基于协同训练SVR的脆性材料亚表面微裂纹深度预测

任闯; 盛鑫; 牛凤丽; 朱永伟

doi:10.13394/j.cnki.jgszz.2023.0006

基于协同训练SVR的脆性材料亚表面微裂纹深度预测

doi: 10.13394/j.cnki.jgszz.2023.0006

南京航空航天大学机电学院, 南京 210016

基金项目: 国家自然科学基金联合基金（U20A20293）。

详细信息

作者简介:
朱永伟，男，1967年生，教授、博士生导师。主要研究方向：精密及超精密加工、表面工程等。E-mail: meeywzhu@nuaa.edu.cn

中图分类号: TG58; TG732
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出版历程
- 收稿日期: 2023-01-10
- 修回日期: 2023-02-28
- 录用日期: 2023-03-15
- 网络出版日期: 2023-11-06
- 刊出日期: 2023-12-01

Prediction of subsurface microcrack depth of brittle materials based on co-training SVR

Mechanical and Electrical College, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要:
为克服固结磨料研磨脆性材料的亚表面微裂纹深度有效样本数不足的困境，实现其准确预测，采用协同训练SVR构建预测模型，对比不同标记训练集划分方法对测试集均方误差的影响；后以监督学习PSO-SVR模型为对照，比较二者的预测性能；最后以标记训练集未包含的脆性材料微晶玻璃和氟化钙为加工对象，进行工件的研磨及角度抛光法裂纹深度检测实验，并将检测的4组亚表面微裂纹深度值与协同训练SVR模型的预测值对比。结果表明：分开划分法下的协同训练SVR模型具有更小的均方误差；相比于PSO-SVR模型，协同训练SVR模型的均方误差和平均绝对百分比误差分别减小9%和17%，且其对4组验证实验的预测误差在1.2%～13.8%。表明协同训练SVR模型，可较为准确地预测固结磨料研磨脆性材料的亚表面微裂纹深度。
- 脆性材料 /
- 亚表面损伤 /
- 支持向量回归 /
- 小样本 /
- 协同训练 /
- 粒子群优化支持向量回归
Abstract:
[OBJECTIVES] Brittle materials, characterized by low fracture toughness, are susceptible to subsurface damages such as microcracks during grinding processes. This damage can adversely affect the performance and lifespan of the components. Precise measurement of the depth of subsurface microcracks is crucial for selecting appropriate machining allowance in subsequent processes. While current methods for measuring subsurface microcracks have limitation, machine learning models show significant potential in predicting machining quality of brittle materials. However, these models often require extensive labeled data, which is difficult to obtain in practice, thus limiting their learning capabilities. To address the challenge of limited effective samples for analyzing subsurface microcrack depths in brittle materials ground with fixed abrasives, this study proposes a collaborative training approach for a Support Vector Regression (SVR) model，tailored for small datasets, capable of accurately predicting microcrack depth caused by grinding different brittle materials.
[METHODS] This study employed the SVR model as the foundational learner, with inputs including Mohs hardness, elastic modulus, fracture toughness of the brittle materials, diamond abrasive grain size and grinding pressure. The output was the depth of subsurface microcracks resulting from grinding. Integrating semi-supervised and supervised learning concepts, the study developed both a collaborative training SVR model and a PSO-SVR model. The model’s predictive performances were assessed using mean square error (MSE) and mean absolute percentage error (MAPE). Further, the impact of various labeled training set partitioning strategies on the MSE of the test set was examined using the collaborative training SVR model. The study also compared the predictive performances of the collaborative training SVR model and the PSO-SVR model under separate dataset partitioning strategies. Finally, the study validated the models through grinding and angle polishing experiments to measure subsurface microcrack depths in materials not included in the training set, evaluating the collaborative training SVR model's predictive accuracy against experimental results.
[RESULTS] When using separate dataset partitioning strategies, the initial MSE values of the two learners in the collaborative SVR model were 5.79 and 0.98, ultimately converging to 1.15 and 0.35, respectively. For mixed dataset partitioning strategy, the initial MSE values were 4.02 and 1.13, converging to 2.0 and 0.70, respectively. When predicting small dataset, the collaborative training SVR model demonstrated a reduction in MSE and MAPE by 9% and 17%, respectively, outperforming the PSO-SVR model. The collaborative model provided more reliable and stable predictions for both individual test samples and entire test sets. The measured subsurface microcrack depths in glass-ceramics and calcium fluoride under different processing conditions were 4.13, 5.03, 5.67, and 5.89 μm, with prediction errors ranging from 1.2% to 13.8%, averaging at 7.7%, which was significantly lower than the test set’s average prediction error of 12.5%.
[CONCLUSION] Dividing the labeled dataset using both separate and mixed partitioning methods can reduce the MSE of the collaborative training SVR model on the test set, with the separate method achieving smaller MSEs and superior outcomes. Compared to the supervised learning PSO-SVR model, the collaborative training SVR model demonstrates smaller MSE and MAPE values, with more stable prediction errors. The close agreement between the experimentally measured subsurface microcrack depths and the model's predictions underscores its robust generalization capability, confirming the model's ability to provide accurate and stable predictions of subsurface microcrack depths in various brittle materials after grinding.
- brittle material /
- subsurface damage /
- support vector regression(SVR) /
- small sample /
- co-training /
- particle swarm optimization support vector regression(PSO-SVR)

HTML全文

图 1 协同训练SVR算法流程图

Figure 1. Algorithm flowchart of co-training SVR

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图 2 不同划分方法下测试集MSE值的变化曲线

Figure 2. Change curves of MSE values of test set under different partition methods

