Abstract
Rolling bearing plays an important role in rotary machines. In rotating machine fault diagnosis, two-channel signals that are recorded from bearing provide sufficient information. It is meaningful to integrate two-channel signals for improving the comprehensiveness and accuracy of status information extracted from the signals. Human auditory nerve system can integrate the binaural information through the mechanism of neurons oscillation and delivery of oscillation. In view of the aspects mentioned above, to simulate the operating mechanism of human binaural auditory system, a double-layer auditory nerve oscillator network (DLNON) model, whose inputs are two-channel vibration signals, is proposed for features extraction and faults diagnosis. By this model, independent component analysis (ICA) is used at the first place to reduce the correlation and increase the independence between the signals; then, outputs of ICA are processed by short-time Fourier transform (STFT) and spectral envelop to reduce the complexity of frequency structure and highlight the formant informant of signal. After that, two results of time–frequency envelop are processed, respectively, by the first-layer oscillator network to obtain synchronous oscillatory period function (SOPF). Finally, information of two SOPFs and two time–frequency envelops is integrated by the second-layer oscillator network, so as to simulate auditory masking effect. The synchronous oscillatory feature function (SOFF) reflected the feature of two-channel signals is obtained by calculating the oscillatory result (SOPF) of the second oscillator network. The performance of DLNON model is evaluated by experiments. The results show that this model can effectively extract fault features, and distinguish fault types, fault severity ratings.
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Data availability
The datasets analyzed during the current study are available in the Case Western Reserve University Bearing Data Center Website repository, [http://csegroups.case.edu/bearingdatacenter/home].
Abbreviations
- \({\mathbf{A}}\) :
-
Original signal matrix
- \(x\) :
-
The first channel signal in \({\mathbf{A}}\)
- \(y\) :
-
The second channel signal in \({\mathbf{A}}\)
- \({\mathbf{A^{\prime}}}\) :
-
Whitened signal matrix
- \({\mathbf{B}}\) :
-
Whitened matrix
- \({\mathbf{D}}\) :
-
Eigenvalue matrix of covariance matrix
- \({\mathbf{U^{\prime}}}\) :
-
Feature vector matrix
- \({\mathbf{Q}}\) :
-
Separation matrix
- \({\mathbf{Y}}\) :
-
Signal matrix removed correlation
- \(x_{1}\) :
-
The first channel signal in \({\mathbf{Y}}\)
- \(y_{1}\) :
-
The second channel signal in \({\mathbf{Y}}\)
- \(w\) :
-
Rectangular window function
- \(M\) :
-
The number of neurons to the \(m\) direction
- \(N\) :
-
The number of neurons to the \(n\) direction
- \(R\) :
-
The number of final SOPF
- \(gs\) :
-
The number of \(\psi^{(2)}\)
- \({\mathbf{\rm O}}\) :
-
The neuron
- \(G\) :
-
Nonlinear time function
- \(2N\) :
-
Length of window function
- \(W\) :
-
Overlapping points of window function
- \({\mathbf{K}}_{mn}\) :
-
External input of neuron
- \({\text{ST}}_{1}\) :
-
Result of short-time Fourier transform of \(x_{1}\)
- \({\text{ST}}_{2}\) :
-
Result of short-time Fourier transform of \(y_{1}\)
- \(en_{1}\) :
-
Spectral envelopes of \({\text{ST}}_{1}\)
- \(en_{2}\) :
-
Spectral envelopes of \({\text{ST}}_{2}\)
- \(P_{mn}\) :
-
Coupling term of oscillation
- \(\chi_{mn}\) :
-
Membrane potential
- \(\zeta_{mn}\) :
-
Activity level of ion channel
- \(S1^{mn}\) :
-
Connection weight of the first-layer network for \(en_{1}\)
- \(S2^{mn}\) :
-
Connection weight of the first-layer network for \(en_{2}\)
- \(\psi_{2}^{(1)}\) :
-
SOPF of the first-layer network for \(en_{2}\)
- \(\psi_{1}^{(1)}\) :
-
SOPF of the first-layer network for \(en_{1}\)
- \(S_{z}^{mn}\) :
-
Connection weight of global inhibitory neuron
- \(S_{{}}^{mn}\) :
-
Connection weight of the second layer
- \({\rm T}_{1}^{\left( 1 \right)}\) :
-
The period of each neuron the first network in the first layer
- \(OC\) :
-
The number of oscillatory neurons
- \(L\) :
-
The number of oscillatory periods of unequal value
- \(C_{l}^{{}}\) :
-
The final period for \(\psi_{1}^{(1)}\)
- \(\psi^{(2)}\) :
-
SOPF of the second-layer network
- \(\omega\) :
-
Synchronous oscillatory feature functions (SOFF)
- \(\varpi\) :
-
The final SOFF
- \(\Omega\) :
-
The number of fault types
- \(\varpi_{s}\) :
-
The final SOFF of identified signal
- \(\eta\) :
-
Euclidean distance
- \(\sigma\) :
-
Manhattan distance
- \(J\) :
-
Recognition distance
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The author appreciates the free download of the original bearing fault data and one picture provided by Case Western Reserve University Bearing Data Center Website.
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Appendices
Appendix 1
See Figs.
Intermediate result of feature extraction of outer ring CE fault type
30,
Intermediate result of feature extraction of inner ring fault type
31,
Intermediate result of feature extraction of ball fault type
32,
Intermediate result of feature extraction of normal bearing and outer ring OR fault type
33.
Appendix 2
1 normal, 2 inner ring (severity rating 1), 3 ball (severity rating 1), 4 outer ring (CE severity rating 1), 5 outer ring (OR severity rating 1), 6 outer ring (OP severity rating 1), 7 inner ring (severity rating 2), 8 ball (severity rating 2), 9 outer ring (CE severity rating 2), 10 inner ring (severity rating 3), 11 ball (severity rating 3), 12 outer ring (CE severity rating 3), 13 outer ring (OR severity rating 3), 14 outer ring (OP severity rating 3).
See Figs.
SOFFs of fault signal under no load
34,
SOFFs of fault signal under load one
35,
SOFFs of fault signal under load two
36,
SOFFs of fault signal under load three
37.
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Liu, X., Li, Y., Sun, M. et al. A model of binaural auditory nerve oscillator network for bearing fault diagnosis by integrating two-channel vibration signals. Nonlinear Dyn 111, 4779–4805 (2023). https://doi.org/10.1007/s11071-022-08079-x
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DOI: https://doi.org/10.1007/s11071-022-08079-x