基于机器学习的新型多胞梯度结构设计与优化

闫凯波; 周鹏; 陆思思; 王俊杰; 范志伟

doi:10.11883/bzycj-2025-0388

基于机器学习的新型多胞梯度结构设计与优化

doi: 10.11883/bzycj-2025-0388

闫凯波^{1, 2,},
周鹏¹,
陆思思^{1, 2, ,},
王俊杰¹,
范志伟¹

1.
重庆交通大学机电与车辆工程学院，重庆 400074
2.
重庆嘉陵特种装备有限公司，重庆 400032

基金项目: 国家自然科学基金（52402466）；中国博土后科学基金（2022M723001, 2022M713014）；重庆市自然科学基金（CSTB2025NSCQ-GPX0885）；重庆市技术创新与应用发展专项重点项目（CSTB2024TIAD-KPX0081）；重庆市博土后研究项目（2022CQBSHTB2020）；重庆市教育委员会科学技术研究项目（KJZD-K202400704, KJQN202400718）；重庆交通大学研究生科研创新项目（2025S0051）

详细信息

作者简介:
闫凯波（1992－　），男，博士，讲师，kaibo_yan@yeah.net

通讯作者:
陆思思（1993－　），女，博士，副教授，sisi_lu2020@yeah.net

中图分类号: O342
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- HTML全文浏览量: 27
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- 被引次数: 0
出版历程
- 网络出版日期: 2026-03-19

Design and Optimization of Corrugated Multi-cell Gradient Structures Based on Machine Learning

YAN Kaibo^{1, 2
,},
ZHOU Peng¹,
LU Sisi^{1, 2
, ,},
WANG Junjie¹,
FAN Zhiwei¹

1.
School of Mechatronics & Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, China
2.
Chongqing Jialing Special Equipment Co., Ltd., Chongqing 400032, China

摘要

摘要: 针对航空航天、交通运输、土木建筑等领域的碰撞防护需求，提出一种新型多胞梯度结构管（CMGHT）设计方法：在普通六边形管内引入正弦波纹肋板，并融合功能梯度设计理念，以实现结构耐撞性能的提升。首先，构建该结构的有限元模型并开展数值模拟分析。结果显示，在相同壁厚条件下，CMGHT的关键吸能指标表现显著优于现有结构，相较于普通六边形管（HT），其吸收能量（E_a）、比吸能（E_sa）、平均压缩力（$ \overline{F} $）及压缩效率（η）分别提升390%、76%、395%和46%；相较于多胞六边形管（MHT），上述指标分别提升121%、58%、121%和97%；相较于波纹多胞六边形管（CMHT），E_a、E_sa、$ \overline{F} $、η分别提升7%、7%、8%、33%，且初始峰值压缩力（F_max）降低18%，充分证明其吸能性能更优。随后，以肋板与外管的几何参数为设计变量，通过全因子试验设计生成540组样本，构建支持向量机（SVM）代理模型，并结合冠豪猪优化（CPO）算法完成模型优选，实现对CMGHT耐撞性能的精准预测。最后，采用多目标浣熊优化算法（MOCOA）进行多目标优化，获取最优特征参数组合。优化结果表明，相较于未经过参数优化的CMGHT基础模型（参数基于工程常用范围初步设定：肋板厚度1 mm、肋板幅值3 mm、外管梯度厚度0.5 mm-1 mm-1.5 mm、外管长度33.3 mm），优化后结构的E_sa提高22%，η提升53%，$ \overline{F} $增强270%，进一步验证了设计方法的有效性。
- 多胞梯度结构 /
- 有限元分析 /
- 机器学习 /
- 多目标优化
Abstract: To address the collision protection requirements in fields such as aeronautics and space, traffic transportation, and civil construction, a novel design method for the corrugated multi-cell gradient hexagonal tube (CMGHT) was proposed. The sinusoidal corrugated ribs were introduced into a conventional hexagonal tube, integrated with the functional gradient design concept to improve the energy absorption performance of the structure. First, the FE model of the structure was established and numerical simulation analysis was conducted. Results indicate that under the same wall thickness condition, the key energy absorption indicators of CMGHT outperform existing structures significantly. Compared with the hexagonal tube (HT), the energy absorption (E_a), specific energy absorption (E_sa), mean crushing force ($ \overline{F} $), and crushing force efficiency (η) are improved by 390%, 76%, 395%, and 46%, respectively; Compared with the multi-cell hexagonal tube (MHT), the aforementioned indicators are increased by 121%, 58%, 121%, and 97%, respectively; Relative to a corrugated multi-cell hexagonal tube (CMHT), the enhancements are 7%, 7%, 8%, and 33% respectively, while the initial peak crushing force (F_max) is decreased by 18%. These results fully demonstrate its superior energy absorption performance. Subsequently, the geometric parameters of the ribs and outer tube were selected as design variables. A total of 540 sample sets were generated via full factorial experimental design, and a support vector machine (SVM) surrogate model was constructed. Combined with the crested porcupine optimization (CPO) algorithm, model optimization was completed to achieve the accurate prediction of the crashworthiness indicators for CMGHT. Finally, the multi-objective coati optimization algorithm (MOCOA) was adopted for multi-objective optimization to obtain the optimal combination of characteristic parameters. The optimization results show that compared with the CMGHT basic model without parameter optimization (the parameters are initially set based on the common range of engineering: rib thickness of 1 mm, rib amplitude of 3mm, outer tube gradient thickness of 0.5-1-1.5 mm, outer tube length of 33.3 mm), the E_sa of the optimized structure is increased by 22%, the η is increased by 53%, and the $ \overline{F} $ is increased by 270%, which further verifies the effectiveness of the design method.
- multi-cell gradient structures /
- FE simulation /
- machine learning /
- multi-objective optimization

