基于NSGA-II算法的缠绕过程多目标工艺参数优化

韩宇泽; 刘雁鹏; 任中杰; 任明法

doi:10.13801/j.cnki.fhclxb.20231218.005

基于NSGA-II算法的缠绕过程多目标工艺参数优化

doi: 10.13801/j.cnki.fhclxb.20231218.005

韩宇泽^{1, 2},
刘雁鹏²,
任中杰²,
任明法^{1, 3, 4, ,}

1.
大连理工大学　机械工程学院，大连 116024
2.
大连理工大学　工程力学系，大连 116024
3.
高性能精密制造全国重点实验室，大连 116024
4.
辽宁省先进复合材料高性能制造重点实验室，大连 116024

基金项目: 国家自然科学基金(12272078)；科技领军人才团队专题(DUT22LAB503)；大连市科技创新基金项目(2020JJ25CY011)

详细信息

通讯作者:
任明法，博士，教授，博士生导师，研究方向为复合材料压力容器　E-mail: renmf@dlut.edu.cn

中图分类号: TB332
计量
- 文章访问数: 72
- HTML全文浏览量: 78
- PDF下载量: 19
- 被引次数: 0
出版历程
- 收稿日期: 2023-11-09
- 修回日期: 2023-12-01
- 录用日期: 2023-12-10
- 网络出版日期: 2023-12-19
- 刊出日期: 2024-10-15

Multi-objective process parameter optimization for winding process based on NSGA-II algorithm

HAN Yuze^{1, 2},
LIU Yanpeng²,
REN Zhongjie²,
REN Mingfa^{1, 3, 4
, ,}

1.
School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China
2.
Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
3.
National Key Laboratory of High Performance Precision Manufacturing, Dalian 116024, China
4.
Liaoning Provincial Key Laboratory of Advanced Composite Materials High Performance Manufacturing, Dalian 116024, China

Funds: National Natural Science Foundation of China (12272078); Science and Technology Leading Talent Team Theme (DUT22LAB503); Dalian Science and Technology Innovation Fund Project (2020JJ25CY011)

摘要

摘要: 基于复合材料缠绕成型工艺过程，采用响应面法设计湿法缠绕成型试验，以缠绕制品的层间剪切强度、孔隙率为关键性能指标，根据试验结果建立缠绕张力、胶辊间隙、缠绕速度对缠绕制品性能的多元回归预测模型，并验证回归模型的准确性。结合回归模型与Morris法进行不同缠绕制品性能表征参数对各工艺参数的敏感度排序，并得到各工艺参数的相对稳定区间，通过缠绕成型试验验证敏感度分析的有效性。以缠绕制品的层间剪切强度大、孔隙率小为目标，通过主成分分析(PCA)得到层间剪切强度的贡献率为60.9%、孔隙率的贡献率为39.1%，利用NSGA-II算法获得工艺参数最优解集：缠绕张力为65.1 N、胶辊间隙为0.12 mm、缠绕速度为0.17 m/s，缠绕制品的层间剪切强度为54.4 MPa、孔隙率为1.24%、纤维体积分数为74.13vol%。
- 复合材料 /
- 纤维缠绕 /
- 层间剪切强度 /
- 孔隙率 /
- 纤维体积分数 /
- NSGA-II算法 /
- 多目标参数优化
Abstract: Based on the composites winding molding process, the response surface methodology was used to design the wet winding molding test. Taking the interlayer shear strength and porosity of the winding products as the key performance indexes, the multivariate regression prediction model of winding tension, the gap between squeezer rollers and winding speed on the performance of winding products was established based on the experimental results, and the accuracy of the regression model was verified. Combining the regression model and Morris method for ranking the sensitivity of different winding product performance characterization parameters to each process parameter, the relative stability intervals of each process parameter were obtained and the validity of sensitivity analysis through the winding molding test was verified. Taking the large interlayer shear strength and small porosity of the winding products as the target, the dedication rate of interlayer shear strength is 60.9% and the dedication rate of porosity is 39.1% through the principal component analysis, and the optimal solution set of the process parameters is obtained by using the NSGA-II algorithm: The winding tension is 65.1 N, the gap between squeezer rollers is 0.12 mm, and the winding speed is 0.17 m/s. The interlayer shear strength of the winding product is 54.4 MPa, the porosity is 1.24%, and the fiber volume fraction is 74.13vol%.
- composite material /
- fiber winding /
- interlayer shear strength /
- porosity /
- fiber volume fraction /
- NSGA-II algorithm /
- multi-objective parameter optimization

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图 1 海军军械实验室(NOL)环尺寸示意图

Figure 1. Schematic of naval ordnance laboratory (NOL) ring dimensions

D—NOL ring diameter; h—NOL ring thickness; b—NOL ring width

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图 2 NOL环试样获取

Figure 2. NOL ring specimen acquisition

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图 3 观测缠绕制品孔隙的显微照片

Figure 3. Photomicrographs for observing the porosity of winding products

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图 4 观测缠绕制品纤维体积分数的显微照片

Figure 4. Photomicrographs for observation of fiber volume fraction of entangled products

