基于ANN-GA协同寻优的动态拉伸试样尺寸优化方法

王清华; 徐丰; 郭伟国

doi:10.11883/bzycj-2021-0218

基于ANN-GA协同寻优的动态拉伸试样尺寸优化方法

doi: 10.11883/bzycj-2021-0218

王清华^1,,
徐丰^{2, 3, ,},
郭伟国¹

1.
西北工业大学航空学院，陕西西安 710072
2.
西北工业大学航天学院，陕西西安 710072
3.
西北工业大学青岛研究院，山东青岛 266200

基金项目: 国家自然科学基金（11702224，11872051）

详细信息

作者简介:
王清华（1993－　），男，博士研究生，QinghuaWang@mail.nwpu.edu.cn

通讯作者:
徐　丰（1985－　），男，博士，副研究员，xufeng@nwpu.edu.cn

中图分类号: O383; TB302.3
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- 被引次数: 0
出版历程
- 收稿日期: 2021-05-28
- 修回日期: 2021-09-10
- 网络出版日期: 2021-12-17
- 刊出日期: 2022-01-20

A method of geometry optimization for dynamic tensile specimen based on artificial neural network and genetic algorithm

WANG Qinghua^1
,,
XU Feng^{2, 3
, ,},
GUO Weiguo¹

1.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
2.
School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
3.
Qingdao Research Institute, Northwestern Polytechnical University, Qingdao 266200, Shandong, China

摘要

摘要: 材料动态拉伸力学性能测试中，动态拉伸试样的几何尺寸对测试结果的准确性与有效性有着较大影响。为对动态拉伸试样的结构进行优化设计，以使其在动态拉伸过程中更好地满足一维应力与变形均匀等基本假设。首先，建立了量化的试样测量准确度指标，即应力平衡达到时间、变形均匀度、非轴向应力相对水平、过渡段相对变形。然后，对试样结构参数进行正交试验设计，通过数值模拟的方法得到了关于试样尺寸与测量准确度指标的正交试验数据库，并对正交试验数据库进行多目标正交试验矩阵分析，得到了试样结构参数对各测量准确度指标影响的主次顺序和规律。最后，以正交试验数据库为训练集，采用人工神经网络（artificial neural network, ANN）协同遗传算法（genetic algorithm, GA）的全局寻优方法对试样的结构尺寸进行优化设计，得到了试样的最优结构尺寸，并对最优尺寸的有效性进行了验证。结果表明，优化后的试样结构在材料动态拉伸力学性能测试精度上的表现明显得以提升。因此，采用ANN-GA协同优化的方法对动态拉伸试样的结构进行优化具有可行性和有效性。
- 霍普金森杆 /
- 尺寸效应 /
- 试样设计 /
- 机器学习 /
- 遗传算法
Abstract: The split Hopkinson tensile bar is one of the most commonly used apparatuses to test the dynamic tensile mechanical properties of materials at the high strain rates from 10² s⁻¹ to 10³ s⁻¹, in which the specimens with a dog-bone shape are usually used. The dimensions of the specimen used are critical to ensure the basic assumptions during dynamic tensile process, such as one-dimensional stress state and uniform deformation of the specimen etc. And whether these assumptions can be satisfied would affect the measurement accuracy of the dynamic tensile properties directly. So, it is urgent to study the influence of the specimen structural parameters on the stress and deformation states of the specimen during the dynamic tensile tests. At the same time, developing and establishing an effective method which can realize the global optimization of specimen structural parameters in the entire parameter space is crucial. In order to actualize the above research objectives, indicators which can quantify the measurement accuracy of the dynamic tensile tests were firstly proposed, namely the time required to reach the stress equilibrium, the deformation uniformity, the relative level of the non-axial stress, and the relative deformation of the transition zones. Orthogonal tests with 6 factors and 5 levels were then designed for the important structural parameters of the dog-bone shaped sheet tensile specimens. According to the rules of the orthogonal test design, 25 dynamic tensile specimens with different structural dimensions were obtained. The commercial finite element software ABAQUS/Explicit was used to establish a finite element model of the split Hopkinson tensile bar, and dynamic tensile test simulations were performed on the dynamic tensile specimens obtained from the orthogonal test design. An orthogonal test dataset with the specimen structural parameters as the input and the measurement accuracy indicators as the output was then constructed. Multi-objective orthogonal test matrix analysis was carried out on the orthogonal test dataset to obtain the influence order as well as the influence law of the structural parameters of the tensile specimens on the measurement accuracy indicators of tests. Taking the orthogonal test dataset as the training dataset, an artificial neural network (ANN) model was used to fit the nonlinear relationship which can predict the measurement accuracy indicators of the test by using the structural parameters of the specimen, and then the fitness function in the genetic algorithm (GA) was established by using this model. Finally, the structural parameters of the dynamic tensile specimen were optimized using the ANN-GA collaborative optimization method, and the optimal structural dimensions of the dynamic tensile specimen were obtained as the result of the optimization. Finite element simulation results show that the optimal structural dimensions obtained by the ANN-GA optimization method are valid. The results of this study demonstrate the practicability and effectiveness of the ANN-GA method in the structural optimization of dynamic tensile specimens. On the other hand, it can provide guidance for the specimen design in the dynamic tensile mechanical properties tests of materials, and can also provide a reference for the validity analysis of the experimentally measured mechanical properties.
- split Hopkinson bar /
- geometry effect /
- specimen design /
- machine learning /
- genetic algorithm