HTML全文

图 1 CMGHT的构建过程

Figure 1. The construction process of CMGHT

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图 2 CMGHT的有限元模型

Figure 2. FE model of CMGHT

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图 3 HT的变形模式与压缩曲线对比

Figure 3. Comparison of the deformation mode and compression curve of HT

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图 4 各结构管力-位移曲线图

Figure 4. The force-displacement curves of the various structural tubes.

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图 5 不同结构管的耐撞性指标雷达图

Figure 5. The radar chart of crashworthiness indicators for various structural tubes.

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图 6 不同结构管的压缩变形

Figure 6. Compressive deformation of different structural tubes

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图 7 测试集的预测结果对比

Figure 7. Comparison of prediction results for test set

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图 8 MOCOA流程

Figure 8. Flowchart of MOCOA.

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图 9 帕累托前沿解

Figure 9. The Pareto front solutions.

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图 10 帕累托解集的平面投影

Figure 10. Plane projection of Pareto solution set.

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图 11 解B有限元仿真力-位移曲线

Figure 11. The force-displacement curve of FE simulation for Solution B

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图 12 优化后CMGHT压缩变形

Figure 12. The deformation sequence of the optimized CMGHT

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表 1 HT的耐撞性指标对比

Table 1. Comparison of the crashworthiness indicators of HT

方法	F_max/kN	E_a/kJ	$ \overline{F} $/kN	η/%	E_sa/(J·g⁻¹)
FE	20.78	0.81	9.64	46	6.982
QS^[23]	20.38	0.82	9.78	47	7.086
误差	1.9%	1.3%	1.4%	2.1%	1.4%

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表 2 不同结构管的耐撞性指标对比

Table 2. Comparison of the crashworthiness indicators of different structural tubes

结构	F_max/kN	E_a/kJ	$ \overline{F} $/kN	$ \eta $/%	E_sa/(J·g⁻¹)
HT	18.18	0.51	7.22	39	6.25
MHT	55.28	1.13	16.20	29	6.96
CMHT	76.20	2.33	33.25	43	10.26
CMGHT	62.27	2.50	35.75	57	10.97

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表 3 CMGHT参数取值范围

Table 3. Design parameter ranges for CMGHT

参数	t_r/mm	A/mm	t₀/mm	D/mm
取值范围	0.5～3	1～3	0.5～5	33.3～70

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表 4 不同优化算法模型收敛性能对比^[31-33]

Table 4. Comparison of convergence performance for different optimization algorithm models^[31–33]

优化算法	平均收敛代数	适应度
遗传算法（GA）	32±8	0.142 00
粒子群算法（PSO）	18±5	0.121 00
CPO	6±3	0.019 89

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表 5 SVM与CPO-SVR模型的超参数

Table 5. Hyperparameters of SVM and CPO-SVR models

核心参数	SVM	CPO-SVR	搜寻范围
核参数	1.0	8.1449	[0.1,100]
惩罚因子	0.25	0.9322	[0.01,10]

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表 6 参数取值边界处与参数范围外CMGHT预测性能

Table 6. CMGHT prediction performance at the parameter boundary and beyond the parameter range

