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

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
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- 文章访问数: 182
- HTML全文浏览量: 107
- PDF下载量: 36
出版历程
- 收稿日期: 2023-11-08
- 修回日期: 2023-11-30
- 录用日期: 2023-12-09
- 网络出版日期: 2023-12-18
- 刊出日期: 2024-10-14

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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长摘要

目的
在缠绕成型工艺过程中，控制复合材料结构件缠绕成型工艺过程中的工艺参数是保证制品性能的关键。然而目前对于湿法缠绕工艺参数的研究并不全面，部分工艺参数往往需要通过经验调节；此外，缠绕制品具有多维度的质量性能评价指标，如何根据实际需求对缠绕制品的不同性能表征进行多目标优化是目前研究存在的难点之一。针对上述问题，本文结合缠绕成型试验并建立缠绕制品性能预测模型，基于NSGA-Ⅱ算法与主成分分析法，对缠绕成型过程进行多目标工艺参数优化，对湿法缠绕成型工艺过程工艺参数的选取具有一定的指导与借鉴意义。
方法
采用响应面法设计湿法缠绕成型试验，对缠绕制品进行层间剪切强度、孔隙率、纤维体积分数测量，并针对测量结果进行多元回归函数拟合，建立面向不同表征参数的缠绕制品性能预测模型，利用残差分析、预测值与实际值对比验证预测模型的准确性。采用Morris法进行缠绕制品不同表征参数对工艺参数的敏感度分析，研究随着单工艺参数不同取值范围敏感度系数的变化趋势，并得到缠绕制品工艺参数稳定区间，得到缠绕成型过程中不同工艺参数对缠绕制品性能影响程度。以层间剪切强度与孔隙率作为缠绕制品的性能表征参数，采用NSGA-Ⅱ算法进行缠绕过程多目标工艺参数优化，获得Pareto最优解集，并结合主成分分析法，得出层间剪切强度与孔隙率的主成分贡献率，通过影响因子加权获得最优工艺参数组合，并基于缠绕成型试验，验证最优工艺参数组合的合理性与准确性。
结果
缠绕制品层间剪切强度对工艺参数的敏感程度从大到小依次为：缠绕张力、缠绕速度、胶辊间隙；孔隙率对工艺参数的敏感程度从大到小依次为：胶辊间隙、缠绕张力、缠绕速度；纤维体积分数对工艺参数的敏感程度从大到小依次为：缠绕张力、胶辊间隙、缠绕速度。对三个表征参数的工艺参数稳定区间进行交集运算，得到缠绕成型过程的整体稳定区间为：缠绕张力：[55N,75N]；胶辊间隙：[0.1mm,0.12mm]；缠绕速度：[0.1m/s,0.22m/s]。针对缠绕制品不同性能表征参数进行主成分分析，得到层间剪切强度与孔隙率的主成分贡献率分别为60.9%、39.1%。对NSGA-Ⅱ算法输出的Pareto最优解集进行加权，得到基于NSGA-Ⅱ算法的最佳工艺参数组合为：缠绕张力65.1N，胶辊间隙0.12mm，缠绕速度0.17m/s；在得出的最佳工艺参数组合下，缠绕制品的层间剪切强度为54.4MPa，孔隙率为1.24%，纤维体积分数为74.13%。为验证工艺参数优化方法的准确性，根据优化得到的工艺参数进行缠绕成型试验，并测试缠绕制品的相应表征参数：其中，层间剪切强度的预测值与实际值的平均相对误差为2.3%，孔隙率的预测值与实际值的平均相对误差为4.2%，预测值与实际值的平均相对误差为1.3%。
结论
在湿法缠绕成型过程中，缠绕张力与胶辊间隙对缠绕制品性能与质量影响较大。相应的缠绕成型试验结果表明，基于NSGA-Ⅱ算法的理论优化值与实际值基本吻合，表明多目标优化方法准确合理，本文所采用的多目标工艺参数优化方法准确可靠，对复合材料湿法缠绕成型工艺中工艺参数的选取具有一定的指导意义与参考价值。

创新点

树脂基复合材料以其优越的性能被广泛应用于航空航天、汽车生产以及民用等领域。在复合材料诸多成型方法中，湿法缠绕具有纤维排列平行度好、强度转化率高、成本较低等优点，使其在复合材料成型领域受到越来越多的关注与使用。在缠绕成型工艺过程中，控制复合材料结构件缠绕成型工艺过程中的工艺参数是保证制品性能的关键。然而目前对于湿法缠绕工艺参数的研究并不全面，部分工艺参数往往需要通过经验调节；此外，缠绕制品具有多维度的质量性能评价指标，如何根据实际需求对缠绕制品的不同性能表征进行多目标优化是目前研究存在的难点之一。
本文引入湿法缠绕中胶辊间隙这一工艺参数，通过缠绕成型试验建立多元回归模型，探究缠绕制品的层间剪切强度、孔隙率、纤维体积分数与缠绕张力、胶辊间隙、缠绕速度之间的关系。采用Morris法进行缠绕制品不同表征参数对工艺参数的敏感度分析，分析结果表明：层间剪切强度对工艺参数的敏感程度从大到小依次为：缠绕张力、缠绕速度、胶辊间隙；孔隙率对工艺参数的敏感程度从大到小依次为：胶辊间隙、缠绕张力、缠绕速度；纤维体积分数对工艺参数的敏感程度从大到小依次为：缠绕张力、胶辊间隙、缠绕速度。获得基于不同表征参数的相对稳定区间，并通过缠绕成型试验验证选取区间的稳定性。以缠绕制品的层间剪切强度大、孔隙率小为目标，采用NSGA-Ⅱ算法获得相应的Pareto解集，结合主成分分析法，得到层间剪切强度、孔隙率的主成分贡献率分别为60.9%和39.1%，并根据主成分分析结果对优化解集进行加权。最终得到优化的工艺参数组合：缠绕张力为65.1N、胶辊间隙为0.12mm、缠绕速度为0.17m/s,对应的缠绕制品层间剪切强度为54.4MPa，孔隙率为1.24%，纤维体积分数为74.13%。相应的缠绕成型试验结果表明，理论预测值与实际值基本吻合，表明优化方法准确合理，对湿法缠绕成型工艺过程工艺参数的选取具有一定的指导与借鉴意义。
层间剪切强度对工艺参数的敏感度系数变化
工艺参数平均敏感度
基于NSGA-Ⅱ算法的最优解集

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基于NSGA-II算法的缠绕过程多目标工艺参数优化

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

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

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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