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图 1 分离式霍普金森拉杆装置

Figure 1. The split Hopkinson tensile bar device

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图 2 基于销钉连接的拉伸试样结构

Figure 2. The structure of tensile specimens based on the pin connection

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图 3 销钉连接拉伸试样的有限元模型

Figure 3. The finite element models of the pin-connected tensile specimen

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图 4 试样与杆端的网格模型

Figure 4. Mesh of the specimen and bar ends

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图 5 材料动态拉伸力学性能的数值模拟、实验以及模型对比

Figure 5. Comparison of the dynamic tensile mechanical properties from simulation, experiment and material model

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图 6 正交试验数据库结构示意图

Figure 6. Data structure of the orthogonal test database

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图 7 神经网络模型结构示意图

Figure 7. Schematic diagram of the neural network model structure

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图 8 神经网络与遗传算法协同优化方案

Figure 8. Collaborative optimization scheme of neural network and genetic algorithm

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图 9 GA模拟进化寻优过程

Figure 9. Optimization process simulated by GA

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图 10 优化后试样结构及尺寸（单位：mm）

Figure 10. Optimized specimen structure and dimensions (unit: mm)

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表 1 片状动态拉伸试样结构参数及其惯用值

Table 1. Structural parameters of the sheet specimen used for dynamic tensile tests and the reference values

l_g/mm	w_g/mm	l_c/mm	w_c/mm	R/mm	$ \delta $/mm
12.0	4.0	18.0	16.0	3.0	2.0

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表 2 试样结构参数正交表与模拟结果

Table 2. Orthogonal table of the specimen structural parameters and the simulation results

序号	结构参数/mm						t/μs	$ {\bar{\sigma }}_{\mathrm{m}} $/%	s²/10⁻³	$ {\bar{D}}_{\mathrm{d}} $/%
序号	l_g	w_g	l_c	w_c	R	δ	t/μs	$ {\bar{\sigma }}_{\mathrm{m}} $/%	s²/10⁻³	$ {\bar{D}}_{\mathrm{d}} $/%
01	6.0	2.0	16.0	14.0	0.5	1.0	18.05	4.55	2.241	0.57
02	6.0	3.0	17.0	15.0	1.0	1.5	18.50	6.11	2.176	3.54
03	6.0	4.0	18.0	16.0	2.0	2.0	19.00	5.90	1.776	7.23
04	6.0	5.0	19.0	17.0	3.0	2.5	18.00	5.76	1.874	11.44
05	6.0	6.0	20.0	18.0	4.0	3.0	19.50	6.17	1.412	15.58
06	8.0	2.0	18.0	17.0	1.0	3.0	18.50	2.94	1.930	2.01
07	8.0	3.0	19.0	18.0	2.0	1.0	19.50	2.59	0.865	4.83
08	8.0	4.0	20.0	14.0	3.0	1.5	20.00	3.33	0.765	8.47
09	8.0	5.0	16.0	15.0	4.0	2.0	20.00	4.29	0.753	12.17
10	8.0	6.0	17.0	16.0	0.5	2.5	21.01	8.42	4.844	1.90
11	10.0	2.0	20.0	15.0	2.0	2.5	22.00	1.68	0.807	3.73
12	10.0	3.0	16.0	16.0	3.0	3.0	22.00	2.63	0.651	6.54
13	10.0	4.0	17.0	17.0	4.0	1.0	23.12	1.91	0.414	9.65
14	10.0	5.0	18.0	18.0	0.5	1.5	21.99	6.32	3.203	1.19
15	10.0	6.0	19.0	14.0	1.0	2.0	21.00	6.88	2.925	2.34
16	12.0	2.0	17.0	18.0	3.0	2.0	23.50	1.39	0.357	5.17
17	12.0	3.0	18.0	14.0	4.0	2.5	24.00	1.99	0.316	8.14
18	12.0	4.0	19.0	15.0	0.5	3.0	21.32	5.21	1.972	1.06
19	12.0	5.0	20.0	16.0	1.0	1.0	21.99	4.58	1.852	1.70
20	12.0	6.0	16.0	17.0	2.0	2.0	23.00	4.46	1.651	4.18
21	14.0	2.0	19.0	16.0	4.0	1.5	26.00	0.94	0.146	6.99
22	14.0	3.0	20.0	17.0	0.5	2.0	24.51	3.53	1.295	0.74
23	14.0	4.0	16.0	18.0	1.0	2.5	25.11	3.93	1.205	1.77
24	14.0	5.0	17.0	14.0	2.0	3.0	25.03	3.95	0.805	4.00
25	14.0	6.0	18.0	15.0	3.0	1.0	25.50	3.39	0.750	5.18