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图 5 预测模型残差正态概率分布图

Figure 5. Residual normal probability distribution diagram of predictive model

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图 6 预测模型残差运行图

Figure 6. Residual train diagram of predictive model

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图 7 预测值与实际值对比

Figure 7. Compare the predicted value with the actual value

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图 8 层间剪切强度对工艺参数的平均敏感度系数

Figure 8. Average sensitivity coefficient of interlayer shear strength to process parameters

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图 9 层间剪切强度对工艺参数的敏感度系数变化

Figure 9. Variation of sensitivity coefficients of interlayer shear strength to process parameters

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图 10 孔隙率对工艺参数的平均敏感度系数

Figure 10. Average sensitivity coefficient of porosity to process parameters

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图 11 孔隙率对工艺参数的敏感度系数变化

Figure 11. Variation of sensitivity coefficients of porosity to process parameters

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图 12 纤维体积分数对工艺参数的平均敏感度系数

Figure 12. Average sensitivity coefficient of fiber volume fraction to process parameters

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图 13 纤维体积分数对工艺参数的敏感度系数变化

Figure 13. Variation of sensitivity coefficients of fiber volume fraction to process parameters

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图 14 工艺参数平均敏感度

Figure 14. Average sensitivity of process parameters

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图 15 NSAG-II算法流程图

Figure 15. NSAG-II algorithm flowchart

POP—Populations

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图 16 基于NSGA-II算法的最优解集

Figure 16. Optimal solution set based on NSGA-II algorithm

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表 1 复合材料湿法缠绕工艺参数水平表

Table 1. Horizontal table of parameters of composite wet winding process

Level	$t$/N	$v$/(m·s⁻¹)	$d$/mm
−1	20	0.1	0.05
0	50	0.25	0.1
1	80	0.4	0.15
Notes: $t$—Winding tension; $d$—Gap between squeezer rollers; $v$—Winding speed.

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表 2 NOL环缠绕试验设计方案及试验结果

Table 2. NOL ring winding test design and test results

$t$/N	$v$/(m·s⁻¹)	$d$/mm	${\tau _{\text{S}}}$/MPa	CV/%	$ V_{ }\mathrm{_C} $/%	CV/%	${V_{\text{f}}}$/vol%	CV/%
80	0.4	0.1	38.11	1.72	1.54	1.88	75.71	0.38
50	0.25	0.1	52.64	0.23	2.3	0.58	75.71	0.18
50	0.4	0.05	41.98	1.14	3.52	2.54	77.36	0.59
20	0.4	0.1	30.12	1.63	3.73	1.82	62.74	0.84
80	0.1	0.1	50.71	0.52	0.4	0.64	75.15	0.54
20	0.1	0.1	35.42	0.98	2.84	0.29	62.60	0.45
20	0.25	0.15	32.14	1.04	2.62	1.38	61.24	1.12
50	0.1	0.15	45.82	0.58	0.38	0.28	67.24	0.95
50	0.25	0.1	54.89	0.38	2.3	0.68	73.23	0.22
80	0.25	0.05	47.99	0.88	2.38	2.42	77.68	0.37
50	0.4	0.15	48.65	0.64	1.4	1.33	69.83	0.57
50	0.1	0.05	48.27	0.79	2.94	0.92	73.03	1.22
50	0.25	0.1	51.98	0.31	2.2	0.61	73.46	0.31
80	0.25	0.15	48.04	1.38	0.27	0.95	75.06	1.34
50	0.25	0.1	53.09	0.45	2.4	0.42	71.98	0.19
50	0.25	0.1	51.7	0.28	2.1	0.59	72.55	0.25
20	0.25	0.05	33.14	0.81	4.28	0.35	65.91	1.04
Notes: ${\tau _{\text{S}}}$—Interlayer shear strength;$ V_{\mathrm{C}} $—Porosity; ${V_{\text{f}}}$—Fiber volume fraction; CV—Coefficient of variation.

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表 3 基于层间剪切强度的工艺参数相对稳定区间

Table 3. Relative stability intervals for process parameters based on interlayer shear strengths

Parm	Interval	Range of process parameter	Range of interlayer shear strength variation/MPa	Magnitude of change/MPa
$t$	Stable	[55 N, 75 N]	[51.5, 53.8]	2.3
$t$	Sensitive	[20 N, 40 N]	[39.8, 51.2]	11.4
$d$	Stable	[0.08 mm, 0.12 mm]	[52.1, 52.8]	0.7
$d$	Sensitive	[0.05 mm, 0.09 mm]	[47.7, 52.6]	4.9
$v$	Stable	[0.1 m/s, 0.22 m/s]	[51.1, 52.9]	1.8
$v$	Sensitive	[0.28 m/s, 0.4 m/s]	[46.2, 52.2]	6.0

