The fault-induced impulses with uneven amplitudes and durations are always accompanied with amplitude modulation and (or) frequency modulation, which leads to that the acquired vibration/acoustic signals for rotating machine fault diagnosis always present nonlinear and nonstationary properties. Such an effect affects precise fault detection, especially when the impulses are submerged in heavy background noise. To address this issue, a nonstationary weak signal detection strategy is proposed based on a time-delayed feedback stochastic resonance (TFSR) model. The TFSR is a long-memory system that can utilize historical information to enhance the signal periodicity in the feedback process, and such an effect is beneficial to periodic signal detection. By selecting the proper parameters including time delay, feedback intensity, and calculation step in the regime of TFSR, the weak signal, the noise, and the potential can be matched with each other to an extreme, and consequently a regular output waveform with low-noise interference can be obtained with the assistant of the distinct band-pass filtering effect. Simulation study and experimental verification are performed to evaluate the effectiveness and superiority of the proposed TFSR method in comparison with a traditional stochastic resonance (SR) method. The proposed method is suitable for detecting signals with strong nonlinear and nonstationary properties and (or) being subjected to heavy multiscale noise interference.

References

References
1.
Jardine
,
A. K. S.
,
Lin
,
D. M.
, and
Banjevic
,
D.
,
2006
, “
A Review on Machinery Diagnostics and Prognostics Implementing Condition-Based Maintenance
,”
Mech. Syst. Signal Process.
,
20
(
7
), pp.
1483
1510
.10.1016/j.ymssp.2005.09.012
2.
Randall
,
R. B.
, and
Antoni
,
J.
,
2011
, “
Rolling Element Bearing Diagnostics—A Tutorial
,”
Mech. Syst. Signal Process.
,
25
(
2
), pp.
485
520
.10.1016/j.ymssp.2010.07.017
3.
Yan
,
R. Q.
, and
Gao
,
R. X.
,
2008
, “
Rotary Machine Health Diagnosis Based on Empirical Mode Decomposition
,”
ASME J. Vib. Acoust.
,
130
(
2
), p.
021007
.10.1115/1.2827360
4.
Yuan
,
J.
,
He
,
Z. J.
,
Ni
,
J.
,
Brzezinski
,
A. J.
, and
Zi
,
Y. Y.
,
2013
, “
Ensemble Noise-Reconstructed Empirical Mode Decomposition for Mechanical Fault Detection
,”
ASME J. Vib. Acoust.
,
135
(
2
), p.
021011
.10.1115/1.4023138
5.
Wang
,
D.
,
Miao
,
Q.
, and
Kang
,
R.
,
2009
, “
Robust Health Evaluation of Gearbox Subject to Tooth Failure With Wavelet Decomposition
,”
J. Sound Vib.
,
324
(
3–5
), pp.
1141
1157
.10.1016/j.jsv.2009.02.013
6.
Bozchalooi
,
I. S.
, and
Liang
,
M.
,
2007
, “
A Smoothness Index-Guided Approach to Wavelet Parameter Selection in Signal De-Noising and Fault Detection
,”
J. Sound Vib.
,
308
(
1–2
), pp.
246
267
.10.1016/j.jsv.2007.07.038
7.
Wu
,
T. Y.
,
Chung
,
Y. L.
, and
Liu
,
C. H.
,
2010
, “
Looseness Diagnosis of Rotating Machinery Via Vibration Analysis Through Hilbert-Huang Transform Approach
,”
ASME J. Vib. Acoust.
,
132
(
3
), p.
031005
.10.1115/1.4000782
8.
Zou
,
J.
, and
Chen
,
J.
,
2004
, “
A Comparative Study on Time-Frequency Feature of Cracked Rotor by Wigner-Ville Distribution and Wavelet Transform
,”
J. Sound Vib.
,
276
(
1–2
), pp.
1
11
.10.1016/j.jsv.2003.07.002
9.
