Abstract

In this work, the reverse dispersion entropy (RDE) is used to process the squared envelope (SE) signal in order to detect nonstationarites. Based on the idea of spectral kurtosis (SK) and kurtogram, the squared envelope signal is first extracted by applying the short time Fourier transform to vibration signal. Then, as an alternative to negative Shannon entropy, the RDE is used to process the squared envelope to detect the range of frequencies at which the transients occur. The RDEgram color-coded map is used to represent the RDE values as a function of frequency and frequency resolution from which the ideal filter parameters can be inferred. Once the best frequency and frequency bandwidth pair are found, an optimum finite impulse response filter can be designed to filter the original vibration signal. The proposed method is tested against simulated and actual vibration signals and proved to be superior to existing methods.

References

1.
Brown
,
D. N.
,
1989
, “
Envelope Analysis Detects Bearing Faults Before Major Damage Occurs
,”
Pulp Pap.
,
63
(
13
), pp.
113
117
.
2.
Tse
,
P. W.
,
Peng
,
Y. H.
, and
Yam
,
R.
,
2001
, “
Wavelet Analysis and Envelope Detection For Rolling Element Bearing Fault Diagnosis—Their Effectiveness and Flexibilities
,”
ASME J. Vib. Acoust.
,
123
(
3
), pp.
303
310
.
3.
Altmann
,
J.
, and
Mathew
,
J.
,
2001
, “
Multiple Band-Pass Autoregressive Demodulation for Rolling-Element Bearing Fault Diagnosis
,”
Mech. Syst. Signal Process
,
15
(
5
), pp.
963
977
.
4.
Al-Raheem
,
K. F.
,
Roy
,
A.
,
Ramachandran
,
K. P.
,
Harrison
,
D. K.
, and
Grainger
,
S.
,
2007
, “
Rolling Element Bearing Fault Diagnosis Using Laplace-Wavelet Envelope Power Spectrum
,”
Eurasip J. Adv. Signal Process
,
2013
(
1
), p.
073629
.
5.
Al-Raheem
,
K. F.
,
Roy
,
A.
,
Ramachandran
,
K. P.
,
Harrison
,
D. K.
, and
Grainger
,
S.
,
2008
, “
Application of the Laplace-Wavelet Combined With ANN for Rolling Bearing Fault Diagnosis
,”
ASME J. Vib. Acoust.
,
130
(
5
), p.
051007
.
6.
Li
,
H.
,
2011
, “
Bearing Fault Detection Based on Order Tracking and Complex Morlet Wavelet Transform
,”
Key Eng. Mater.
,
474–476
, pp.
639
644
.
7.
Gu
,
X.
,
Yang
,
S.
,
Liu
,
Y.
,
Deng
,
F.
, and
Ren
,
B.
,
2018
, “
Compound Faults Detection of the Rolling Element Bearing Based on the Optimal Complex Morlet Wavelet Filter
,”
Proc. Inst. Mech. Eng., Part C
,
232
(
10
), pp.
1786
1801
.
8.
Malla
,
C.
,
Rai
,
A.
,
Kaul
,
V.
, and
Panigrahi
,
I.
,
2019
, “
Rolling Element Bearing Fault Detection Based on the Complex Morlet Wavelet Transform and Performance Evaluation Using Artificial Neural Network and Support Vector Machine
,”
Noise Vibr. Worldwide
,
50
(
9–11
), pp.
313
327
.
9.
Wang
,
D.
,
Shen
,
C.
, and
Tse
,
P. W.
,
2013
, “
A Novel Adaptive Wavelet Stripping Algorithm for Extracting the Transients Caused by Bearing Localized Faults
,”
J. Sound Vib.
,
332
(
25
), pp.
6871
6890
.
10.
Antoni
,
J.
,
2006
, “
The Spectral Kurtosis: A Useful Tool for Characterising Non-Stationary Signals
,”
Mech. Syst. Signal Process
,
20
(
2
), pp.
282
307
.
11.
