一种用于滚动轴承故障诊断的改进EWT方法

盛嘉玖; 陈果; 康玉祥; 贺志远; 王浩; 尉询楷

doi:10.13224/j.cnki.jasp.20220677

一种用于滚动轴承故障诊断的改进EWT方法

doi: 10.13224/j.cnki.jasp.20220677

盛嘉玖^1,,
陈果^2,*, ,,
康玉祥¹,
贺志远¹,
王浩³,
尉询楷³

1.
南京航空航天大学民航学院，南京 211106
2.
南京航空航天大学通用航空与飞行学院，江苏溧阳 213300
3.
北京航空工程技术研究中心，北京 100076

基金项目: 国家重大专项计划（J2019-Ⅳ-004-0071）；国家自然科学基金（52272436）；江苏省研究生科研与实践创新计划项目（KYCX20_0211）

详细信息

作者简介:
盛嘉玖（1999-），男，硕士生，主要从事航空发动机信号处理和故障诊断研究

通讯作者:
陈果（1972-），男，博士、教授、博士生导师，研究领域为航空发动机整机振动分析、状态监测与故障诊断。E-mail：cgzyx@263.net

中图分类号: V263.6
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- 文章访问数: 112
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- 被引次数: 0
出版历程
- 收稿日期: 2022-09-12
- 网络出版日期: 2023-11-02

An improved EWT method for fault diagnosis of rolling bearings

1.
College of Civil Aviation，Nanjing University of Aeronautics and Astronautics，Nanjing 211106，China
2.
College of General Aviation and Flight，Nanjing University of Aeronautics and Astronautics，Liyang Jiangsu 213300，China
3.
Beijing Aeronautical Engineering Technical Research Center，Beijing 100076，China

摘要

摘要:
针对经验小波变换（EWT）在滚动轴承故障信号最优频带提取中存在的问题，提出一种基于提取能量包络趋势线以自适应划分频带的改进EWT方法，并应用于滚动轴承故障诊断。利用Teager能量算子将频谱转换成能量谱，通过反复希尔伯特变换得到能量包络线。提取极大值并平滑处理，获得能量包络趋势线，对其进行1阶差分，选取有效极值点以自适应划分频带。构造一种归一化故障特征频率显著性指标，作为故障诊断和最优共振频带选取的有效判据。通过滚动轴承故障仿真和试验数据对算法进行验证。结果表明：相比于原始EWT，该方法可有效识别滚动轴承早期故障并合理选取最优共振频带。针对外、内圈故障数据所提指标可平均提升48.0%和174.1%。
- 滚动轴承 /
- 经验小波变换 /
- 故障诊断 /
- 共振解调 /
- 自适应信号分解
Abstract:
Considering the problem of empirical wavelet transform (EWT) in extracting optimal frequency band of the rolling bearing fault signal, an improved EWT method based on extracting energy envelope trend line to adaptively divide frequency band was proposed and applied to rolling bearing fault diagnosis. The Teager energy operator was used to convert the spectrum into energy spectrum, and the energy envelope was obtained by repeated Hilbert transform. Local maximum values were extracted and smoothed to obtain the energy envelope trend line, and the first-order difference was performed to select effective extreme points to adaptively divide the frequency band. A normalized fault characteristic frequency saliency index was constructed as an effective criterion for fault diagnosis and optimal resonance frequency band selection. The algorithm was verified by rolling bearing fault simulation and experiment data. The results showed that compared with the original EWT, the proposed method can effectively identify the early faults of rolling bearings and reasonably select the optimal resonance frequency band. The proposed indexes for the outer and inner race fault data can be increased by 48.0% and 174.1% on average.
- rolling bearings /
- empirical wavelet transform /
- fault diagnosis /
- resonance demodulation /
- adaptive signal decomposition

HTML

图 1 EWT边界分割示意图

Figure 1. Schematic diagram of EWT boundary segmentation

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图 2 算法流程

Figure 2. Algorithm flow

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图 3 仿真信号时域波形及频谱

Figure 3. Time domain waveform and spectrum of simulated signal

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图 4 仿真信号能量谱

Figure 4. Simulation signal energy spectrum

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图 5 第5次使用希尔伯特变换结果

Figure 5. Fifth time using Hilbert transform result

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图 6 能量包络趋势线及其1阶差分归一化结果

Figure 6. Normalization results of energy envelope trend line and first-order difference

