Research on sparsity indexes for fault diagnosis of rotating machinery

Abstract This paper originated from an investigation of sparsity indexes for fault diagnosis of rotating machinery. Although various sparsity indexes have been widely applied in machinery fault feature extraction, there is little information on the guideline available for the selection of the best sparsity index for the specified scenarios with different interferences. To solve the problem, this article firstly analyzes the performance of the representative sparsity indexes, containing Gini index, l2/l1 norm, Hoyer measure and kurtosis. Aiming at the feature of the machinery fault signal, three performance attributes, including data-length independency, random-impulse resistance and fault-impulse discernibility, are originally proposed to quantitatively evaluate the sparsity index. Based on the comparison results, a guideline for the selection of the optimal sparsity measure is summarized. After that, this guideline is used for the improvement of kurtogram and protrugram, and the results are evaluated. Finally, the comparison result, using both simulated and experimental bearing fault signals, confirms that an optimal scheme can be designed for the sparsity-based improvement under the proposed guideline.

[1]  Yaguo Lei,et al.  Application of an improved maximum correlated kurtosis deconvolution method for fault diagnosis of rolling element bearings , 2017 .

[2]  Viliam Makis,et al.  Optimal swarm decomposition with whale optimization algorithm for weak feature extraction from multicomponent modulation signal , 2019, Mechanical Systems and Signal Processing.

[3]  Qing Zhao,et al.  Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection , 2012 .

[4]  Rolf Aaberge,et al.  Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings , 2000, J. Econ. Theory.

[5]  C. Gini.  Measurement of Inequality of Incomes , 1921 .

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

[7]  Scott T. Rickard,et al.  Comparing Measures of Sparsity , 2008, IEEE Transactions on Information Theory.

[8]  R. M. Stewart,et al.  Detection of Rolling Element Bearing Damage by Statistical Vibration Analysis , 1978 .

[9]  Robert B. Randall,et al.  Differential diagnosis of spall vs. cracks in the gear tooth fillet region: Experimental validation , 2009 .

[10]  Robert B. Randall,et al.  The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis , 2007 .

[11]  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 .

[12]  Robert X. Gao,et al.  Wavelet domain principal feature analysis for spindle health diagnosis , 2011 .

[13]  Robert B. Randall,et al.  Enhancement of autoregressive model based gear tooth fault detection technique by the use of minimum entropy deconvolution filter , 2007 .

[14]  Michael Elad,et al.  Sparse and Redundant Modeling of Image Content Using an Image-Signature-Dictionary , 2008, SIAM J. Imaging Sci..

[15]  Thomas R. Kurfess,et al.  Rolling element bearing diagnostics in run-to-failure lifetime testing , 2001 .

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

[17]  Qiang Miao,et al.  A parameter-adaptive VMD method based on grasshopper optimization algorithm to analyze vibration signals from rotating machinery , 2018, Mechanical Systems and Signal Processing.

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

[19]  Yonghao Miao,et al.  Sparse maximum harmonics-to-noise-ratio deconvolution for weak fault signature detection in bearings , 2016 .

[20]  J. Preisig,et al.  Estimation of Rapidly Time-Varying Sparse Channels , 2007, IEEE Journal of Oceanic Engineering.

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

[22]  Dejie Yu,et al.  A new rolling bearing fault diagnosis method based on GFT impulse component extraction , 2016 .

[23]  Jay Lee,et al.  A geometrical investigation on the generalized lp/lq norm for blind deconvolution , 2017, Signal Process..

[24]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[26]  Jing Lin,et al.  Feature Mining and Health Assessment for Gearboxes Using Run-Up/Coast-Down Signals , 2016, Sensors.

[27]  Han Zhang,et al.  Compressed sensing based on dictionary learning for extracting impulse components , 2014, Signal Process..

[28]  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 .

[29]  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 .

[30]  Yimin Shao,et al.  Fast time-frequency manifold learning and its reconstruction for transient feature extraction in rotating machinery fault diagnosis , 2019, Measurement.

[31]  Michael Elad,et al.  Sparse Representation for Color Image Restoration , 2008, IEEE Transactions on Image Processing.

[32]  Jay Lee,et al.  Investigation on the kurtosis filter and the derivation of convolutional sparse filter for impulsive signature enhancement , 2017 .

[33]  S. Yitzhaki,et al.  The Mean-Gini Efficient Portfolio Frontier , 2005 .

[34]  Ruqiang Yan,et al.  Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis , 2016 .

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

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

[37]  Yaguo Lei,et al.  Application of an improved kurtogram method for fault diagnosis of rolling element bearings , 2011 .

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

[39]  Han Zhang,et al.  Sparse Feature Identification Based on Union of Redundant Dictionary for Wind Turbine Gearbox Fault Diagnosis , 2015, IEEE Transactions on Industrial Electronics.

[40]  Ming Zhao,et al.  Identification of multiple faults in rotating machinery based on minimum entropy deconvolution combined with spectral kurtosis , 2016 .

[41]  Ming Zhao,et al.  Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal , 2020 .

[42]  Ming Liang,et al.  An adaptive SK technique and its application for fault detection of rolling element bearings , 2011 .

[43]  Yi Qin,et al.  Kurtogram manifold learning and its application to rolling bearing weak signal detection , 2018, Measurement.

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

[45]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..