基于VMD的调制谱强度分布在齿轮故障诊断中的应用研究
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摘要
变分模态分解(Variational mode decomposition, VMD)是一种具有良好带通滤波特性的信号处理方法,它能够非递归地将实信号分解成一定数量在时域中具有准正交和稀疏特性的有限带宽模态分量。考虑到VMD分解多模态信号时的优势,为了弥补调制强度分布(Modulation intensity distribution, MID)分析多谐波调制信号时的不足,研究将VMD作为调制强度分布的前处理,提出了一种基于VMD的调制强度分布的齿轮故障诊断方法,并通过数值仿真和实验分析验证了该方法的有效性。
VMD has better band-pass filtering characteristic, which can non-recursively decomposition a real-valued multi-composition signal into a discrete number of quasi-orthogonal band-limited sub-signals with specific sparsity properties in the spectral. Modulation intensity distribution(MID) combined with VMD is applied to detect second-order cyclostationary components in gear fault diagnosis. Impulsive signatures generally represent the transients in the signals and are often caused by local defect in the gear of rotating machinery. Detecting these signatures is vital for mechanical signal processing and fault diagnosis. The impulsive signatures can be successfully extracted using VMD, meanwhile, Signal-noise can be separated to some extent. It is very useful tool to MID detects modulation components. However, when the analyzed signal contains multiple modulations usually mixed with other harmonic components, visual examination of the spectrum may not be accurate for identification of all carriers together with their modulation signals. Considering the shortcomings of MID in the analysis of multi-harmonic modulation signals, VMD is used as the signal preprocessing before MID analysis. Results of simulation and the experimental analysis have demonstrated the effectiveness of the method.
VMD has better band-pass filtering characteristic, which can non-recursively decomposition a real-valued multi-composition signal into a discrete number of quasi-orthogonal band-limited sub-signals with specific sparsity properties in the spectral. Modulation intensity distribution(MID) combined with VMD is applied to detect second-order cyclostationary components in gear fault diagnosis. Impulsive signatures generally represent the transients in the signals and are often caused by local defect in the gear of rotating machinery. Detecting these signatures is vital for mechanical signal processing and fault diagnosis. The impulsive signatures can be successfully extracted using VMD, meanwhile, Signal-noise can be separated to some extent. It is very useful tool to MID detects modulation components. However, when the analyzed signal contains multiple modulations usually mixed with other harmonic components, visual examination of the spectrum may not be accurate for identification of all carriers together with their modulation signals. Considering the shortcomings of MID in the analysis of multi-harmonic modulation signals, VMD is used as the signal preprocessing before MID analysis. Results of simulation and the experimental analysis have demonstrated the effectiveness of the method.
引文
[1] 雷亚国,何正嘉,林京,等. 行星齿轮箱故障诊断技术的研究进展[J]. 机械工程学报, 2011, 47(19): 59-67.LEI YaGuo, HE ZhengJia, LIN Jing, et al. Research advances of fault diagnosis technique for planetary gearboxes[J].Journal of Mechanical Engineering, 2011, 47(9): 59-67 (In Chinese).
[2] 王凯, 张永祥, 李军. 齿轮裂纹故障的双谱分析[J]. 机械強度, 2006, 28(3): 346-348.WANGKai, ZHANG yongXiang, LI Jun. Bispectrum analysis of gear crack fault [J] Journal of Mechanical Strength, 2006, 28(3): 346-348 (In Chinese).
[3] Sawalhi N, Randall R B. Simulating gear and bearing interactions in the presence of faults: Part I. The combined gear bearing dynamic model and the simulation of localised bearing faults [J]. Mechanical Systems and Signal Processing, 2008, 22(8): 1924-1951.
[4] 巩晓赟, 韩捷, 陈宏. 矢 Hilbert 解调及其在齿轮故障诊断中的应用[J]. 机械强度, 2010, 32(6):1008-1011GONG XioBin, HAN Jie, CHEN Hong, Vector-Hilbert demodulation and its application in the gear failure-diagnosis [J]. 2010, 32(6):1008-1011 (In Chinese).
[5] 冯志鹏, 赵镭镭, 褚福磊. 行星齿轮箱齿轮局部故障振动频谱特征 [J]. 中国电机工程学报, 2013, 33(5): 119-127.FENG ZhiPeng, ZHAO LeiLei, CHU FuLei, Vibration spectral characteristics of localized gear fault of planetary gearboxes[J]. Proceedings of the CSEE, 2013, 33(5): 119-127 (In Chinese).
[6] 李怀俊,刘越琪,谢小鹏. 齿轮箱振动与输入能量信号的频域相干分析与关系识别 [J]. 农业工程学报,2015,31(4):175-182.LI HuaiJun, LIU YueQi, XIE XiaoPeng. Frequency domaincoherence analysis and relationship recognition between gearbox vibration and input energy signal[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(4): 175-182 (In Chinese).
[7] Capdessus CA, Sidahmed MB, Lacoume JL. Cyclostationary processes:application in gear faults early diagnosis. Mech Syst Signal Process, 2000;14(3):371-385.
[8] Urbanek J, Antoni J, Barszcz T. Detection of signal component modulations using modulation intensity distribution [J]. Mechanical Systems and Signal Processing, 2012, 28: 399-413.
[9] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[C]//Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 1998, 454(1971): 903-995.
[10] Dragomiretskiy K, Zosso D. Variational mode decomposition [J]. IEEE transactions on signal processing, 2014, 62(3): 531-544.
[11] Wang Y, Markert R, Xiang J, et al. Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system [J]. Mechanical Systems and Signal Processing, 2015, 60: 243-251.
[12] Wang Y, Markert R. Filter bank property of variational mode decomposition and its applications [J]. Signal Processing, 2016, 120: 509-521.