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图 7 仿真信号有效极值点与改进EWT频带分割结果

Figure 7. Effective extreme points and the frequency band division result by improved EWT of simulation signal

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图 8 IMF2、IMF3、IMF4平方包络谱

Figure 8. Squared envelope spectrum of IMF2, IMF3, IMF4

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图 9 模拟试验器及预设故障

Figure 9. Simulated experimenter and preset faults

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图 10 外圈故障信号时域波形及频谱

Figure 10. Time domain waveform and spectrum of outer race fault signal

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图 11 外圈故障信号有效极值点与改进EWT频带分割结果

Figure 11. Effective extreme points and the frequency band division result by improved EWT of outer race fault signal

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图 12 IMF8、IMF9、IMF10平方包络谱

Figure 12. Envelope spectrum of IMF8, IMF9, IMF10

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图 13 原始EWT频带划分结果和IMF10平方包络谱

Figure 13. Frequency band division results decomposed by original EWT and IMF10 squared envelope spectrum

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图 14 内圈故障信号时域波形及频谱

Figure 14. Time domain waveform and spectrum of inner race fault signal

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图 15 内圈故障信号有效极值点与改进EWT频带分割结果

Figure 15. Effective extreme points and the frequency band division result by improved EWT of inner race fault signal

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图 16 IMF3平方包络谱

Figure 16. Square envelope spectrum of IMF3

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图 17 原始EWT频带划分结果和IMF4平方包络谱

Figure 17. Frequency band division results decomposed by original EWT and IMF4 squared envelope spectrum

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图 18 外圈故障数据9原始和改进EWT解调结果对比

Figure 18. Comparison of original and improved EWT demodulation results of outer race fault data 9

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图 19 内圈故障数据4原始和改进EWT解调结果对比

Figure 19. Comparison of original and improved EWT demodulation results of inner race fault data 4

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表 1 反复希尔伯特变换V_s结果

Table 1. V_s results of repeated Hilbert transform

变换次数	第1次	第2次	第3次	第4次	第5次
V_s	1.123 1	1.092 4	1.061 7	1.013 4	0.946 6

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表 2 仿真信号改进EWT分解得到各IMF的S_0-1

Table 2. S_0-1 of each IMF decomposed by improved EWT of simulation signal

IMF	IMF1	IMF2	IMF3	IMF4	IMF5
$ {S_{0 {\text{-}} 1}} $	0.017 5	0.180 8	0.216 9	0.927 4	0.028 3

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表 3 HRB 6206深沟球轴承参数

Table 3. Parameters of HRB 6206 deep groove ball bearings

内径/ mm	外径/ mm	厚度/ mm	滚珠直径/ mm	节径/ mm	滚珠数/ 个	接触角/ （°）
30	62	16	9.5	46	9	0

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表 4 外圈故障信号改进EWT分解得到各IMF的S_0-1

Table 4. S_0-1 of each IMF decomposed by improved EWT of outer race fault signal

IMF	IMF1	IMF2	IMF3	IMF4	IMF5
S_0-1	0.049 5	0.038 8	0.000 1	0.002 0	0.061 7

IMF	IMF6	IMF7	IMF8	IMF9	IMF10
S_0-1	0.008 7	0.014 8	0.912 1	0.999 8	0.853 6

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表 5 外圈故障信号原始EWT分解得到各IMF的S_0-1

Table 5. S_0-1 of each IMF decomposed by original EWT of outer race fault signal

IMF	IMF1	IMF2	IMF3	IMF4	IMF5
S_0-1	0.003 6	0.088 7	0.013 0	0.015 7	0.000 1

IMF	IMF6	IMF7	IMF8	IMF9	IMF10
S_0-1	0.000 1	0.000 1	0.000 1	0.000 1	0.999 2

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表 6 内圈故障信号改进EWT分解得到各IMF的S_0-1

Table 6. S_0-1 of each IMF decomposed by improved EWT of inner race fault signal

IMF	IMF1	IMF2	IMF3	IMF4
$ {S_{0-1}} $	0.000 6	0.000 7	0.648 5	0.002 7

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表 7 内圈故障信号原始EWT分解得到各IMF的S_0-1

Table 7. S_0-1 of each IMF decomposed by original EWT of inner race fault signal

IMF	IMF1	IMF2	IMF3	IMF4
$ {S_{0 {\text{-}} 1}} $	0.001 2	0.004 8	0.000 1	0.064 5

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表 8 不同转速下外圈故障信号S_0-1及频带划分结果

Table 8. Outer race fault signal S_0-1 and frequency band division result at different speeds

