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Chinese Journal of Engineering Design  2024, Vol. 31 Issue (2): 188-200    DOI: 10.3785/j.issn.1006-754X.2024.03.159
Mechanical Optimization Design     
Multi-objective reliability optimization design for cast aluminum integrated car door
Bofu WU(),Yaoye WU(),Jing BEI,Zongyang WU,Liang SUN
School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009, China
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Abstract  

In order to improve the lightweight level and performance of the car door, the integrated method of "material-structure-performance" is adopted to design the cast aluminum integrated car door. Based on the constructed finite element model of the cast aluminum integrated car door, with the thickness of the car door as the design variable, the radial basis function (RBF) neural network approximation model and the second-order response surface approximation model were used in combination with the non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ), multi-objective particle swarm optimization (MOPSO) algorithm and multi-island genetic algorithm (MIGA) to conduct the deterministic optimization design for the sinking stiffness condition displacement, upper torsional stiffness condition displacement, lower torsional stiffness condition displacement, first-order bending mode frequency, first-order torsional mode frequency and mass of the car door. On this basis, the 6Sigma reliability analysis and optimization for the quality level of the deterministic optimization solution were carried out considering the uncertainties of materials and manufacturing. The results showed the optimal combination of second-order response surface approximation model and MOPSO algorithm achieved the optimal lightweight of the car door, and the optimal combination of RBF neural network approximation model and MOPSO algorithm could minimize the the displacement of the car door under the sinking stiffness condition. The above two combinations achieved the design goals of lightweight and safety for the car door, respectively. The research results can provide reference for the optimization design of car parts.



Key wordscast aluminum integrated car door      lightweight      radial basis function neural network approximation model      second-order response surface approximation model      multi-objective particle swarm optimization algorithm      6Sigma reliability     
Received: 26 April 2023      Published: 26 April 2024
CLC:  U 463.82  
Corresponding Authors: Yaoye WU     E-mail: bbfwu@163.com;wuyaoyee@163.com
Cite this article:

Bofu WU,Yaoye WU,Jing BEI,Zongyang WU,Liang SUN. Multi-objective reliability optimization design for cast aluminum integrated car door. Chinese Journal of Engineering Design, 2024, 31(2): 188-200.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2024.03.159     OR     https://www.zjujournals.com/gcsjxb/Y2024/V31/I2/188


铸铝一体化车门的多目标可靠性优化设计

为提升车门的轻量化水平与性能,采用“材料—结构—性能”一体化集成方法设计铸铝一体化车门。基于构建的铸铝一体化车门有限元模型,以车门的厚度为设计变量,采用径向基函数(radial basis function, RBF)神经网络近似模型和二阶响应面近似模型并分别结合二代非支配排序遗传算法(non-dominated sorting genetic algorithm-Ⅱ, NSGA-Ⅱ)、多目标粒子群优化(multi-objective particle swarm optimization, MOPSO)算法以及多岛遗传算法(multi-island genetic algorithm, MIGA)对车门的下沉刚度工况位移、上扭转刚度工况位移、下扭转刚度工况位移、一阶弯曲模态频率、一阶扭转模态频率和质量进行确定性优化设计。在此基础上,考虑材料及加工制造等不确定性因素,对确定性优化解的质量水平进行6Sigma可靠性分析与优化。结果表明,二阶响应面近似模型与MOPSO算法的优化组合方案实现了车门的最佳轻量化,RBF神经网络近似模型与MOPSO算法的优化组合方案实现了车门下沉刚度工况位移的最小化。上述2种组合分别实现了车门轻量化与安全化的设计目标。研究结果可为车身零部件的优化设计提供参考。


关键词: 铸铝一体化车门,  轻量化,  径向基函数神经网络近似模型,  二阶响应面近似模型,  多目标粒子群优化算法,  6Sigma可靠性 
参数数值
密度/(kg/m3)2 800
弹性模量/GPa69
泊松比0.33
抗拉强度/MPa≥390
伸长率/%≥8
Table 1 Material property parameters of ZL201A aluminum alloy
Fig.1 Finite element model of steel car door
Fig.2 Finite element model of cast aluminum integrated car door
Fig.3 Sinking stiffness condition of cast aluminum integrated car door
Fig.4 Upper torsional stiffness condition of cast aluminum integrated car door
Fig.5 Lower torsional stiffness condition of cast aluminum integrated car door
Fig.6 Modal simulation results of cast aluminum integrated car door
Fig.7 Modal test point arrangement for cast aluminum integrated car door
Fig.8 Modal test results of cast aluminum integrated car door
模态频率/Hz相对误差/%
仿真值试验值
一阶弯曲模态36.6237.873.4
一阶扭转模态54.5956.493.5
Table 2 Comparison of modal simulation and test results of cast aluminum integrated car door
Fig.9 Sampling strategies of different Latin hypercube experimental design methods
Fig.10 Schematic of thickness of each component in cast aluminum integrated car door
试验编号设计变量m/kgf1/Hzf2/Hzd1/mmd2/mmd3/mm
T1/mmT2/mmT3/mmT4/mmT5/mm
12.0693.8622.8283.1033.44812.9025.7246.062.0733.1451.301
22.2073.1722.2763.2412.27611.4927.1747.503.5882.8601.174
33.4482.2763.2414.0003.10315.8337.3558.591.8571.3780.460
43.0343.7932.3453.8622.96613.6334.3654.942.2521.6160.604
52.4832.3452.0002.4833.17210.9729.5550.204.6992.4480.951
????????????
