Weighted Cyclic Harmonic-to-Noise Ratio for Rolling Element Bearing Fault Diagnosis

A novel index termed weighted cyclic harmonic-to-noise ratio (WCHNR) is proposed to directly evaluate the quality and quantity of harmonics of bearing characteristic frequency (BCF) in the squared envelope spectrum (SES). There are four steps to construct the proposed index. First, cyclic harmonic-to-noise ratio (CHNR) is defined to evaluate the prominence of harmonic, which is inspired by harmonic-to-noise ratio (HNR) and ratio of cyclic content (RCC). Interestingly, it is showed in this paper that a special case of CHNR is a local $L\infty /L1$ norm, which bridges the proposed index with other indexes such as spectral Gini index and spectral kurtosis. Second, a local 0-dB threshold and a global threshold derived from a statistical hypothesis test are utilized to decide the detection of prominent harmonic. Third, if two consecutive harmonics are not prominent, the following higher order harmonics would not be considered, which helps avoid large gap between prominent harmonics and reduce the influence of random cyclic frequency noise. Finally, the sum of each type of CHNR is weighted based on the number of detected harmonics. The proposed index is compared with the spectral Gini index and spectral kurtosis in three case studies, which indicates that the proposed index is less sensitive to outliers and more effective in bearing fault diagnosis. It is also found that the number of detected harmonics can be potentially used in bearing fault classification easily and practically.

[1]  Peter J. Murphy.  A cepstrum-based harmonics-to-noise ratio in voice signals , 2000, INTERSPEECH.

[2]  Paolo Pennacchi,et al.  Testing second order cyclostationarity in the squared envelope spectrum of non-white vibration signals , 2013 .

[3]  Jérôme Antoni,et al.  The infogram: Entropic evidence of the signature of repetitive transients , 2016 .

[4]  Robert B. Randall,et al.  The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines , 2006 .

[5]  Tomasz Barszcz,et al.  A novel method for the optimal band selection for vibration signal demodulation and comparison with the Kurtogram , 2011 .

[6]  L. T. DeCarlo.  On the meaning and use of kurtosis. , 1997 .

[7]  Robert X. Gao,et al.  Wavelets for fault diagnosis of rotary machines: A review with applications , 2014, Signal Process..

[8]  Dong Wang,et al.  Some further thoughts about spectral kurtosis, spectral L2/L1 norm, spectral smoothness index and spectral Gini index for characterizing repetitive transients , 2018 .

[9]  Jing Na,et al.  Envelope order tracking for fault detection in rolling element bearings , 2012 .

[10]  Thomas A. Jones,et al.  Skewness and kurtosis as criteria of normality in observed frequency distributions , 1969 .

[11]  Wei Qiao,et al.  Current-Aided Order Tracking of Vibration Signals for Bearing Fault Diagnosis of Direct-Drive Wind Turbines , 2016, IEEE Transactions on Industrial Electronics.

[12]  T. Baer,et al.  Harmonics-to-noise ratio as an index of the degree of hoarseness. , 1982, The Journal of the Acoustical Society of America.

[13]  Y. Qi,et al.  Temporal and spectral estimations of harmonics-to-noise ratio in human voice signals. , 1997, The Journal of the Acoustical Society of America.

[14]  Robert B. Randall,et al.  Differential Diagnosis of Gear and Bearing Faults , 2002 .

[15]  Dong Wang,et al.  Smoothness index-guided Bayesian inference for determining joint posterior probability distributions of anti-symmetric real Laplace wavelet parameters for identification of different bearing faults , 2015 .

[16]  Fang Liu,et al.  A Novel Contactless Angular Resampling Method for Motor Bearing Fault Diagnosis Under Variable Speed , 2016, IEEE Transactions on Instrumentation and Measurement.

[17]  Qingbo He,et al.  Wavelet Packet Envelope Manifold for Fault Diagnosis of Rolling Element Bearings , 2016, IEEE Transactions on Instrumentation and Measurement.

[18]  J. Antoni.  The spectral kurtosis: a useful tool for characterising non-stationary signals , 2006 .

[19]  I. S. Bozchalooi,et al.  A smoothness index-guided approach to wavelet parameter selection in signal de-noising and fault detection , 2007 .

[20]  Yue Hu,et al.  Instantaneous Frequency Estimation for Nonlinear FM Signal Based on Modified Polynomial Chirplet Transform , 2017, IEEE Transactions on Instrumentation and Measurement.

[21]  Yaguo Lei,et al.  Condition monitoring and fault diagnosis of planetary gearboxes: A review , 2014 .

[22]  Roger F. Dwyer,et al.  Detection of non-Gaussian signals by frequency domain Kurtosis estimation , 1983, ICASSP.

[23]  J. Antoni.  Cyclic spectral analysis of rolling-element bearing signals : Facts and fictions , 2007 .

[24]  Paolo Pennacchi,et al.  The relationship between kurtosis- and envelope-based indexes for the diagnostic of rolling element bearings , 2014 .

[25]  Dong Wang,et al.  Spectral L2 / L1 norm: A new perspective for spectral kurtosis for characterizing non-stationary signals , 2018 .

[26]  Yonghao Miao,et al.  Improvement of kurtosis-guided-grams via Gini index for bearing fault feature identification , 2017 .

[27]  Robert B. Randall,et al.  Rolling element bearing diagnostics—A tutorial , 2011 .

[28]  Robert B. Randall,et al.  Applications of Spectral Kurtosis in Machine Diagnostics and Prognostics , 2005 .

[29]  Zhigang Liu,et al.  An Approach to Recognize the Transient Disturbances With Spectral Kurtosis , 2014, IEEE Transactions on Instrumentation and Measurement.

[30]  Ming Liang,et al.  Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications , 2016 .

[31]  Guiji Tang,et al.  Fault diagnosis for rolling bearing based on improved enhanced kurtogram method , 2016, 2016 13th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI).

[32]  N. Tandon,et al.  A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings , 1999 .

[33]  Pengcheng Jiang,et al.  Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis , 2017, Sensors.

[34]  J. Antoni.  Fast computation of the kurtogram for the detection of transient faults , 2007 .

[35]  P. Boersma.  ACCURATE SHORT-TERM ANALYSIS OF THE FUNDAMENTAL FREQUENCY AND THE HARMONICS-TO-NOISE RATIO OF A SAMPLED SOUND , 1993 .

[36]  Yaguo Lei,et al.  Envelope harmonic-to-noise ratio for periodic impulses detection and its application to bearing diagnosis , 2016 .

[37]  Yaguo Lei,et al.  Periodicity-based kurtogram for random impulse resistance , 2015 .

[38]  Yi Qin,et al.  A New Family of Model-Based Impulsive Wavelets and Their Sparse Representation for Rolling Bearing Fault Diagnosis , 2018, IEEE Transactions on Industrial Electronics.

[39]  Yonghao Miao,et al.  Detection and recovery of fault impulses via improved harmonic product spectrum and its application in defect size estimation of train bearings , 2016 .

[40]  H. Dalton.  The Measurement of the Inequality of Incomes , 1920 .

[41]  Peter W. Tse,et al.  The design of a new sparsogram for fast bearing fault diagnosis: Part 1 of the two related manuscripts that have a joint title as “Two automatic vibration-based fault diagnostic methods using the novel sparsity measurement – Parts 1 and 2” , 2013 .