模型的高速列车头型气动多目标优化[J]. 西南交通大学学报, 2024, 59(1): 46-53.
DAI Z Y, LI T, ZHANG W H, et al. Multi-objective aerodynamic optimization on head shape of high-speed train using Kriging surrogate model with hybrid infill criterion[J]. Journal of Southwest Jiaotong University, 2024, 59(1): 46-53.
[[13]]   WANG L Q, SHAN S Q, WANG G G. Mode-pursuing sampling method for global optimization on expensive black-box functions[J]. Engineering Optimization, 2004, 36(4): 419-438.
[[14]]   魏锋涛, 卢凤仪, 郑建明. 基于多策略的改进径向基代理模型方法[J]. 计算机集成制造系统, 2019, 25(3): 764-771.
WEI F T, LU F Y, ZHENG J M. Augmented radial basis function metamodel method based on multi-strategy[J]. Computer Integrated Manufacturing Systems, 2019, 25(3): 764-771.
[[15]]   高月华, 王希诚. 基于Kriging代理模型的多点加点序列优化方法[J]. 工程力学, 2012, 29(4): 90-95.
GAO Y H, WANG X C. A sequential optimization method with multi-point sampling criterion based on Kriging surrogate model[J]. Engineering Mechanics, 2012, 29(4): 90-95.
[[16]]   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 T, GUO X S, PENG L, et al. Optimization strategy using dynamic radial basis function metamodel based on trust region[J]. Journal of Mechanical Engineering, 2014, 50(7): 184-190.
[[17]]   陈吉清, 张钰奇, 兰凤崇, 等. 基于主动学习PC-Kriging模型的复杂结构可靠性分析方法[J]. 汽车工程, 2025, 47(2): 383-390.
CHEN J Q, ZHANG Y Q, LAN F C, et al. Reliability analysis method of complex structures based on active learning PC-Kriging model[J]. Automotive Engineering, 2025, 47(2): 383-390.
[[18]]   ZHAN X X, ZHANG W R, CHEN R J, et al. Non-dominated sorting genetic algorithm-II: a multi-objective optimization method for building renovations with half-life cycle and economic costs[J]. Building and Environment, 2025, 267: 112155.
[[19]]   于宝石, 王志祥, 王婕, 等. 基于Voronoi序列采样的加筋壁板优化设计[J]. 南京航空航天大学学报, 2022, 54(1): 121-131.
YU B S, WANG Z X, WANG J, et al. Optimum design of stiffened panels based on voronoi sequence sampling method[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2022, 54(1): 121-131.
[1] Jianbo CHE,Donglin TANG,Yuanyuan HE,Yuanyao HU,Bingsheng LU,Junhui ZHANG. Research on path planning method based on dynamic fusion of ant colony optimization and genetic algorithm[J]. Chinese Journal of Engineering Design, 2025, 32(6): 789-802.
[2] Dong LIU,Guoliang HU,Jiawei ZHANG,Lifan YU. Optimization design and performance analysis of variable stiffness and variable damping magnetorheological damper[J]. Chinese Journal of Engineering Design, 2025, 32(5): 686-695.
[3] Yinxian LI,Youbao JIANG,Yan LIU,Pengxiang GAO. Splitting method and forming experiment of 3D printed concrete spherical shell structure considering self-supporting critical angle[J]. Chinese Journal of Engineering Design, 2025, 32(2): 151-158.
[4] Qing DONG,Tianxiang ZHANG,Qisong QI,Gening XU. Optimization design of metal structure of bridge crane based on structural function derivative coefficients[J]. Chinese Journal of Engineering Design, 2024, 31(6): 810-822.
[5] Heng CUI,Zongfang MA,Lin SONG,Chao LIU,Yixuan HAN. Path planning algorithm for concrete 3D printing based on continuous vertex partitioning[J]. Chinese Journal of Engineering Design, 2024, 31(3): 271-279.
[6] Xiaobo YU,Sujiao CHEN,Yonghua ZHANG,Binjun MA. Research on gear modification and modal optimization of centralized transmission system based on genetic algorithm[J]. Chinese Journal of Engineering Design, 2024, 31(3): 340-347.
[7] Binghui JI,Jian MAO,Bo QIAN. Temperature control method for dual-nozzle FDM 3D printer based on genetic algorithm-fuzzy PID[J]. Chinese Journal of Engineering Design, 2024, 31(2): 151-159.
[8] Wangcheng CAO,Jiaxuan HAN,Tingqiang YAO. Dynamic optimization design of internal toothed toothed slewing bearing based on parametric multi-body dynamic model[J]. Chinese Journal of Engineering Design, 2024, 31(2): 168-177.
[9] Jinyun CAI,Zhong LIU,Gang WANG,Qingbin ZHAO,Ning AN,Xuwei DU,Dongliang LI,Yuanzhou LI. Optimization design of auxiliary tail rope pulling device for winch mill based on response surface methodology[J]. Chinese Journal of Engineering Design, 2024, 31(2): 178-187.
[10] Yaqin TIAN,Menghui HU,Wentao LIU,Yinzhi HOU. Path planning of autonomous mobile robot based on jump point search-genetic algorithm[J]. Chinese Journal of Engineering Design, 2023, 30(6): 697-706.
[11] Di ZHAO,Guo CHEN,Xiaoli CHEN,Xiongjin WANG. Terrain adaptive mechanism design and obstacle-surmounting performance analysis of wheeled search and rescue robot[J]. Chinese Journal of Engineering Design, 2023, 30(5): 579-589.
[12] Fangjian DOU,Qingying QIU,Cheng GUAN,Jinjie SHAO,Haifeng WU. Optimization design of acceleration and deceleration curve of winding machine with large moment of inertia[J]. Chinese Journal of Engineering Design, 2023, 30(4): 503-511.
[13] Xin MI,Hong LI,Yan-qing GUO,Hong-wei GAO,Hao-nan WANG,Yi-fan NING. Parameter optimization of single plunger pump check valve based on linear regression[J]. Chinese Journal of Engineering Design, 2022, 29(6): 705-712.
[14] Zheng-feng ZHANG,Xiao-yu SONG,Xiao-lei YUAN,Wen-juan CHEN,Wei-dong ZHANG. Reliability optimization design for crashworthiness of Al/CFRP hybrid thin-walled structure[J]. Chinese Journal of Engineering Design, 2022, 29(6): 720-730.
[15] Guang-ming SUN,Yi-miao WANG,Qian WAN,Kun GONG,Wen-jin WANG,Jian ZHAO. Optimization design of precision machine tool bed considering assembly deformation[J]. Chinese Journal of Engineering Design, 2022, 29(3): 318-326.