282.0002.9663.5862.5522.48314.0524.8245.342.2952.4261.416
293.6554.0002.8972.6903.24116.1938.5860.321.2811.1990.444
303.5863.7243.6553.7932.75917.7538.1159.711.0091.2140.426
Table 3 Experimental design scheme and results of deterministic optimization for cast aluminum integrated car door
响应RBF神经网络近似模型二阶响应面近似模型
d10.974 860.931 54
d20.980 790.979 53
d30.970 830.961 69
f10.999 210.999 93
f20.999 430.999 50
m0.999 110.999 98
Table 4 Accuracy evaluation results of approximation model of each response of cast aluminum integrated car door
参数数值
种群数/个100
迭代数/次50
交叉率0.9
交叉分布指数10
突变分布指数20
Table 5 Parameter setting for NSGA-II
参数数值
迭代数/次50
粒子数/个100
惯性权重0.9
全局增量0.9
粒子增量0.9
Table 6 Parameter setting for MOPSO algorithm
参数数值
种群数/个50
岛屿数/个10
迭代数/次10
交叉率1.0
变异率0.01
迁移率0.01
Table 7 Parameter setting for MIGA
参数初始值1)优化值
NSGA-ⅡMOPSOMIGA
T1/mm0.703.716 23.730 83.738 8
T2/mm1.402.000 62.000 02.003 7
T3/mm0.652.000 12.000 02.017 2
T4/mm0.703.999 13.990 83.980 5
T5/mm1.803.999 74.000 03.973 9
d1/mm4.4021.843 51.837 91.866 9
d2/mm2.9041.115 31.104 11.100 7
d3/mm1.4430.352 10.347 90.347 1
f1/Hz49.2240.0040.1140.17
f2/Hz75.5361.2161.3361.41
m/kg17.4613.32213.35013.406
Table 8 Deterministic optimization results of cast aluminum integrated car door based on RBF neural network approximation model
参数初始值1)优化值
NSGA-ⅡMOPSOMIGA
T1/mm0.703.726 83.722 83.747 0
T2/mm1.402.000 72.000 02.014 5
T3/mm0.652.000 02.000 02.007 9
T4/mm0.703.301 33.469 23.469 3
T5/mm1.803.994 13.948 83.982 5
d1/mm4.4022.551 32.566 82.546 4
d2/mm2.9041.172 11.170 31.160 2
d3/mm1.4430.390 40.388 70.386 6
f1/Hz49.2240.0140.0340.21
f2/Hz75.5361.3861.3561.56
m/kg17.4613.30213.30213.376
Table 9 Deterministic optimization results of cast aluminum integrated car door based on second-order response surface approximation model
参数RBF神经网络近似模型二阶响应面近似模型
NSGA-IIMOPSOMIGANSGA-IIMOPSOMIGA
QRQRQRQRQRQR
d2/mm818181818181
d3/mm818181818181
f1/Hz0.6780.5030.9370.6511.0650.7130.6940.5120.7380.5391.1920.767
f2/Hz3.8690.9994.2310.9994.4170.9994.3730.9994.2940.9994.8880.999
Table 10 Quality level and reliability of deterministic optimization results of cast aluminum integrated car door
参数初始值1)优化值
NSGA-ⅡMOPSOMIGA
T1/mm0.703.998 03.941 63.961 3
T2/mm1.402.135 12.000 02.066 5
T3/mm0.652.018 92.000 02.031 3
T4/mm0.703.968 84.000 03.948 0
T5/mm1.803.986 64.000 03.990 7
d1/mm4.4021.696 61.680 11.744 4
d2/mm2.9040.910 70.964 10.952 2
d3/mm1.4430.276 20.278 80.280 1
f1/Hz49.2242.4542.3142.35
f2/Hz75.5364.1863.9163.98
m/kg17.4614.15413.78613.983
Table 11 Reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model
参数NSGA-IIMOPSOMIGA
QRQRQR
d2818181
d3818181
f17.5716.1716.551
f2818181
Table 12 Quality level and reliability of reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model
参数优化值仿真值相对误差/%
d1/mm1.680 11.650 01.8
d2/mm0.964 10.936 72.8
d3/mm0.278 80.282 41.3
f1/Hz42.3141.761.3
f2/Hz63.9163.211.1
m/kg13.78613.7610.2
Table 13 Simulation verification of reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model and MOPSO algorithm
Fig.11 Fitting surfaces of reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model and MOPSO algorithm
参数初始值1)优化值
NSGA-ⅡMOPSOMIGA
T1/mm0.703.951 93.954 73.953 2