数据	转速/（r/min）	S_0-1		频带/Hz
数据	转速/（r/min）	原始EWT	改进EWT	原始EWT	改进EWT
1	1500	0.119 5	1.000 0	700～892	8 866～16 000
2		0.046 4	0.956 8	338～680	8 869～16 000
3		0.006 7	0.763 8	1 058～16 000	8 881～16 000
4		0.506 3	1.000 0	759～925	8 877～16 000
5		0.476 2	1.000 0	982～16 000	8 897～16 000
6	2500	1.000 0	1.000 0	442～977	435～975
7		1.000 0	1.000 0	442～977	452～975
8		1.000 0	1.000 0	442～977	427～918
9		0.141 2	1.000 0	368～809	438～913
10		0.990 4	1.000 0	442～883	434～970
11	3500	0.845 1	0.998 3	981～16 000	14 252～16000
12		0.989 8	0.999 7	981～15 192	8 796～15 192
13		0.976 6	0.999 4	981～16 000	8 778～15 268
14		0.978 2	0.999 5	1 829～16 000	10 002～14 399
15		0.834 2	0.947 7	914～16 000	14 369～15 265
S_0-1平均值		0.660 7	0.977 7
大于0.8占比/%		60.0	93.3

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表 9 不同转速下内圈故障信号S_0-1及频带划分结果

Table 9. Inner race fault signal S_0-1 and frequency band division result at different speeds

数据	转速/（r/min）	S_0-1		频带/Hz
数据	转速/（r/min）	原始EWT	改进EWT	原始EWT	改进EWT
1	1 500	0.376 7	1.000 0	353～773	351～897
2		1.000 0	1.000 0	353～883	345～875
3		0.409 4	1.000 0	705～1767	345～874
4		0.357 8	1.000 0	353～773	349～880
5		0.410 4	1.000 0	353～773	351～897
6	2 500	0.186 0	0.659 2	1060～16 000	941～2 371
7		0.125 2	0.691 1	1211～16 000	1 777～3 279
8		0.275 0	0.646 3	1211～16 000	1 175～2 372
9		0.696 0	0.815 5	881～16 000	862～8 968
10		0.040 4	0.547 3	1101～16 000	1 174～2 550
11	3 500	0.166 5	0.633 5	87～401	1 442～2 314
12		0.021 1	0.570 5	882～16 000	1 102～1 741
13		0.033 6	0.642 8	784～16 000	792～4 256
14		0.029 7	0.735 6	882～16 000	807～1 520
15		0.055 4	0.526 2	784～16 000	807～4 508
S_0-1平均值		0.278 9	0.764 5
大于0.5占比/%		13.3	100.0

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参考文献(21)