结构参数	E_sa/(J·g⁻¹)	误差	F_max/kN	误差	$ \overline{F} $/kN	误差
3.2-3-4.1-72（仿真）	18.12	7.4%	251.89	5.2%	208.54	6.6%
3.2-3-4.1-72（预测）	16.77	7.4%	238.73	5.2%	194.71	6.6%
3.4-3-1-30（仿真）	13.41	1.8%	181.16	5.9%	110.41	5.2%
3.4-3-1-30（预测）	13.16	1.8%	170.44	5.9%	116.20	5.2%
0.5-1-1-30（仿真）	6.78	2.3%	31.17	9.2%	12.67	6.5%
0.5-1-1-30（预测）	6.62	2.3%	34.05	9.2%	13.5	6.5%
3.1-1-4.3-74（仿真）	15.09	4.9%	211.02	7.2%	154.7	1.9%
3.1-1-4.3-74（预测）	14.34	4.9%	195.82	7.2%	151.71	1.9%
3-1-0.9-30（仿真）	9.99	3.2%	113.01	6.5%	53.81	4.9%
3-1-0.9-30（预测）	9.67	3.2%	105.60	6.5%	56.49	4.9%
3-3-4.2-70（仿真）	16.36	3.4%	244.92	0.4%	193.25	3.6%
3-3-4.2-70（预测）	15.81	3.4%	246.14	0.4%	186.11	3.6%
3-1-1-30（仿真）	10.38	9.7%	117.85	4.2%	57.45	2.2%
3-1-1-30（预测）	11.39	9.7%	122.88	4.2%	56.14	2.2%
3-3-5-70（仿真）	16.17	0.3%	238.62	0.4%	187.2	0.5%
3-3-5-70（预测）	16.12	0.3%	237.59	0.4%	186.2	0.5%

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表 7 COA与PSO和GA的对比^[37]

Table 7. Comparison of COA, PSO, and GA^[37]

对比维度	COA	PSO	GA
CEC-2017（维度为10）核心函数表现	C1（单模态）：均值为100，标准差为1.33·10⁻⁵ C3（单模态）：均值为300，标准差为4.64·10⁻¹⁴ C10（多模态）：均值为1270.97，标准差为112.83	C1：均值为3347.23，标准差为4427.81 C3：均值为329.38，标准差为8.604 C10：均值为2013.59，标准差为348.99	C1：均值为12641048，标准差为4849091 C3：均值为15733.23，标准差为10584.32 C10：均值为1766.65，标准差为320.45
CEC-2017（维度为100）核心函数表现	C4（多模态）：均值为770.53，标准差为51.36 C6（复合函数）：均值为636.39，标准差为2.37 C8（复合函数）：均值为1393.98，标准差为128.98	C4：均值为2592.37，标准差为746.46 C6：均值为663.56，标准差为6.46 C8：均值为1733.68，标准差为66.67	C4：均值为9756.10，标准差为535.13 C6：均值为665.26，标准差为6.76 C8：均值为2070.20，标准差为45.98
CEC-2011（实际问题）表现	C11-F1：均值为2.84，标准差为5.69 C11-F7：均值为0.75，标准差为0.12 C11-F12：均值为1186100，标准差为42666.96	C11-F1：均值为19.48，标准差为6.94 C11-F7：均值为1.15，标准差为0.32 C11-F12：均值为2428911，标准差为176214.5	C11-F1：均值为25.59，标准差为1.27 C11-F7：均值为1.83，标准差为0.28 C11-F12：均值为15862796，标准差为113798.6
收敛速度（CEC-2017 维度为30）	迭代500步时，C10函数均值为4032.98，接近全局最优；收敛曲线陡峭	迭代500步时，C10函数均值为228.98，仅达到COA的81.3%；前期探索缓慢	迭代500步时，C10函数均值为6407.28，仅达到COA的62.9%；后期收敛停滞

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表 8 三个帕累托最优解的结构参数

Table 8. Structural parameters of three Pareto optimal solutions

解	t_r/mm	A/mm	t₀/mm	D/mm
A	3	3	1.5-2.2-2.4	65
B	2.5	3	0.9-2.2-5	48
C	3	3	0.5-1.8-4.1	44

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表 9 三种帕累托最优解的对比

Table 9. Comparison of the three Pareto optimal solutions

解	E_sa/(J·g⁻¹)	F_max/kN	$ \overline{F} $/kN	η/%
A	12.35	118.92	96.3	80
B	13.06	146.03	129.1	88
C	12.86	187.11	156.2	83

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表 10 模拟结果与预测结果的对比

Table 10. Comparison of the simulation and prediction results

	E_sa/(J·g⁻¹)	F_max/kN	$ \overline{F} $/kN
预测	13.06	146.03	129.1
仿真	13.33	150.81	132.1
误差	2%	3.1%	2.2%

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表 11 CMGHT优化前后各组件吸能对比

Table 11. Comparison of energy absorption of each component before and after CMGHT optimization

对照组	外管吸能/kJ	占比/%	肋板吸能/kJ	占比/%	外管-肋板相互作用耗能/kJ	占比/%	E_a/kJ
优化前	0.59	23.6	1.8	72	0.11	4.4	2.5
优化后	3.25	35.1	5.61	60.7	0.39	4.2	9.25

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表 12 CMGHT基础模型与优化后CMGHT的耐撞性能对比

Table 12. Comparison of the crashworthiness performance of original CMGHT and optimized CMGHT

对照组	E_sa/(J·g⁻¹)	η/%	$ \overline{F} $/kN
优化前	10.96	57.41	35.7
优化后	13.33	87.59	132.1

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