T2/mm1.402.040 72.000 02.007 9
T3/mm0.652.00132.000 02.033 3
T4/mm0.703.861 03.182 53.494 7
T5/mm1.803.670 33.900 83.993 2
d1/mm4.4022.558 32.521 42.476 6
d2/mm2.9041.110 91.112 01.101 7
d3/mm1.4430.383 90.384 00.378 7
f1/Hz49.2242.2242.0242.04
f2/Hz75.5363.7163.7363.73
m/kg17.4613.89413.85113.924
Table 14 Reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model
参数NSGA-IIMOPSOMIGA
QRQRQR
d2818181
d3818181
f16.8016.1816.411
f2818181
Table 15 Quality level and reliability of reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model
参数优化值仿真值相对误差/%
d1/mm2.521 42.526 40.2
d2/mm1.112 01.119 00.7
d3/mm0.384 00.388 41.1
f1/Hz42.0241.660.9
f2/Hz63.7363.350.6
m/kg13.85113.7340.8
Table 16 Simulation verification of reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model and MOPSO algorithm
Fig.12 Fitting surfaces of reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model and MOPSO algorithm
[1]   徐建全,杨沿平.纯电动汽车与传统汽车轻量化全生命周期多目标优化研究[J].汽车工程,2019,41(8):885-891,914.
XU J Q, YANG Y P. A multi-objective lightweight optimization study on full life cycle of electric and conventional vehicles[J]. Automotive Engineering, 2019, 41(8): 885-891, 914.
[2]   WANG B, ZHANG Z Y, XU G C, et al. Wrought and cast aluminum flows in China in the context of electric vehicle diffusion and automotive lightweighting[J]. Resources, Conservation & Recycling, 2023, 191: 106877.
[3]   高云凯,申振宇,冯兆玄,等.多目标优化在车门轻量化设计中的应用[J].同济大学学报(自然科学版),2017,45(2):275-280,308.
GAO Y K, SHEN Z Y, FENG Z X, et al. Application of multi-objective optimization in vehicle door lightweight[J]. Journal of Tongji University (Natural Science), 2017, 45(2): 275-280, 308.
[4]   李军,冷川.基于RBF神经网络模型的车门多目标轻量化设计[J].重庆交通大学学报(自然科学版),2019,38(11):127-132.
LI J, LENG C. Multi-objective lightweight design of vehicle door based on RBF neural network model[J]. Journal of Chongqing Jiaotong University (Natural Science), 2019, 38(11): 127-132.
[5]   马彬彬,谭继锦,林彧群.基于径向基函数神经网络的车门轻量化设计[J].汽车工程学报,2015,5(2):136-143. doi:10.3969/j.issn.2095-1469.2015.02.08
MA B B, TAN J J, LIN Y Q. A research on lightweight car door design based on RBF neural network[J]. Chinese Journal of Automotive Engineering, 2015, 5(2): 136-143.
doi: 10.3969/j.issn.2095-1469.2015.02.08
[6]   侯振方,胡海欧,张爱兵,等.车门结构多目标轻量化研究[J].机电工程,2020,37(4):359-364. doi:10.3969/j.issn.1001-4551.2020.04.004
HOU Z F, HU H O, ZHANG A B, et al. Multi-objective lightweight research of a door structure[J]. Journal of Mechanical & Electrical Engineering, 2020, 37(4): 359-364.
doi: 10.3969/j.issn.1001-4551.2020.04.004
[7]   方柘林,王丽娟,陈宗渝,等.基于车门结构的多目标优化设计方法研究[J].机械设计,2014,31(8):60-64.
FANG Z L, WANG L J, CHEN Z Y, et al. Study of multi-objective optimization design based on the vehicle door structure[J]. Journal of Machine Design, 2014, 31(8): 60-64.
[8]   陈静,崔晓凡,郑晋军,等.基于加点多目标粒子群算法的碳纤维防撞梁优化设计[J].湖南大学学报(自然科学版),2022,49(8):21-28. doi:10.5755/j02.eie.31232
CHEN J, CUI X F, ZHENG J J, et al. Optimization design of carbon fiber anti-collision beam based on multi-objective particle swarm with additional points[J]. Journal of Hunan University (Natural Sciences), 2022, 49(8): 21-28.
doi: 10.5755/j02.eie.31232
[9]   任明,孙涛,石永金,等.基于Kriging近似模型的车架轻量化优化[J].机械强度,2019,41(6):1372-1377.