Antoni
,
J.
, and
Randall
,
R. B.
,
2006
, “
The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating Machines
,”
Mech. Syst. Signal Process
,
20
(
2
), pp.
308
331
.
12.
Antoni
,
J.
,
2007
, “
Fast Computation of the Kurtogram for the Detection of Transient Faults
,”
Mech. Syst. Signal Process
,
21
(
1
), pp.
108
124
.
13.
Zhang
,
Y.
,
Liang
,
M.
,
Li
,
C.
, and
Hou
,
S.
,
2013
, “
A Joint Kurtosis-Based Adaptive Bandstop Filtering and Iterative Autocorrelation Approach to Bearing Fault Detection
,”
ASME J. Vib. Acoust.
,
135
(
5
), p.
051026
.
14.
Wang
,
D.
,
Tse
,
P. W.
, and
Tsui
,
K. L.
,
2013
, “
An Enhanced Kurtogram Method for Fault Diagnosis of Rolling Element Bearings
,”
Mech. Syst. Signal Process
,
35
(
1
), pp.
176
199
.
15.
Jing
,
S.
,
Yuan
,
J.
,
Li
,
X.
, and
Leng
,
J.
,
2018
, “
Weak Fault Feature Identification
,”
2018 International Conference on Information Systems and Computer Aided Education (ICISCAE)
,
Changchun, China
,
July 6–8
, IEEE, pp.
235
239
.
16.
Xu
,
Y.
,
Tian
,
W.
,
Zhang
,
K.
, and
Ma
,
C.
,
2019
, “
Application of an Enhanced Fast Kurtogram Based on Empirical Wavelet Transform for Bearing Fault Diagnosis
,”
Meas. Sci. Technol.
,
30
(
3
), p.
035001
.
17.
Wan
,
S.
, and
Peng
,
B.
,
2019
, “
The FERgram: A Rolling Bearing Compound Fault Diagnosis Based on Maximal Overlap Discrete Wavelet Packet Transform and Fault Energy Ratio
,”
J. Mech. Sci. Technol.
,
33
(
1
), pp.
157
172
.
18.
Moshrefzadeh
,
A.
, and
Fasana
,
A.
,
2018
, “
The Autogram: An Effective Approach for Selecting the Optimal Demodulation Band in Rolling Element Bearings Diagnosis
,”
Mech. Syst. Signal Process
,
105
, pp.
294
318
.
19.
Sheng
,
Z.
,
Xu
,
Y.
, and
Zhang
,
K.
,
2021
, “
Applications in Bearing Fault Diagnosis of an Improved Kurtogram Algorithm Based on Flexible Frequency Slice Wavelet Transform Filter Bank
,”
Meas.
,
174
, p.
108975
.
20.
Yan
,
Z.
,
Miyamoto
,
A.
, and
Jiang
,
Z.
,
2009
, “
Frequency Slice Wavelet Transform for Transient Vibration Response Analysis
,”
Mech. Syst. Signal Process
,
23
(
5
), pp.
1474
1489
.
21.
Khanam
,
S.
,
Dutt
,
J. K.
, and
Tandon
,
N.
,
2014
, “
Extracting Rolling Element Bearing Faults From Noisy Vibration Signal Using Kalman Filter
,”
ASME J. Vib. Acoust.
,
136
(
3
), p.
031008
.
22.
Van Hecke
,
B.
,
He
,
D.
, and
Qu
,
Y.
,
2014
, “
On the Use of Spectral Averaging of Acoustic Emission Signals for Bearing Fault Diagnostics
,”
ASME J. Vib. Acoust.
,
136
(
6
), p.
061009
.
23.
Westfall
,
P. H.
,
2014
, “
Kurtosis as Peakedness, 1905–2014. R.I.P
,”
Am Stat.
,
68
(
3
), pp.
191
195
.
24.
Antoni
,
J.
,
2016
, “
The Infogram: Entropic Evidence of the Signature of Repetitive Transients
,”
Mech. Syst. Signal Process
,
74
, pp.
