一种二维时频多尺度熵的滚动轴承故障诊断方法

李嘉绮; 郑近德; 潘海洋; 童靳于

doi:10.13433/j.cnki.1003-8728.20220157

一种二维时频多尺度熵的滚动轴承故障诊断方法

doi: 10.13433/j.cnki.1003-8728.20220157

安徽工业大学机械工程学院，安徽马鞍山　243032

基金项目: 国家自然科学基金项目（51975004）与安徽省自然科学基金项目（2008085QE215）

详细信息

作者简介:
李嘉绮（1996−），硕士研究生，研究方向为设备状态监测与故障诊断，735028407@qq.com

通讯作者:
郑近德，副教授，硕士生导师，博士，lqdlzheng@126.com

中图分类号: TN911.7；TH165.3
计量
- 文章访问数: 690
- HTML全文浏览量: 23
- PDF下载量: 10
- 被引次数: 0
出版历程
- 收稿日期: 2021-08-08
- 刊出日期: 2023-12-25

A Two-dimensional Time-frequency Multi-scale Entropy Method for Rolling Bearing Fault Diagnosis

School of Mechanical Engineering, Anhui University of Technology, Ma′anshan 243032 Anhui, China

摘要

摘要: 多尺度熵是一种有效表征一维振动信号复杂性和不规则程度的非线性动力学方法，但其只考虑了信号的时域复杂性，而忽略了频域信息。为了综合利用振动信号时频域信息和量度时频分布的复杂性特征，将二维多尺度熵引入到滚动轴承的故障诊断中，提出了一种基于二维时频多尺度熵和萤火虫算法优化支持向量机的滚动轴承故障诊断方法。首先，采用连续小波变换将一维时间序列转换为时频图像；其次，计算时频图像的二维多尺度熵值；再次，将得到的二维多尺度熵值输入到萤火虫优化的支持向量机中进行分类和预测；最后，通过滚动轴承试验数据分析验证所提方法的有效性。结果表明：论文所提方法能够准确地识别滚动轴承的故障类型和故障程度。
- 二维时频多尺度熵 /
- 时频分布 /
- 滚动轴承 /
- 萤火虫优化支持向量机 /
- 故障诊断
Abstract: Multi-scale entropy is an effective nonlinear dynamic method to characterize the complexity and irregularity of one-dimensional vibration signal, but it only considers the time-domain complexity of the signal and ignores the frequency-domain information. For comprehensive utilization of the vibration signal frequency domain information and measure of the complexity of the time-frequency distribution characteristics, the two-dimensional multi-scale entropy is introduced into the fault diagnosis of rolling bearings, and a new rolling bearing fault diagnosis method based on two-dimensional time-frequency multi-scale entropy (TFMSE_2D) and firefly algorithm optimization support vector machine is proposed. Firstly, a one-dimensional time series is transformed into a time-frequency image by continuous wavelet transform. Secondly, the TFMSE_2D of time-frequency image is calculated. Then, the TFMSE_2D is input into the firefly optimized support vector machine for classification and prediction. Finally, through the rolling bearing experiment data verify the validity of the proposed method. The results show that the proposed method can accurately identify roller bearing fault type and fault degree.
- two-dimensional time-frequency multi-scale entropy /
- time-frequency distribution /
- rolling bearing /
- fireflies optimization support vector machine /
- fault diagnosis

HTML全文

图 1 尺度因子$ \tau = 2 $时二维粗粒化示意图

Figure 1. Two-dimensional coarse-grained schematic diagram for $\tau = 2 $

下载: 全尺寸图片幻灯片

图 2 FA-SVM流程图

Figure 2. The flow chart of FA-SVM

下载: 全尺寸图片幻灯片

图 3 MIX_2D（ p ）生成的示例图像

Figure 3. Sample images generated by MIX_2D(p)

下载: 全尺寸图片幻灯片

图 4 MIX_2D（p）像素为256 × 256时不同p值的TFMSE_2D

Figure 4. TFMSE_2D with different p for 256×256 pixels generated by MIX_2D(p)

下载: 全尺寸图片幻灯片

图 5 1/f噪声和MIX_2D混合过程的TFMSE_2D值曲线

Figure 5. TFMSE_2D curve of 1/f noise and MIX_2D(p)