[13] 唐贵基, 王晓龙. 参数优化变分模态分解方法在滚动轴承早期故障诊断中的应用 [J]. 西安交通大学学报, 2015, 49(5): 73-81.TANG GuiJi, WANG XiaoLong, Parameter optimized variational mode decomposition method with application to incipient fault diagnosis of rolling bearing[J]. Journal of Xi’an Jiaotong University, 2015, 49(5): 73-81 (In Chinese).
[14] 刘长良, 武英杰, 甄成刚. 基于变分模态分解和模糊 C 均值聚类的滚动轴承故障诊断 [J]. 中国电机工程学报, 2015, 35(13): 3358-3365.LIU ChangLiang, WU YingJie, ZHEN ChengGang, Rolling bearing fault diagnosis based on variational mode decomposition and fuzzy C means clustering[J]. Proceedings of the CSEE, 2015, 35(13): 3358-3365 (In Chinese).
[15] Urbanek J, Barszcz T, Antoni J. Integrated modulation intensity distribution as a practical tool for condition monitoring [J]. Applied Acoustics, 2014, 77: 184-194.
[16] Xiang J, Zhong Y, Gao H. Rolling element bearing fault detection using PPCA and spectral kurtosis[J]. Measurement, 2015(75): 180-191.
[17] Urbanek J, Barszcz T, Sawalhi N, et al. Comparison of amplitude-based and phase-based methods for speed tracking in application to wind turbines [J]. Metrology and measurement systems, 2011, 18(2): 295-304.
[2] 王凯, 张永祥, 李军. 齿轮裂纹故障的双谱分析[J]. 机械強度, 2006, 28(3): 346-348.WANGKai, ZHANG yongXiang, LI Jun. Bispectrum analysis of gear crack fault [J] Journal of Mechanical Strength, 2006, 28(3): 346-348 (In Chinese).
[3] Sawalhi N, Randall R B. Simulating gear and bearing interactions in the presence of faults: Part I. The combined gear bearing dynamic model and the simulation of localised bearing faults [J]. Mechanical Systems and Signal Processing, 2008, 22(8): 1924-1951.
[4] 巩晓赟, 韩捷, 陈宏. 矢 Hilbert 解调及其在齿轮故障诊断中的应用[J]. 机械强度, 2010, 32(6):1008-1011GONG XioBin, HAN Jie, CHEN Hong, Vector-Hilbert demodulation and its application in the gear failure-diagnosis [J]. 2010, 32(6):1008-1011 (In Chinese).
[5] 冯志鹏, 赵镭镭, 褚福磊. 行星齿轮箱齿轮局部故障振动频谱特征 [J]. 中国电机工程学报, 2013, 33(5): 119-127.FENG ZhiPeng, ZHAO LeiLei, CHU FuLei, Vibration spectral characteristics of localized gear fault of planetary gearboxes[J]. Proceedings of the CSEE, 2013, 33(5): 119-127 (In Chinese).
[6] 李怀俊,刘越琪,谢小鹏. 齿轮箱振动与输入能量信号的频域相干分析与关系识别 [J]. 农业工程学报,2015,31(4):175-182.LI HuaiJun, LIU YueQi, XIE XiaoPeng. Frequency domaincoherence analysis and relationship recognition between gearbox vibration and input energy signal[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(4): 175-182 (In Chinese).
[7] Capdessus CA, Sidahmed MB, Lacoume JL. Cyclostationary processes:application in gear faults early diagnosis. Mech Syst Signal Process, 2000;14(3):371-385.
[8] Urbanek J, Antoni J, Barszcz T. Detection of signal component modulations using modulation intensity distribution [J]. Mechanical Systems and Signal Processing, 2012, 28: 399-413.
[9] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[C]//Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 1998, 454(1971): 903-995.
[10] Dragomiretskiy K, Zosso D. Variational mode decomposition [J]. IEEE transactions on signal processing, 2014, 62(3): 531-544.
[11] Wang Y, Markert R, Xiang J, et al. Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system [J]. Mechanical Systems and Signal Processing, 2015, 60: 243-251.
[12] Wang Y, Markert R. Filter bank property of variational mode decomposition and its applications [J]. Signal Processing, 2016, 120: 509-521.
[13] 唐贵基, 王晓龙. 参数优化变分模态分解方法在滚动轴承早期故障诊断中的应用 [J]. 西安交通大学学报, 2015, 49(5): 73-81.TANG GuiJi, WANG XiaoLong, Parameter optimized variational mode decomposition method with application to incipient fault diagnosis of rolling bearing[J]. Journal of Xi’an Jiaotong University, 2015, 49(5): 73-81 (In Chinese).
[14] 刘长良, 武英杰, 甄成刚. 基于变分模态分解和模糊 C 均值聚类的滚动轴承故障诊断 [J]. 中国电机工程学报, 2015, 35(13): 3358-3365.LIU ChangLiang, WU YingJie, ZHEN ChengGang, Rolling bearing fault diagnosis based on variational mode decomposition and fuzzy C means clustering[J]. Proceedings of the CSEE, 2015, 35(13): 3358-3365 (In Chinese).
[15] Urbanek J, Barszcz T, Antoni J. Integrated modulation intensity distribution as a practical tool for condition monitoring [J]. Applied Acoustics, 2014, 77: 184-194.
[16] Xiang J, Zhong Y, Gao H. Rolling element bearing fault detection using PPCA and spectral kurtosis[J]. Measurement, 2015(75): 180-191.
[17] Urbanek J, Barszcz T, Sawalhi N, et al. Comparison of amplitude-based and phase-based methods for speed tracking in application to wind turbines [J]. Metrology and measurement systems, 2011, 18(2): 295-304.