面向铝合金加工的GRA-SVM-CPSO混合多目标优化方法

庄可佳; 张服林; 代星; 翁剑

doi:10.13433/j.cnki.1003-8728.20200463

面向铝合金加工的GRA-SVM-CPSO混合多目标优化方法

doi: 10.13433/j.cnki.1003-8728.20200463

1.
武汉理工大学机电工程学院湖北省数字制造重点实验室，武汉　430070
2.
华中科技大学机械科学与工程学院数字制造装备与技术国家重点实验室，武汉　430074

基金项目: 国家自然科学基金项目（52175482）

详细信息

作者简介:
庄可佳（1988−），副教授，硕士生导师，博士，研究方向为数字化制造，zhuangkj@whut.edu.cn

中图分类号: TG501.2
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- 文章访问数: 80
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- 被引次数: 0
出版历程
- 收稿日期: 2020-08-06
- 刊出日期: 2023-02-04

Multi-objective Parameter Optimization of Aluminum Alloy Machining via GRA-SVM-CPSO Hybrid Method

1.
Hubei Digital Manufacturing Key Laboratory, School of Mechanical and Electrical Engineering, Wuhan University of Technology, Wuhan 430070, China
2.
State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

摘要

摘要: 为有效改善铝合金切削时不同指标优化出现的冲突问题，本文提出了一种新的多目标优化方法。首先，应用灰色关联分析（Grey relations analysis，GRA）将切削加工过程中切削力、表面粗糙度和材料去除率等多目标问题转化为灰色关联度（Grey relational grade，GRG）的单目标问题；然后，基于支持向量机模型（Support vector machine，SVM）建立切削参数与GRG之间关联模型；最后，以切削力和表面粗糙度最小化、材料去除率最大化为优化目标，采用混沌粒子群优化算法（Chaos particle swarm optimization, CPSO）优选得到的铝合金加工最优参数（切速为400 m/min，进给为0.15 mm/r，切深为1 mm）。将优化结果与粒子群算法（Particle swarm optimization，PSO）对比发现，CPSO算法具有更强的全局搜索能力，能够更快地收敛至全局最佳位置，获得更好的优化结果。
- GRA /
- SVM /
- CPSO /
- 切削力 /
- 表面粗糙度 /
- 多目标优化
Abstract: In order to improve the conflict problem of different index optimization in aluminum alloy machining effectively, a new multi-objective optimization method has been proposed in this paper. Firstly, grey relations analysis (GRA) has been applied to convert the multi-objective problems of cutting force, surface roughness and material removal rate in the machining into single-objective problem of grey relational grade (GRG). Then, a correlation model between the cutting parameters and GRG has been constructedvia support vector machine (SVM). Finally, the chaos particle swarm optimization (CPSO) has been applied to find the optimal processing parameters for minimizing cutting force and surface roughness and maximizing material removal rate at a cutting speed of 400 m/min, feed rate of 0.15 mm/r and cutting depth of 1 mm in the turning of aluminum alloy and it turns out that the CPSO algorithm has better global search capabilities,can converge to the global optimal position faster and obtain better optimization results comparing with particle swarm optimization (PSO) algorithm.
- GRA /
- SVM /
- CPSO /
- cutting force /
- surface roughness /
- multi-objective optimization

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图 1 实验装置图

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图 2 基于GRA-SVM-CPSO混合方法的多目标优化流程图

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图 3 SVM预测效果

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图 4 SVM预测误差

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图 5 CPSO与PSO迭代曲线图

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表 1 6061铝合金各元素的质量分数 %

Cu	Mn	Mg	Zn	Fe	Ti	Si	Cr	Al
0.15 ~ 0.4	0.15	0.8 ~1.2	0.25	0.7	0.15	0.4 ~ 0.8	0.04 ~ 0.35	其余

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表 2 6061铝合金物理力学性能

弹性模量	屈服强度	弯曲强度	抗拉强度	杨氏模量	泊松比
68.9 GPa	240 MPa	228 MPa	290 MPa	69 GPa	0.33

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表 3 切削参数的编码及水平

切削参数	编码水平
切削参数	−1	0	1
切削速度V_c/（m·min⁻¹）	300	350	400
进给速度f /（mm·r⁻¹）	0.15	0.2	0.25
切削深度a_p/mm	1	1.5	2