Yan
,
R. Q.
,
Gao
,
R. X.
, and
Wang
,
C. T.
,
2009
, “
Experimental Evaluation of a Unified Time-Scale-Frequency Technique for Bearing Defect Feature Extraction
,”
ASME J. Vib. Acoust.
,
131
(
4
), p.
041012
.10.1115/1.3147125
10.
Leng
,
Y.-G.
,
Leng
,
Y.-S.
,
Wang
,
T.-Y.
, and
Guo
,
Y.
,
2006
, “
Numerical Analysis and Engineering Application of Large Parameter Stochastic Resonance
,”
J. Sound Vib.
,
292
(
3–5
), pp.
788
801
.10.1016/j.jsv.2005.09.040
11.
Li
,
J.
,
Chen
,
X.
, and
He
,
Z.
,
2013
, “
Multi-Stable Stochastic Resonance and Its Application Research on Mechanical Fault Diagnosis
,”
J. Sound Vib.
,
332
(
22
), pp.
5999
6015
.10.1016/j.jsv.2013.06.017
12.
Lu
,
S.
,
He
,
Q.
,
Hu
,
F.
, and
Kong
,
F.
,
2014
, “
Sequential Multiscale Noise Tuning Stochastic Resonance for Train Bearing Fault Diagnosis in an Embedded System
,”
IEEE Trans. Instrum. Meas.
,
63
(
1
), pp.
106
116
.10.1109/TIM.2013.2275241
13.
Li
,
Q.
,
Wang
,
T. Y.
,
Leng
,
Y. G.
,
Wang
,
W.
, and
Wang
,
G. F.
,
2007
, “
Engineering Signal Processing Based on Adaptive Step-Changed Stochastic Resonance
,”
Mech. Syst. Signal Process.
,
21
(
5
), pp.
2267
2279
.10.1016/j.ymssp.2006.10.003
14.
Tan
,
J.
,
Chen
,
X.
,
Wang
,
J.
,
Chen
,
H.
,
Cao
,
H.
,
Zi
,
Y.
, and
He
,
Z.
,
2009
, “
Study of Frequency-Shifted and Re-Scaling Stochastic Resonance and Its Application to Fault Diagnosis
,”
Mech. Syst. Signal Process.
,
23
(
3
), pp.
811
822
.10.1016/j.ymssp.2008.07.011
15.
Zhang
,
X. F.
,
Hu
,
N. Q.
,
Hu
,
L.
, and
Cheng
,
Z.
,
2013
, “
Multi-Scale Bistable Stochastic Resonance Array: A Novel Weak Signal Detection Method and Application in Machine Fault Diagnosis
,”
Sci. China Technol. Sci.
,
56
(
9
), pp.
2115
2123
.10.1007/s11431-013-5246-x
16.
Lei
,
Y.
,
Han
,
D.
,
Lin
,
J.
, and
He
,
Z.
,
2013
, “
Planetary Gearbox Fault Diagnosis Using an Adaptive Stochastic Resonance Method
,”
Mech. Syst. Signal Process.
,
38
(
1
), pp.
113
124
.10.1016/j.ymssp.2012.06.021
17.
Li
,
J.
,
Chen
,
X.
, and
He
,
Z.
,
2013
, “
Adaptive Stochastic Resonance Method for Impact Signal Detection Based on Sliding Window
,”
Mech. Syst. Signal Process.
,
36
(
2
), pp.
240
255
.10.1016/j.ymssp.2012.12.004
18.
Mcnamara
,
B.
, and
Wiesenfeld
,
K.
,
1989
, “
Theory of Stochastic Resonance
,”
Phys. Rev. A
,
39
(
9
), pp.
4854
4869
.10.1103/PhysRevA.39.4854
19.
Shao
,
R. H.
, and
Chen
,
Y.
,
2009
, “
Stochastic Resonance in Time-Delayed Bistable Systems Driven by Weak Periodic Signal
,”
Physica A
,
388
(
6
), pp.
977
983
.10.1016/j.physa.2008.12.001
20.
Tsimring
,
L. S.
, and
Pikovsky
,
A.