73
94
.
25.
Rostaghi
,
M.
, and
Azami
,
H.
,
2016
, “
Dispersion Entropy: A Measure for Time-Series Analysis
,”
IEEE Signal Process. Lett.
,
23
(
5
), pp.
610
614
.
26.
Bandt
,
C.
, and
Pompe
,
B.
,
2002
, “
Permutation Entropy: A Natural Complexity Measure for Time Series
,”
Phys. Rev. Lett.
,
88
(
17
), p.
174102
.
27.
Li
,
Y.
,
Chen
,
X.
,
Yu
,
J.
,
Yang
,
X.
, and
Yang
,
H.
,
2019
, “
The Data-Driven Optimization Method and Its Application in Feature Extraction of Ship-Radiated Noise With Sample Entropy
,”
Energies
,
12
(
3
), p.
359
.
28.
Delgado-Bonal
,
A.
, and
Marshak
,
A.
,
2019
, “
Approximate Entropy and Sample Entropy: A Comprehensive Tutorial
,”
Entropy
,
21
(
6
), p.
541
.
29.
Yan
,
R.
,
Liu
,
Y.
, and
Gao
,
R. X.
,
2012
, “
Permutation Entropy: A Nonlinear Statistical Measure for Status Characterization of Rotary Machines
,”
Mech. Syst. Signal Process
,
29
, pp.
474
484
.
30.
Tian
,
Y.
,
Wang
,
Z.
, and
Lu
,
C.
,
2019
, “
Self-Adaptive Bearing Fault Diagnosis Based on Permutation Entropy and Manifold-Based Dynamic Time Warping
,”
Mech. Syst. Signal Process
,
114
, pp.
658
673
.
31.
Tang
,
G.
,
Pang
,
B.
,
He
,
Y.
, and
Tian
,
T.
,
2019
, “
Gearbox Fault Diagnosis Based on Hierarchical Instantaneous Energy Density Dispersion Entropy and Dynamic Time Warping
,”
Entropy
,
21
(
6
), p.
593
.
32.
Rostaghi
,
M.
,
Ashory
,
M. R.
, and
Azami
,
H.
,
2019
, “
Application of Dispersion Entropy to Status Characterization of Rotary Machines
,”
J. Sound Vib.
,
438
, pp.
291
308
.
33.
Zhang
,
Y.
,
Tong
,
S.
,
Cong
,
F.
, and
Xu
,
J.
,
2018
, “
Research of Feature Extraction Method Based on Sparse Reconstruction and Multiscale Dispersion Entropy
,”
Appl. Sci.
,
8
(
6
), p.
888
.
34.
Li
,
Y.
,
Gao
,
X.
, and
Wang
,
L.
,
2019
, “
Reverse Dispersion Entropy: A New Complexity Measure for Sensor Signal
,”
Sensors
,
19
(
23
), p.
5203
.
35.
Pincus
,
S.
,
1995
, “
Approximate Entropy (ApEn) as a Complexity Measure
,”
Chaos: Interdiscip. J. Nonlinear Sci.
,
5
(
1
), pp.
110
117
.
36.
Richman
,
J. S.
, and
Moorman
,
J. R.
,
2000
, “
Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy
,”
Am. J. Physiol. Heart Circ.
,
278
(
6
), pp.
H2039
H2049
.
37.
Namdari
,
A.
, and
Li
,
Z.
,
2019
, “
A Review of Entropy Measures for Uncertainty Quantification of Stochastic Processes
,”
Adv. Mech. Eng.
,
11
(
6
), p.
168781401985735
.
38.
Case Western Reserve University Bearing Data Center
, https://engineering.case.edu/bearingdatacenter
39.
Smith
,
W. A.
, and
Randall
,
R. B.
,
2015
, “
Rolling Element Bearing Diagnostics Using the Case Western Reserve University Data: A Benchmark Study
,”
Mech. Syst. Signal Process.
,
64
, pp.
100
131
.
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