[1]	尉询楷,杨立,刘芳. 航空发动机预测与健康管理[M]. 北京: 国防工业出版社,2014.
[2]	张西宁,李霖,刘书语,等. 基于能量峰定位的经验小波变换及在轴承微弱故障诊断中的应用[J]. 西安交通大学学报,2021,55(8): 1-8. ZHANG Xining,LI Lin,LIU Shuyu,et al. Empirical wavelet transform based on energy peak location with applications to bearing weak fault diagnosis[J]. Journal of Xi’an Jiaotong University,2021,55(8): 1-8. (in Chinese ZHANG Xining, LI Lin, LIU Shuyu, et al. Empirical wavelet transform based on energy peak location with applications to bearing weak fault diagnosis[J]. Journal of Xi’an Jiaotong University, 2021, 55(8): 1-8. (in Chinese)
[3]	陈果,贺志远,尉询楷,等. 基于整机的中介轴承外圈剥落故障振动分析[J]. 航空动力学报,2020,35(3): 658-672. CHEN Guo,HE Zhiyuan,WEI Xunkai,et al. Vibration analysis of peeling fault of intermediate bearing outer ring based on whole aero-engine[J]. Journal of Aerospace Power,2020,35(3): 658-672. (in Chinese CHEN Guo, HE Zhiyuan, WEI Xunkai, et al. Vibration analysis of peeling fault of intermediate bearing outer ring based on whole aero-engine[J]. Journal of Aerospace Power, 2020, 35(3): 658-672. (in Chinese)
[4]	陈果,郝腾飞,程小勇,等. 基于机匣测点信号的航空发动机滚动轴承故障诊断灵敏性分析[J]. 航空动力学报,2014,29(12): 2874-2884. CHEN Guo,HAO Tengfei,CHENG Xiaoyong,et al. Sensitivity analysis of fault diagnosis of aero-engine rolling bearing based on vibration signal measured on casing[J]. Journal of Aerospace Power,2014,29(12): 2874-2884. (in Chinese doi: 10.13224/j.cnki.jasp.2014.12.013 CHEN Guo, HAO Tengfei, CHENG Xiaoyong, et al. Sensitivity analysis of fault diagnosis of aero-engine rolling bearing based on vibration signal measured on casing[J]. Journal of Aerospace Power, 2014, 29(12): 2874-2884. (in Chinese) doi: 10.13224/j.cnki.jasp.2014.12.013
[5]	RANDALL R B,ANTONI J. Rolling element bearing diagnostics:a tutorial[J]. Mechanical Systems and Signal Processing,2011,25(2): 485-520. doi: 10.1016/j.ymssp.2010.07.017
[6]	张爽,王晓东,李祥,等. 基于FVMD的滚动轴承故障特征提取方法[J]. 振动与冲击,2022,41(6): 236-244. ZHANG Shuang,WANG Xiaodong,LI Xiang,et al. Extraction method of rolling bearing fault characteristics based on FVMD[J]. Journal of Vibration and Shock,2022,41(6): 236-244. (in Chinese ZHANG Shuang, WANG Xiaodong, LI Xiang, et al. Extraction method of rolling bearing fault characteristics based on FVMD[J]. Journal of Vibration and Shock, 2022, 41(6): 236-244. (in Chinese)
[7]	MARAGOS P,KAISER J F,QUATIERI T F. On amplitude and frequency demodulation using energy operators[J]. IEEE Transactions on Signal Processing,1993,41(4): 1532-1550. doi: 10.1109/78.212729
[8]	ZHENG Jinde,CAO Shijun,PAN Haiyang,et al. Spectral envelope-based adaptive empirical Fourier decomposition method and its application to rolling bearing fault diagnosis[J]. ISA Transactions,2022,129: 476-492. doi: 10.1016/j.isatra.2022.02.049
[9]	HUANG N E,SHEN Zheng,LONG S R,et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society of London Series A: Mathematical,Physical and Engineering Sciences,1998,454(1971): 903-995.
[10]	GILLES J. Empirical wavelet transform[J]. IEEE Transactions on Signal Processing,2013,61(16): 3999-4010. doi: 10.1109/TSP.2013.2265222
[11]	GILLES J,HEAL K. A parameterless scale-space approach to find meaningful modes in histograms:application to image and spectrum segmentation[J]. International Journal of Wavelets,Multiresolution and Information Processing,2014,12(6): 1450044. doi: 10.1142/S0219691314500441
[12]	CHEGINI S N,BAGHERI A,NAJAFI F. Application of a new EWT-based denoising technique in bearing fault diagnosis[J]. Measurement,2019,144: 275-297. doi: 10.1016/j.measurement.2019.05.049
[13]	向玲,高雪媛,张力佳,等. IEWT和FSK在齿轮与滚动轴承故障诊断中的应用[J]. 振动测试与诊断,2017,37(6): 1256-1261,1286. XIANG Ling,GAO Xueyuan,ZHANG Lijia,et al. Gear and rolling bearing fault diagnosis based on improved EWT and fast spectral kurtosis filtering[J]. Journal of Vibration,Measurement & Diagnosis,2017,37(6): 1256-1261,1286. (in Chinese XIANG Ling, GAO Xueyuan, ZHANG Lijia, et al. Gear and rolling bearing fault diagnosis based on improved EWT and fast spectral kurtosis filtering[J]. Journal of Vibration, Measurement & Diagnosis, 2017, 37(6): 1256-1261, 1286. (in Chinese)