下载: 全尺寸图片幻灯片

图 6 滚动轴承试验测试台（西储大学）

Figure 6. The rolling bearing test bench of Case Western Reserve University

下载: 全尺寸图片幻灯片

图 7 滚动轴承振动信号的时域波形图

Figure 7. Time domain waveform of vibration signal of a rolling bearing

下载: 全尺寸图片幻灯片

图 8 4种不同方法的均值方差图

Figure 8. The mean variances of four different methods

下载: 全尺寸图片幻灯片

图 9 4种不同故障诊断方法的分类结果

Figure 9. Classification results of four different fault diagnosis methods

下载: 全尺寸图片幻灯片

图 10 安徽工业大学轴承试验测试台

Figure 10. Bearing test bench of Anhui University of Technology

下载: 全尺寸图片幻灯片

图 11 滚动轴承振动信号的时域波形图

Figure 11. Time domain waveform of vibration signal of a rolling bearing

下载: 全尺寸图片幻灯片

图 12 TFMSE_2D均值方差图

Figure 12. The mean variances of TFMSE_2D

下载: 全尺寸图片幻灯片

图 13 基于TFMSE_2D的故障诊断方法分类结果

Figure 13. Classification results of fault diagnosis method based on TFMSE_2D

下载: 全尺寸图片幻灯片

图 14 MSE_1D均值方差图

Figure 14. The mean variances of MSE_1D

下载: 全尺寸图片幻灯片

图 15 基于MSE_1D的故障诊断方法分类结果

Figure 15. Classification results of fault diagnosis method based on MSE_1D

下载: 全尺寸图片幻灯片

图 16 MPE_1D均值方差图

Figure 16. The mean variances of MPE_1D

下载: 全尺寸图片幻灯片

图 17 基于MPE_1D的故障诊断方法分类结果

Figure 17. Classification results of fault diagnosis method based on MPE_1D

下载: 全尺寸图片幻灯片

图 18 MFE_1D均值方差图

Figure 18. The mean variances of MFE_1D

下载: 全尺寸图片幻灯片

图 19 基于MFE_1D的故障诊断方法分类结果

Figure 19. Classification results of fault diagnosis method based on MFE_1D

下载: 全尺寸图片幻灯片

表 1 不同方法的参数及识别率

Table 1. Parameters and recognition rate of different methods

方法	参数设置	最优参数	识别率/%
TFMSE_2D	m=2 r=0.25	c=34.3589 g=0.9373	100
MSE_1D	m=2 r=0.25	c=74.1677 g=18.7573	100
MPE_1D	m=2 λ=1	c=29.0371 g=31.6586	100
MFE_1D	m=2 r=0.15 n=2	c=28.5010 g=6.9890	100

下载: 导出CSV

表 2 不同方法的参数及识别率

Table 2. Parameters and recognition rates of different methods

方法	参数设置	最优参数	识别率/%
TFMSE_2D	m=2 r=0.25	c=26.3190 g=1.0245	100
MSE_1D	m=2 r=0.25	c=46.9301 g=10.5754	97.619
MPE_1D	m=2 λ=1	c=11.2882 g=60.1983	95.2381
MFE_1D	m=2 r=0.15 n=2	c=19.7435 g=2.5664	98.4172

下载: 导出CSV

参考文献(21)