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图 3 模型预测误差

Figure 3. Prediction error of the models

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图 4 1#工件不同深度的亚表面微裂纹分布

Figure 4. Subsurface microcrack distribution at different depths of 1# workpiece

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图 5 亚表面微裂纹消失的终点

Figure 5. End point of subsurface microcrack disappearance

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图 6 检测值与模型预测值对比

Figure 6. Comparison between the measured values and the predicted values of the model

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表 1 亚表面微裂纹深度训练样本集

Table 1. Subsurface microcrack depth training sample set

样本编号	输入参数						输出参数
样本编号	材料种类	莫氏硬度 M	弹性模量 E / GPa	断裂韧性 K_IC / (MPa·m^1/2)	磨粒粒径 D₅₀ / μm	研磨压力 p / kPa	亚表面微裂纹深度 d / μm
1	K9玻璃	7.0	61.0	0.70	40	7.10	3.62
2	K9玻璃	7.0	61.0	0.70	28	7.10	2.91
3	石英玻璃	7.5	70.0	0.75	70	10.37	14.42
4	石英玻璃	7.5	70.0	0.75	30	10.37	6.45
5	石英玻璃	7.5	70.0	0.75	5	10.37	1.36
6	镁铝尖晶石	8.2	190.0	1.44	30	10.37	7.12
7	镁铝尖晶石	8.2	190.0	1.44	50	10.37	10.73
8	铌酸锂	5.0	195.0	0.70	14	15.00	1.73
9	硫化锌	3.0	85.5	1.06	5	20.00	2.02
10	蓝宝石	9.0	380.0	3.50	28	28.00	4.98
11	K9玻璃	7.0	61.0	0.70	20	7.10	1.17
12	石英玻璃	7.5	70.0	0.75	50	10.37	9.94
13	镁铝尖晶石	8.2	190.0	1.44	70	10.37	14.95
14	镁铝尖晶石	8.2	190.0	1.44	5	10.37	1.81
15	铌酸锂	5.0	195.0	0.70	28	15.00	5.53
16	铌酸锂	5.0	195.0	0.70	25	12.50	4.82
17	铌酸锂	5.0	195.0	0.70	14	12.50	1.34
18	硫化锌	3.0	85.5	1.06	15	20.00	3.98
19	硫化锌	3.0	85.5	1.06	30	20.00	8.27
20	蓝宝石	9.0	380.0	3.50	50	28.00	7.53
21	蓝宝石	9.0	380.0	3.50	14	28.00	2.84

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表 2 亚表面微裂纹深度测试样本集

Table 2. Subsurface microcrack depth test sample set

样本编号	输入参数						输出参数
样本编号	材料种类	莫氏硬度 M	弹性模量 E / GPa	断裂韧性 K_IC / (MPa·m^1/2)	磨粒粒径 D₅₀ / μm	研磨压力 p / kPa	亚表面微裂纹深度 d / μm
22	石英玻璃	7.5	70.0	0.75	14	10.37	3.59
23	镁铝尖晶石	8.2	190.0	1.44	14	10.37	3.71
24	铌酸锂	5.0	195.0	0.70	28	7.10	3.28
25	硫化锌	3.0	85.5	1.06	25	20.00	6.27
26	蓝宝石	9.0	380.0	3.50	65	28.00	10.64

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表 3 部分未标记数据集

Table 3. Partial unlabeled data set

材料种类	输入参数
材料种类	莫氏硬度 M	弹性模量 E / GPa	断裂韧性 K_IC / (MPa·m^1/2)	磨粒粒径 D₅₀ / μm	研磨压力 p / kPa
YAG晶体	8.5	280.0	1.04	20	21.00
氧化镓	5.5	200.0	0.85	40	10.00
单晶硅	7.0	187.0	0.82	28	7.10
单晶锗	6.0	115.0	0.56	28	21.00

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表 4 模型评价指标

Table 4. Evaluation metrics of the models

评价指标	PSO-SVR	协同训练SVR
MSE	0.8265	0.7525
MAPE / %	15.0	12.5

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表 5 验证样本集

Table 5. Validation sample set

实验编号	材料种类	输入参数
实验编号	材料种类	莫氏硬度 M	弹性模量 E / GPa	断裂韧性 K_IC / (MPa·m^1/2)	磨粒粒径 D₅₀ / μm	研磨压力 p / kPa
1#	微晶玻璃	6.5	90.0	0.90	20	10.00
2#	微晶玻璃	6.5	90.0	0.90	20	20.00
3#	微晶玻璃	6.5	90.0	0.90	28	10.00
4#	氟化钙	4.0	187.0	0.82	20	20.00

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表 6 研磨工艺参数

Table 6. Lapping process parameters

参数类型	取值
参数类型	微晶玻璃	氟化钙
磨料垫转速 n₁ / (r·min⁻¹)	85	85
工件转速 n₂ / (r·min⁻¹)	80	80
研磨液流量 Q / (mL·min⁻¹)	60	60
研磨时间 t₀ / min	15	5

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表 7 角度抛光工艺参数

Table 7. Angle polishing process parameters

参数类型	取值
参数类型	微晶玻璃	氟化钙
抛光压力 p₁ / kPa	10	15
磨料垫转速 n₃ / (r·min⁻¹)	85	85
工件转速 n₄ / (r·min⁻¹)	80	80
聚氨酯抛光时间 t₁ / min	30	10
绒布抛光时间 t₂ / min	40	40

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表 8 腐蚀液及腐蚀条件

Table 8. Corrosion liquids and corrosion conditions

材料种类	腐蚀液（质量比）	腐蚀时间 t₃ / min	腐蚀温度 θ / ℃
微晶玻璃	HF∶NH₄F=1∶20	4	20
氟化钙	浓硫酸	5	20

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