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表 3 模拟用材料模型参数

Table 3. Parameters of the material model used for simulations

材料	密度/(kg·m⁻³)	弹性模量/GPa	泊松比	Johnson-Cook 模型参数
材料	密度/(kg·m⁻³)	弹性模量/GPa	泊松比	A/MPa	B/MPa	N	C
45钢	7 850	210	0.30
AA7075-T6	2 800	71	0.33	473	210	0.3813	0.033

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表 4 试样结构参数对测量精度指标影响的主次顺序及规律

Table 4. The influence order and law of the specimen structural parameters on the measurement accuracy indicators

指标	主次顺序	关键因素	规律
t	l_g, R, l_c, δ, w_g, w_c	l_g、R	l_g、R与t呈正相关
s²	R, l_g, w_g, δ, w_c, l_c	R、l_g	R、l_g与s²呈负相关
$ {\bar{\sigma }}_{\mathrm{m}} $	w_g, R, l_g, δ, w_c, l_c	w_g、R	w_g与$ {\bar{\sigma }}_{\mathrm{m}} $呈正相关，R与$ {\bar{\sigma }}_{\mathrm{m}} $呈负相关
$ {\bar{D}}_{\mathrm{d}} $	R, l_g, w_g, δ, l_c, w_c	R、l_g	R与$ {\bar{D}}_{\mathrm{d}} $呈正相关，l_g与$ {\bar{D}}_{\mathrm{d}} $呈负相关

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表 5 验证集

Table 5. Validation data set

编号	结构参数/mm						t/μs	$ {\bar{\sigma }}_{\mathrm{m}} $/%	s²/10^–3	$ {\bar{D}}_{\mathrm{d}} $/%
编号	l_g	w_g	l_c	w_c	R	δ	t/μs	$ {\bar{\sigma }}_{\mathrm{m}} $/%	s²/10^–3	$ {\bar{D}}_{\mathrm{d}} $/%
01	6.0	3.0	18.0	15.0	2.0	1.5	16.0	4.45	1.018	7.02
02	8.0	2.0	16.0	14.0	3.0	1.0	18.5	1.24	0.275	7.59
03	10.0	4.0	19.0	17.0	1.0	2.5	21.0	5.43	1.946	2.34

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表 6 验证集真实值与预测值的对比

Table 6. Comparison of the true and predicted values of the validation dataset

编号	t			${\bar{\sigma } }_{\mathrm{m} }$			s²			${\bar{D} }_{\mathrm{d} }$
编号	真实值/μs	预测值/μs	误差/%	真实值/%	预测值/%	误差/%	真实值/10^–³	预测值/10^–3	误差/%	真实值/%	预测值/%	误差/%
01	16.00	15.62	2.38	4.45	4.87	9.44	1.018	1.072	5.30	7.02	6.73	4.13
02	18.50	17.36	6.16	1.24	1.37	10.48	0.275	0.261	5.09	7.59	8.18	7.77
03	21.00	20.78	1.05	5.43	4.99	8.10	1.946	1.778	8.63	2.34	2.43	3.85

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表 7 优化前后试样测量准确度指标对比

Table 7. Comparison of the measurement accuracy indicators of specimens before and after optimization

t			$ {\bar{\sigma }}_{\mathrm{m}} $			s²			$ {\bar{D}}_{\mathrm{d}} $
优化前/μs	优化后/μs	减小/%	优化前/%	优化后/%	减小/%	优化前/10⁻³	优化后/10⁻³	减小/%	优化前/%	优化后/%	减小/%
27.0	21.0	22.2	2.4	1.57	34.6	0.871	0.803	7.8	5.57	5.16	7.9

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