,
2001
, “
Noise-Induced Dynamics in Bistable Systems With Delay
,”
Phys. Rev. Lett.
,
87
(
25
), p.
250602
.10.1103/PhysRevLett.87.250602
21.
Kim
,
S.
,
Park
,
S. H.
, and
Pyo
,
H. B.
,
1999
, “
Stochastic Resonance in Coupled Oscillator Systems With Time Delay
,”
Phys. Rev. Lett.
,
82
(
8
), pp.
1620
1623
.10.1103/PhysRevLett.82.1620
22.
Gammaitoni
,
L.
,
Hanggi
,
P.
,
Jung
,
P.
, and
Marchesoni
,
F.
,
1998
, “
Stochastic Resonance
,”
Rev. Mod. Phys.
,
70
(
1
), pp.
223
287
.10.1103/RevModPhys.70.223
23.
Oppenheim
,
A. V.
,
Schafer
,
R. W.
, and
Buck
,
J. R.
,
1989
,
Discrete-Time Signal Processing
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
24.
Guillouzic
,
S.
,
L'Heureux
,
I.
, and
Longtin
,
A.
,
1999
, “
Small Delay Approximation of Stochastic Delay Differential Equations
,”
Phys. Rev. E
,
59
(
4
), pp.
3970
3982
.10.1103/PhysRevE.59.3970
25.
Frank
,
T. D.
,
2005
, “
Delay Fokker-Planck Equations, Novikov's Theorem, and Boltzmann Distributions as Small Delay Approximations
,”
Phys. Rev. E
,
72
(
1
), p.
011112
.10.1103/PhysRevE.72.011112
26.
Frank
,
T. D.
,
2005
, “
Delay Fokker-Planck Equations, Perturbation Theory, and Data Analysis for Nonlinear Stochastic Systems With Time Delays
,”
Phys. Rev. E
,
71
(
3
), p.
031106
.10.1103/PhysRevE.71.031106
27.
Risken
,
H.
,
1989
,
The Fokker-Planck Equation: Methods of Solution and Applications
,
Springer
,
Berlin
.
28.
Huang
,
K.
,
2001
,
Introduction to Statistical Physics
,
CRC Press
,
London
.
29.
Lu
,
S.
,
He
,
Q.
, and
Kong
,
F.
,
2014
, “
Stochastic Resonance With Woods–Saxon Potential for Rolling Element Bearing Fault Diagnosis
,”
Mech. Syst. Signal Process.
,
45
(
2
), pp.
488
503
.10.1016/j.ymssp.2013.12.004
30.
Casado-Pascual
,
J.
,
Gomez-Ordonez
,
J.
,
Morillo
,
M.
, and
Hanggi
,
P.
,
2002
, “
Rocking Bistable Systems: Use and Abuse of Linear Response Theory
,”
Europhys. Lett.
,
58
(
3
), pp.
342
348
.10.1209/epl/i2002-00644-6
31.
Antoni
,
J.
, and
Randall
,
R. B.
,
2003
, “
A Stochastic Model for Simulation and Diagnostics of Rolling Element Bearings With Localized Faults
,”
ASME J. Vib. Acoust.
,
125
(
3
), pp.
282
289
.10.1115/1.1569940
32.
Antoni
,
J.
, and
Randall
,
R. B.
,
2002
, “
Differential Diagnosis of Gear and Bearing Faults
,”
ASME J. Vib. Acoust.
,
124
(
2
), pp.
165
171
.10.1115/1.1456906
33.
Cheng
,
J.
,
Yu
,
D.
, and
Yu
,
Y.
,
2007
, “
The Application of Energy Operator Demodulation Approach Based on EMD in Machinery Fault Diagnosis
,”
Mech. Syst. Signal Process.
,
21
(
2
), pp.
668
677
.10.1016/j.ymssp.2005.10.005
34.
CWRU, 2015, “Bearing Data Center,” “Case Western Reserve University, Cleveland, OH,” http://csegroups.case.edu/bearingdatacenter/pages/download-data-file
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