REN M, SUN T, SHI Y J, et al. Lightweight optimization of vehicle frame structure based on the Kriging approximate model[J]. Journal of Mechanical Strength, 2019, 41(6): 1372-1377.
[10]   朱茂桃,钱洋,顾娅欣,等.基于Kriging模型的车门刚度和模态优化[J].汽车工程,2013,35(11):1047-1050,1042. doi:10.3969/j.issn.1000-680X.2013.11.019
ZHU M T, QIAN Y, GU Y X, et al. Stiffness and modal optimization of car door based on Kriging model[J]. Automotive Engineering, 2013, 35(11): 1047-1050, 1042.
doi: 10.3969/j.issn.1000-680X.2013.11.019
[11]   史朝军.基于多学科设计优化的车门结构轻量化研究[D].武汉:武汉科技大学,2014.
SHI C J. Research on structure lightweight of car-door base on multidisciplinary design optimization[D]. Wuhan: Wuhan University of Science and Technology, 2014.
[12]   高杰.某皮卡车门布置设计及多目标轻量化优化设计研究[D].镇江:江苏大学,2016.
GAO J. A study on layout design and multi-objective lightweight design and optimization for a pickup truck door[D]. Zhenjiang: Jiangsu University, 2016.
[13]   ZAHIR H, WALEED F F, KARTINI A. An investigation into NVC characteristics of vehicle behaviour using modal analysis[J]. IOP Conference Series: Materials Science and Engineering, 2017, 184(1): 012027.
[14]   殷晓伟,张瑞乾,陈勇.径向基函数近似模型在车门轻量化中的应用[J].机械设计与制造,2022(8):22-27. doi:10.3969/j.issn.1001-3997.2022.08.005
YIN X W, ZHANG R Q, CHEN Y. Application of radial basis function approximate model in lightweight of automobile door[J]. Machinery Design & Manufacture, 2022(8): 22-27.
doi: 10.3969/j.issn.1001-3997.2022.08.005
[15]   季宁,张卫星,于洋洋,等.基于最优拉丁超立方抽样方法和NSGA-Ⅱ算法的注射成型多目标优化[J].工程塑料应用,2020,48(3):72-77.
JI N, ZHANG W X, YU Y Y, et al. Multi-objective optimization of injection molding based on optimal Latin hypercube sampling method and NSGA-Ⅱ algorithm[J]. Engineering Plastics Application, 2020, 48(3): 72-77.
[16]   兰凤崇,周建华,赖番结,等.基于径向基函数神经网络的白车身减重优化研究[J].机械设计与制造,2018(8):29-32. doi:10.3969/j.issn.1001-3997.2018.08.009
LAN F C, ZHOU J H, LAI F J, et al. Lightweight design of BIW based on radial basis function neural networks[J]. Machinery Design & Manufacture, 2018(8): 29-32.
doi: 10.3969/j.issn.1001-3997.2018.08.009
[17]   张帅,郭志军,王传青.基于分析驱动设计的参数化白车身前端结构轻量化多目标优化[J].汽车工程,2019,41(9):1102-1107.
ZHANG S, GUO Z J, WANG C Q. Multi-objective lightweight optimization of parametric frontend BIW structure based on analysis-driven design[J]. Automotive Engineering, 2019, 41(9): 1102-1107.
[18]   袁发庭,姜发,刘健犇,等.基于神经网络模型与多岛遗传算法的空心电抗器隔音装置优化设计[J].高电压技术,2023,49(3):1213-1223.
YUAN F T, JIANG F, LIU J B, et al. Optimization design of sound-insulation device of air-core reactor based on neural network model and multi-island genetic algorithm[J]. High Voltage Engineering, 2023, 49(3): 1213-1223.
[19]   ESFE M H, MAHIAN O, HAJMOHAMMAD M H, et al. Design of a heat exchanger working with organic nanofluids using multi-objective particle swarm optimization algorithm and response surface method[J]. International Journal of Heat and Mass Transfer, 2018, 119: 922-930.
[20]   李书华,吴宗扬,吴钇陶,等.一体化铸铝防撞梁的多目标可靠性优化设计[J].重庆理工大学学报(自然科学),2022,36(12):18-25.
LI S H, WU Z Y, WU Y T, et al. Multi-objective reliability optimization design of anti-collision beams made of integrated cast aluminum[J]. Journal of Chongqing University of Technology (Natural Science), 2022, 36(12): 18-25.
[21]   李书华,贝璟,吴宗扬,等.铸铝一体化发动机罩的可靠性优化设计[J].汽车工程学报,2023,13(3):353-361.
LI S H, BEI J, WU Z Y, et al. Reliability optimization design for cast aluminum integrated engine hood[J]. Chinese Journal of Automotive Engineering, 2023, 13(3): 353-361.
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