[1]	胥永刚, 何正嘉. 分形维数和近似熵用于度量信号复杂性的比较研究[J]. 振动与冲击, 2003, 22(3): 25-27. doi: 10.3969/j.issn.1000-3835.2003.03.007 XU Y G, HE Z J. Research on comparison between approximate entropy and fractal dimension for complexity measure of signals[J]. Journal of Vibration and Shock, 2003, 22(3): 25-27. (in Chinese) doi: 10.3969/j.issn.1000-3835.2003.03.007
[2]	何志坚, 周志雄. 基于ELMD的样本熵及Boosting-SVM的滚动轴承故障诊断[J]. 振动与冲击, 2016, 35(18): 190-195. HE Z J, ZHOU Z X. Fault diagnosis of roller bearings based on ELMD sample entropy and Boosting-SVM[J]. Journal of Vibration and Shock, 2016, 35(18): 190-195. (in Chinese)
[3]	刘慧, 谢洪波, 和卫星, 等. 基于模糊熵的脑电睡眠分期特征提取与分类[J]. 数据采集与处理, 2010, 25(4): 484-489. LIU H, XIE H B, HE W X, et al. Characterization and classification of EEG sleep stage based on fuzzy entropy[J]. Journal of Data Acquisition & Processing, 2010, 25(4): 484-489. (in Chinese)
[4]	PINCUS S M. Approximate entropy as a measure of system complexity[J]. Proceedings of the National Academy of Sciences of the United States of America, 1991, 88(6): 2297-2301. doi: 10.1073/pnas.88.6.2297
[5]	赵志宏, 杨绍普. 基于小波包变换与样本熵的滚动轴承故障诊断[J]. 振动、测试与诊断, 2012, 32(4): 640-644. ZHAO Z H, YANG S P. Roller bearing fault diagnosis based on wavelet packet transform and sample entropy[J]. Journal of Vibration, Measurement & Diagnosis, 2012, 32(4): 640-644. (in Chinese)
[6]	郑近德, 程军圣, 胡思宇. 多尺度熵在转子故障诊断中的应用[J]. 振动、测试与诊断, 2013, 33(2): 294-297. ZHENG J D, CHENG J S, HU S Y. Rotor fault diagnosis based on multiscale entropy[J]. Journal of Vibration, Measurement & Diagnosis, 2013, 33(2): 294-297. (in Chinese)
[7]	ZHENG J D, PAN H Y, TONG J Y, et al. Generalized refined composite multiscale fuzzy entropy and multi-cluster feature selection based intelligent fault diagnosis of rolling bearing[J]. ISA Transactions, 2022, 123: 136-151. doi: 10.1016/j.isatra.2021.05.042
[8]	郑近德, 程军圣, 杨宇. 多尺度排列熵及其在滚动轴承故障诊断中的应用[J]. 中国机械工程, 2013, 24(19): 2641-2646. doi: 10.3969/j.issn.1004-132X.2013.19.017 ZHENG J D, CHENG J S, YANG Y. Multi-scale permutation entropy and its applications to rolling bearing fault diagnosis[J]. China Mechanical Engineering, 2013, 24(19): 2641-2646. (in Chinese) doi: 10.3969/j.issn.1004-132X.2013.19.017
[9]	SILVA L E V, FILHO A C S S, FAZAN V P S, et al. Two-dimensional sample entropy: assessing image texture through irregularity[J]. Biomedical Physics & Engineering Express, 2016, 2(4): 045002.
[10]	AZAMI H, DA SILVA L E V, OMOTO A C M, et al. Two-dimensional dispersion entropy: an information-theoretic method for irregularity analysis of images[J]. Signal Processing:Image Communication, 2019, 75: 178-187. doi: 10.1016/j.image.2019.04.013
[11]	SILVA L E V, DUQUE J J, FELIPE J C, et al. Two-dimensional multiscale entropy analysis: applications to image texture evaluation[J]. Signal Processing, 2018, 147: 224-232. doi: 10.1016/j.sigpro.2018.02.004
[12]	刘佳敏, 赵知劲, 曹越飞, 等. 基于时频分析的多跳频信号盲检测[J]. 信号处理, 2021, 37(5): 763-771. LIU J M, ZHAO Z J, CAO Y F, et al. Blind detection of multi-frequency hopping signals based on time-frequency analysis[J]. Journal of Signal Processing, 2021, 37(5): 763-771. (in Chinese)
[13]	杨晓敏. 改进灰狼算法优化支持向量机的网络流量预测[J]. 电子测量与仪器学报, 2021, 35(3): 211-217. YANG X M. Improved gray wolf algorithm to optimize support vector machine for network traffic prediction[J]. Journal of Electronic Measurement and Instrumentation, 2021, 35(3): 211-217. (in Chinese)
[14]	李宝胜, 秦传东. 基于粒子群优化的SVM多分类的电动车价格预测研究[J]. 计算机科学, 2020, 47(11A): 421-424. LI B S, QIN C D. Study on electric vehicle price prediction based on PSO-SVM multi-classification Method[J]. Computer Science, 2020, 47(11A): 421-424. (in Chinese)
[15]	张兢, 曾建梅, 李冠迪, 等. FA-SVM优化算法在情感识别中的应用[J]. 激光杂志, 2016, 37(9): 76-79. ZHANG J, ZENG J M, LI G D, et al. Application of FA-SVM optimization algorithm in emotion recognition[J]. Laser Journal, 2016, 37(9): 76-79. (in Chinese)
[16]	YANG X S. Firefly algorithms for mutimodal optimizatiom[M]. Sapporo: Springer, 2009.
[17]	董治麟, 郑近德, 潘海洋, 等. 基于复合多尺度排列熵与FO-SVM的滚动轴承故障诊断方法[J]. 噪声与振动控制, 2020, 40(2): 102-108. doi: 10.3969/j.issn.1006-1355.2020.02.019 DONG Z L, ZHENG J D, PAN H Y, et al. Fault diagnosis for rolling bearings based on composite multi-scale permutation entropy and FO-SVM[J]. Noise and Vibration Control, 2020, 40(2): 102-108. (in Chinese) doi: 10.3969/j.issn.1006-1355.2020.02.019
[18]	WU H C, ZHOU J, XIE C H, et al. Two-dimensional time series sample entropy algorithm: applications to rotor axis orbit feature identification[J]. Mechanical Systems and Signal Processing, 2021, 147: 107-123.
[19]	RICHMAN J S, MOORMAN J R. Physiological time-series analysis using approximate entropy and sample entropy[J]. American Journal of Physiology-Heart and Circulatory Physiology, 2000, 278(6): H2039-H2049. doi: 10.1152/ajpheart.2000.278.6.H2039
[20]	HILAL M, BERTHIN C, MARTIN L, et al. Bidimensional multiscale fuzzy entropy and its application to pseudoxanthoma elasticum[J]. IEEE Transactions on Biomedical Engineering, 2020, 67(7): 2015-2022. doi: 10.1109/TBME.2019.2953681
[21]	Bearing Data Center Website. Case western reserve university[DB/OL]. [2017-06-20]. http://www.eecs.cwru.edu/laboratory/bearing.