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表 4 实验数据

编号	切削参数			响应
编号	V_c/ （m·min⁻¹）	f/ （mm·r⁻¹）	a_p/ mm	F_c/ N	R_a/ μm	MRR/ （cm³·min⁻¹）
1	400	0.25	1.0	72.27	3.30	100.00
2	400	0.20	1.0	61.92	2.47	80.00
3	400	0.15	1.0	48.30	1.64	60.00
4	350	0.25	1.0	69.02	3.36	87.50
5	350	0.20	1.0	65.37	2.86	70.00
6	350	0.15	1.0	54.59	1.80	52.50
7	300	0.25	1.0	79.67	4.41	75.00
8	300	0.20	1.0	68.85	3.06	60.00
9	300	0.15	1.0	57.78	1.89	45.00
10	400	0.25	2.0	181.61	3.65	200.00
11	400	0.20	2.0	154.72	2.55	160.00
12	400	0.15	2.0	126.16	1.99	120.00
13	400	0.25	1.5	119.62	3.35	150.00
14	400	0.20	1.5	101.17	2.61	120.00
15	400	0.15	1.5	86.43	1.73	90.00
16	350	0.25	1.5	121.31	3.03	131.25
17	350	0.25	2.0	182.89	3.63	175.00
18	350	0.20	2.0	154.74	2.90	140.00
19	350	0.15	2.0	125.73	2.35	105.00
20	300	0.25	2.0	198.47	3.64	150.00
21	350	0.20	1.5	95.73	3.10	105.00
22	350	0.15	1.5	82.82	2.04	78.75
23	300	0.25	1.5	119.47	3.59	112.50
24	300	0.20	1.5	104.40	2.84	90.00
25	300	0.20	2.0	159.16	2.64	120.00
26	300	0.15	2.0	128.47	2.03	90.00
27	300	0.15	1.5	87.97	1.77	67.50

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表 5 灰色关联系数和灰色关联度

试验编号	比较序列			偏差序列			灰色关联系数			GRG
试验编号	$ x_{i}^{*}\left(F_{c}\right)$	$ x_{i}^{*}\left(R_{a}\right)$	$ x_{i}^{*}（M R R）$	$ \Delta_{i}\left(F_{c}\right)$	$ \Delta_{i}\left(R_{a}\right)$	$ \Delta_{i}（M R R）$	$\gamma_{_{0 i} }\left(F_{c}\right)$	$\gamma_{_{0 i} }\left(R_{a}\right)$	$\gamma_{_{0 i} }（M R R）$	GRG
1	0.84	0.40	0.35	0.16	0.60	0.65	0.76	0.45	0.44	0.51
2	0.91	0.70	0.23	0.09	0.30	0.77	0.85	0.62	0.39	0.58
3	1.00	1.00	0.10	0.00	0.00	0.90	1.00	1.00	0.36	0.74
4	0.86	0.38	0.27	0.14	0.62	0.73	0.78	0.45	0.41	0.50
5	0.89	0.56	0.16	0.11	0.44	0.84	0.81	0.53	0.37	0.52
6	0.96	0.94	0.05	0.04	0.06	0.95	0.92	0.89	0.34	0.68
7	0.79	0.00	0.19	0.21	1.00	0.81	0.71	0.33	0.38	0.43
8	0.86	0.49	0.10	0.14	0.51	0.90	0.79	0.49	0.36	0.50
9	0.94	0.91	0.00	0.06	0.09	1.00	0.89	0.84	0.33	0.65
10	0.11	0.27	1.00	0.89	0.73	0.00	0.36	0.41	1.00	0.63
11	0.29	0.67	0.74	0.71	0.33	0.26	0.41	0.60	0.66	0.59
12	0.48	0.87	0.48	0.52	0.13	0.52	0.49	0.80	0.49	0.61
13	0.53	0.38	0.68	0.47	0.62	0.32	0.51	0.45	0.61	0.52
14	0.65	0.65	0.48	0.35	0.35	0.52	0.59	0.59	0.49	0.55
15	0.75	0.97	0.29	0.25	0.03	0.71	0.66	0.94	0.41	0.67
16	0.51	0.50	0.56	0.49	0.50	0.44	0.51	0.50	0.53	0.51
17	0.10	0.28	0.84	0.90	0.72	0.16	0.36	0.41	0.76	0.54
18	0.29	0.54	0.61	0.71	0.46	0.39	0.41	0.52	0.56	0.52
19	0.48	0.74	0.39	0.52	0.26	0.61	0.49	0.66	0.45	0.54
20	0.00	0.28	0.68	1.00	0.72	0.32	0.33	0.41	0.61	0.47
21	0.68	0.47	0.39	0.32	0.53	0.61	0.61	0.49	0.45	0.50
22	0.77	0.85	0.22	0.23	0.15	0.78	0.69	0.77	0.39	0.60
23	0.53	0.29	0.44	0.47	0.71	0.56	0.51	0.41	0.47	0.46
24	0.63	0.56	0.29	0.37	0.44	0.71	0.57	0.53	0.41	0.49
25	0.26	0.64	0.48	0.74	0.36	0.52	0.40	0.58	0.49	0.51
26	0.47	0.86	0.29	0.53	0.14	0.71	0.48	0.78	0.41	0.57
27	0.74	0.95	0.15	0.26	0.05	0.85	0.65	0.91	0.37	0.64

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表 6 参数设置

PSO优化算法		混沌搜索算法
参数名	参数值	参数名	参数值
学习因子c	c₁=1.5	迭代次数M	M=10
学习因子c	c₂=1.5
惯性权重w	w_min=0.1
惯性权重w	w_max=0.5
种群规模N	N=20	适应度阈值α	α=0.01
最大迭代次数T_max	T_max=100
位置边界POS	上边界POS_max=[400,0.25,2]
位置边界POS	下边界POS_min=[300,0.15,1]	平均粒距阈值β	β=10
速度边界V	速度上限V_max=[40,0.025,0.1]
速度边界V	速度下限V_min=[−40,−0.025,−0.1]

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