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表 4 基于孔隙率的工艺参数相对稳定区间

Table 4. Relative stability intervals of process parameters based on porosity

Parm	Interval	Range of process parameter	Range of porosity variation/ %	Magnitude of change/ %
$t$	Stable	[55 N, 80 N]	[1.24, 1.88]	0.64
$t$	Sensitive	[20 N, 55 N]	[1.88, 3.31]	1.43
$d$	Stable	[0.1 mm, 0.15 mm]	[1.02, 1.92]	0.80
$d$	Sensitive	[0.05 mm, 0.1 mm]	[1.92, 3.35]	1.43
$v$	Stable	[0.1 m/s, 0.25 m/s]	[1.27, 1.85]	0.58
$v$	Sensitive	[0.25 m/s, 0.4 m/s]	[1.85, 2.68]	0.83

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表 5 基于纤维体积分数的工艺参数稳定区间

Table 5. Relative stability intervals of process parameters based on fiber volume fraction

Parm	Interval	Range of process parameter	Range of fiber volume fraction variation/%	Magnitude of change/ %
$t$	Stable	[50 N, 80 N]	[74.4, 76.5]	2.1
$t$	Sensitive	[20 N, 50 N]	[63.6, 74.4]	10.8
$d$	Stable	[0.05 mm, 0.1 mm]	[74.4, 75.8]	1.4
$d$	Sensitive	[0.1 mm, 0.15 mm]	[70.2, 74.4]	4.2
$v$	Stable	[0.1 m/s, 0.25 m/s]	[73.8, 74.4]	0.6
$v$	Sensitive	[0.25 m/s, 0.4 m/s]	[74.4, 75.7]	1.3

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表 6 单目标工艺参数优化

Table 6. Single-objective process parameter optimization

Characterization parameter	$t$/N	$d$/mm	$v$/(m·s⁻¹)	$ V_{\mathrm{f}} $/vol%	Optimum value
${\tau _{\text{S}}}$	61	0.09	0.2	74.97	56.6 MPa
$ V_{\text{C}} $	48	0.15	0.12	65.76	0.01%

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表 7 主成分分析结果

Table 7. Results of principal component analysis

Principal component	Eigenvalue	Principal component contribution ratio/%
${\tau _{\text{S}}}$	1.2176	60.9
$ V_{\text{C}} $	0.7824	39.1
Total	–	100

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表 8 基于NSGA-II与主成分分析法的多目标优化结果

Table 8. Multi-objective optimization results based on NSGA-II with principal component analysis

$t$/N	$d$/mm	$v$/(m·s⁻¹)	${V_{\text{f}}}$/%	${\tau _{\text{S}}}$/MPa	$ V_{\text{C}} $/%
65.1	0.12	0.17	74.13	54.4	1.24

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表 9 层间剪切强度的理论值与实际值对比

Table 9. Comparison of theoretical and actual values of interlayer shear strength

No.	$t$/N	$d$/mm	$v$/(m·s⁻¹)	${\tau _{\text{S}}}$/MPa		Relative error/%
No.	$t$/N	$d$/mm	$v$/(m·s⁻¹)	Predict	Actual	Relative error/%
1	65.1	0.12	0.17	54.4	56.5	3.8
2	65.1	0.12	0.17	54.4	53.2	2.2
3	65.1	0.12	0.17	54.4	55.6	2.2
4	65.1	0.12	0.17	54.4	53.4	1.8
5	65.1	0.12	0.17	54.4	55.3	1.7

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表 10 孔隙率的理论值与实际值对比

Table 10. Comparison of theoretical and actual values of porosity

No.	$t$/N	$d$/mm	$v$/(m·s⁻¹)	Porosity/%		Relative error/%
No.	$t$/N	$d$/mm	$v$/(m·s⁻¹)	Predict	Actual	Relative error/%
1	65.1	0.12	0.17	1.24	1.32	6.5
2	65.1	0.12	0.17	1.24	1.21	2.4
3	65.1	0.12	0.17	1.24	1.22	1.6
4	65.1	0.12	0.17	1.24	1.15	7.3
5	65.1	0.12	0.17	1.24	1.28	3.2

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表 11 纤维体积分数的理论值与实际值对比

Table 11. Comparison of theoretical and actual values of fiber volume fraction

No.	$t$/N	$d$/mm	$v$/(m·s⁻¹)	${V_{\text{f}}}$/vol%		Relative error/%
No.	$t$/N	$d$/mm	$v$/(m·s⁻¹)	Predict	Actual	Relative error/%
1	65.1	0.12	0.17	74.13	73.28	1.1
2	65.1	0.12	0.17	74.13	74.8	0.9
3	65.1	0.12	0.17	74.13	75.09	1.3
4	65.1	0.12	0.17	74.13	75.88	2.4
5	65.1	0.12	0.17	74.13	74.64	0.7

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