Separation of multiple local-damage-related components from vibration data using Nonnegative Matrix Factorization and multichannel data fusion

Abstract The problem of local damage detection in case of analyzing vibration signal from rotating machines is mostly related to the detection of periodic impulsive components. Depending on various features of the signal, this task can be relatively simple in some cases (e.g. for an impulsive component in the presence of Gaussian noise). However, in our case multiple impulsive components occupying with the overlapping frequency bands are present. For all components, the impulses can be periodic. In this article, authors present a novel methodology based on data fusion from multichannel vibration data from heavy-duty industrial gearbox operating in the driving station of a belt conveyor. The proposed method is based on the factorization of spectrograms using Generalized Hierarchical Alternating Least Squares Nonnegative Matrix Factorization with Beta-Divergence (later referred to as β -HALS NMF). Partial information obtained from the factorization is fused into a single data set for each impulsive component present in the signal. Finally, Griffin-Lim algorithm is used to estimate the complex phase layer of artificial spectrograms allowing to recover the near-perfect time series of each impulsive component extracted from the signal. This method has been tested on four-channel vibration data.

[1]  D. Joanes,et al.  Comparing measures of sample skewness and kurtosis , 1998 .

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

[3]  Radoslaw Zimroz,et al.  Novel method of informative frequency band selection for vibration signal using Nonnegative Matrix Factorization of spectrogram matrix , 2019, Mechanical Systems and Signal Processing.

[4]  Yasuhiro Oikawa,et al.  Deep Griffin–Lim Iteration , 2019, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[5]  Jérôme Antoni,et al.  Cyclostationary modelling of rotating machine vibration signals , 2004 .

[6]  Robert B. Randall,et al.  Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applications , 2011 .

[7]  Fakher Chaari,et al.  Modelling of gearbox dynamics under time-varying nonstationary load for distributed fault detection and diagnosis , 2010 .

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

[9]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[10]  Jakub Obuchowski,et al.  Modified Protrugram Method for Damage Detection in Bearing Operating Under Impulsive Load , 2017 .

[11]  Radoslaw Zimroz,et al.  Application of tempered stable distribution for selection of optimal frequency band in gearbox local damage detection , 2017 .

[12]  Tomasz Barszcz,et al.  Impulsive source separation using combination of Nonnegative Matrix Factorization of bi-frequency map, spatial denoising and Monte Carlo simulation , 2019, Mechanical Systems and Signal Processing.

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

[14]  Rafal Zdunek,et al.  Data Clustering with Semi-binary Nonnegative Matrix Factorization , 2006, ICAISC.

[15]  M. V. Van Benthem,et al.  Fast algorithm for the solution of large‐scale non‐negativity‐constrained least squares problems , 2004 .

[16]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[17]  Jae Lim,et al.  Signal estimation from modified short-time Fourier transform , 1984 .

[18]  W. Cioch,et al.  Finding a frequency signature for a cyclostationary signal with applications to wheel bearing diagnostics , 2013 .

[19]  Agnieszka Wyłomańska,et al.  Data-driven vibration signal filtering procedure based on the α-stable distribution , 2016, Journal of Vibroengineering.

[20]  Y. L. Tong.  The multivariate normal distribution , 1989 .

[21]  Radoslaw Zimroz,et al.  Selection of informative frequency band in local damage detection in rotating machinery , 2014 .

[22]  Darryll J. Pines,et al.  A review of vibration-based techniques for helicopter transmission diagnostics , 2005 .

[23]  F. Combet,et al.  Optimal filtering of gear signals for early damage detection based on the spectral kurtosis , 2009 .

[24]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[25]  Radoslaw Zimroz,et al.  Optimal filter design with progressive genetic algorithm for local damage detection in rolling bearings , 2018 .

[26]  Jont B. Allen,et al.  Short term spectral analysis, synthesis, and modification by discrete Fourier transform , 1977 .

[27]  A. Cichocki,et al.  Flexible HALS algorithms for sparse non-negative matrix/tensor factorization , 2008, 2008 IEEE Workshop on Machine Learning for Signal Processing.

[28]  Andrzej Cichocki,et al.  Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations , 2009, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[29]  Radoslaw Zimroz,et al.  Periodically impulsive behavior detection in noisy observation based on generalized fractional order dependency map , 2017, Applied Acoustics.

[30]  Mihoko Minami,et al.  Robust Blind Source Separation by Beta Divergence , 2002, Neural Computation.

[31]  Konstantinos Gryllias,et al.  Application of Cyclo-Non-Stationary Indicators for Bearing Monitoring Under Varying Operating Conditions , 2017 .

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

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

[34]  Radoslaw Zimroz,et al.  Impulsive Noise Cancellation Method for Copper Ore Crusher Vibration Signals Enhancement , 2016, IEEE Transactions on Industrial Electronics.

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

[36]  Jacek Wodecki,et al.  Local fault detection of rolling element bearing components by spectrogram clustering with semi-binary NMF , 2017 .