[14]	SONG Yueheng,ZENG Shengkui,MA Jiming,et al. A fault diagnosis method for roller bearing based on empirical wavelet transform decomposition with adaptive empirical mode segmentation[J]. Measurement,2018,117: 266-276. doi: 10.1016/j.measurement.2017.12.029
[15]	邹磊. 基于共振解调的滚动轴承复合故障分析方法研究[D]. 南京: 东南大学,2021. ZOU Lei. Research on analysis method of rolling bearing compound fault based on resonance demodulation[D]. Nanjing: Southeast University,2021. (in Chinese ZOU Lei. Research on analysis method of rolling bearing compound fault based on resonance demodulation[D]. Nanjing: Southeast University, 2021. (in Chinese)
[16]	李志农,刘跃凡,胡志峰,等. 经验小波变换-同步提取及其在滚动轴承故障诊断中的应用[J]. 振动工程学报,2021,34(6): 1284-1292. LI Zhinong,LIU Yuefan,HU Zhifeng,et al. Empirical wavelet transform-synchroextracting transform and its applications in fault diagnosis of rolling bearing[J]. Journal of Vibration Engineering,2021,34(6): 1284-1292. (in Chinese LI Zhinong, LIU Yuefan, HU Zhifeng, et al. Empirical wavelet transform-synchroextracting transform and its applications in fault diagnosis of rolling bearing[J]. Journal of Vibration Engineering, 2021, 34(6): 1284-1292. (in Chinese)
[17]	李政,张炜,明安波,等. 基于IEWT和MCKD的滚动轴承故障诊断方法[J]. 机械工程学报,2019,55(23): 136-146. LI Zheng,ZHANG Wei,MING Anbo,et al. A novel fault diagnosis method based on improved empirical wavelet transform and maximum correlated kurtosis deconvolution for rolling element bearing[J]. Journal of Mechanical Engineering,2019,55(23): 136-146. (in Chinese doi: 10.3901/JME.2019.23.136 LI Zheng, ZHANG Wei, MING Anbo, et al. A novel fault diagnosis method based on improved empirical wavelet transform and maximum correlated kurtosis deconvolution for rolling element bearing[J]. Journal of Mechanical Engineering, 2019, 55(23): 136-146. (in Chinese) doi: 10.3901/JME.2019.23.136
[18]	刘尚坤,唐贵基,何玉灵. Teager能量算子结合MCKD的滚动轴承早期故障识别[J]. 振动与冲击,2016,35(15): 98-102. LIU Shangkun,TANG Guiji,HE Yuling. Incipient fault diagnosis of rolling bearings based on Teager energy operator and MCKD[J]. Journal of Vibration and Shock,2016,35(15): 98-102. (in Chinese doi: 10.13465/j.cnki.jvs.2016.15.016 LIU Shangkun, TANG Guiji, HE Yuling. Incipient fault diagnosis of rolling bearings based on Teager energy operator and MCKD[J]. Journal of Vibration and Shock, 2016, 35(15): 98-102. (in Chinese) doi: 10.13465/j.cnki.jvs.2016.15.016
[19]	裴迪,岳建海,焦静. 基于自相关与能量算子增强的滚动轴承微弱故障特征提取[J]. 振动与冲击,2021,40(11): 101-108,123. PEI Di,YUE Jianhai,JIAO Jing. Weak fault feature extraction of rolling bearing based on autocorrelation and energy operator enhancement[J]. Journal of Vibration and Shock,2021,40(11): 101-108,123. (in Chinese PEI Di, YUE Jianhai, JIAO Jing. Weak fault feature extraction of rolling bearing based on autocorrelation and energy operator enhancement[J]. Journal of Vibration and Shock, 2021, 40(11): 101-108, 123. (in Chinese)
[20]	王天金,冯志鹏,郝如江,等. 基于Teager能量算子的滚动轴承故障诊断研究[J]. 振动与冲击,2012,31(2): 1-5,85. WANG Tianjin,FENG Zhipeng,HAO Rujiang,et al. Fault diagnosis of rolling element bearings based on Teager energy operator[J]. Journal of Vibration and Shock,2012,31(2): 1-5,85. (in Chinese WANG Tianjin, FENG Zhipeng, HAO Rujiang, et al. Fault diagnosis of rolling element bearings based on Teager energy operator[J]. Journal of Vibration and Shock, 2012, 31(2): 1-5, 85. (in Chinese)
[21]	张萌物. 对离散系数定义及公式的完善与改进[J]. 西安石油学院学报(社会科学版),1999,8(2): 55-56. ZHANG Mengwu. Perfection and improvement of the definition and formula of discrete coefficient[J]. Journal of Xi’an Petrdleum Institute (Social Sciences Edition),1999,8(2): 55-56. (in Chinese ZHANG Mengwu. Perfection and improvement of the definition and formula of discrete coefficient[J]. Journal of Xi’an Petrdleum Institute (Social Sciences Edition), 1999, 8(2): 55-56. (in Chinese)