Wear experiments are performed to explore dynamic states changes of friction noise signals. A new characteristic parameter, moving cut data-approximate entropy (MC-ApEn), is adopted to quantitatively recognize dynamic states. Additionally, determinism (DET), one key parameter of recurrence quantification analysis, is applied to verify the reliability of recognition results of MC-ApEn. Results illustrate that MC-ApEn of friction noise has distinct changes in different wear processes, and it can accurately detect abrupt change points of dynamic states for friction noise. Furthermore, DET of friction noise rapidly declines first, then fluctuates around a small value, and finally increases sharply, which just corresponds to the evolution process of MC-ApEn. So, the reliability of wear state recognition on the basis of MC-ApEn can be confirmed. It makes it possible to accurately and reliably recognize wear states of friction pairs based on MC-ApEn.

References

References
1.
Wu
,
T. H.
,
Peng
,
Y. H.
,
Wu
,
H. K.
,
Zhang
,
X. G.
, and
Wang
,
J. Q.
,
2014
, “
Full-Life Dynamic Identification of Wear State Based on On-Line Wear Debris Image Features
,”
Mech. Syst. Signal Process
,
42
(
1–2
), pp.
404
414
.
2.
Grassberger
,
P.
, and
Procaccia
,
I.
,
1983
, “
Characterization of Strange Attractors
,”
Phys. Rev. Lett.
,
50
(
5
), pp.
346
349
.
3.
Wolf
,
A.
,
Swift
,
J. B.
, and
Swinney
,
H. L.
,
1985
, “
Determining Lyapunov Exponents From a Time Series
,”
Phys. D
,
16
(
3
), pp.
285
317
.
4.
Kolmogorov
,
A. N.
,
1958
, “
A New Metric Invariant of Transient Dynamical Systems and Automorphisms in Lebesgue Spaces
,”
Dokl. Akad. Nauk. SSSR
,
951
(
5
), pp.
861
864
.
5.
Zhu
,
H.
, and
Ge
,
S. R.
,
2004
, “
Chaotic Characteristics of Tribological Systems
,”
Chin. J. Mech. Eng.
,
40
(
12
), pp.
10
13
.
6.
Oleksowicz
,
S.
, and
Polak
,
A.
,
2011
, “
Modeling of the Friction Process in a Frictional Pair Using Chaos Theory Tools
,”
Tribol. Lett.
,
41
(
3
), pp.
495
501
.
7.
Zhou
,
Y. K.
,
Zhou
,
H.
,
Zuo
,
X.
, and
Yang
,
J. H.
,
2014
, “
Chaotic Characteristics of Measured Temperatures During Sliding Friction
,”
Wear
,
317
(
1–2
), pp.
17
25
.
8.
Zhou
,
Y. K.
,
Zhou
,
H.
, and
Zuo
,
X.
,
2016
, “
Dynamic Evolutionary Consistency Between Friction Force and Friction Temperature From the Perspective of Morphology and Structure of Phase Trajectory
,”
Tribol. Int.
,
94
, pp.
606
615
.
9.
Sun
,
D.
,
Li
,
G. B.
,
Wei
,
H. J.
, and
Liao
,
H. F.
,
2015
, “
Experimental Study on the Chaotic Attractor Evolvement of the Friction Vibration in a Running-In Process
,”
Tribol. Int.
,
88
, pp.
290
297
.
10.
Grassberger
,
P.
, and
Procaccia
,
I.
,
1983
, “
Estimation of the Kolmogorov Entropy From a Chaotic Signal
,”
Phys. Rev. A
,
28
(
4
), pp.
2591
2593
.
11.
Li
,
H. Y.
, and
Zhou
,
S. F.
,
2012
, “
Kolmogorov ε-Entropy of Attractor for a Non-Autonomous Strongly Damped Wave Equation
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
9
), pp.
3579
3586
.
12.
Maragos
,
P.
, and
Sun
,
F. K.
,
1993
, “
Measuring the Fractal Dimension of Signals
,”
IEEE Trans. Signal Process.
,
41
, pp.
108
121
.
13.
Smith
,
L. A.
,
1988
, “
Intrinsic Limits on Dimension Calculations
,”
Phys. Lett. A
,
133
(
6
), pp.
283
288
.
14.
Nerenberg
,
M. A.
, and
Essex
,
C.
,
1990
, “
Correlation Dimension and Systematic Geometric Effects
,”
Phys. Rev. A
,
42
(
12
), pp.
7065
7074
.
15.
Eckmann
,
J. P.
, and
Ruelle
,
D.
,
1992
, “
Fundamental Limitations for Estimating Dimensions and Lyapunov Exponents in Dynamical Systems
,”
Phys. D: Nonlinear Phenom.
,
56
(
2–3
), pp.
185
187
.
16.
Bonachela
,
J. A.
,
Hinrichsen
,
H.
, and
Munoz
,
M. A.
,
2008
, “
Entropy Estimates of Small Data Sets
,”
J. Phys. A. Math Theor.
,
41
(
20
), pp.
1357
1366
.
17.
Pincus
,
S. M.
,
1991
, “
Approximate Entropy as a Measure of System Complexity
,”
Proc. Natl. Acad. Sci.
,
88
(
6
), pp.
2297
2301
.
18.
Pincus
,
S.
,
1995
, “
Approximate Entropy (ApEn) as a Complexity Measure
,”
Chaos
,
5
(
1
), pp.
110
117
.
19.
Pincus
,
S. M.
,
Gladstone
,
I. M.
, and
Ehrenkranz
,
R. A.
,
1991
, “
A Regularity Statistic for Medical Data Analysis
,”
J. Clin. Monit. Comput.
,
7
(
4
), pp.
335
345
.
20.
Pincus
,
S. M.
, and
Goldberger
,
A. L.
,
1994
, “
Physiological Time-Series Analysis: What Does Regularity Quantify?
,”
Am. J. Physiol.
,
266
(
4
), pp.
1643
1656
.
21.
Rose, M. H.
,
Bandholm, T.
, and
Jensen, B. R.
,
2009
, “
Approximate Entropy Based on Attempted Steady Isometric Contractions With the Ankle Dorsal- and Pantarflexors: Reliability and Optimal Sampling Frequency
,”
J. Neurosci. Methods
,
177
(
1
), pp.
212
216
.
22.
Xu
,
Y. L.
,
Ma
,
X. F.
, and
Ning
,
X. B.
,
2007
, “
Estimation of ApEn for Short-Time HFECG Based on Multi-Resolution Analysis
,”
Phys. A
,
376
(
1
), pp.
401
408
.
23.
Zhao
,
S. F.
,
Liang
,
L.
,
Xu
,
G. H.
, and
Wang
,
J.
,
2013
, “
Quantitative Diagnosis of a Spall-Like Fault of a Rolling Element Bearing by Empirical Mode Decomposition and the Approximate Entropy Method
,”
Mech. Syst. Signal Process.
,
40
(
1
), pp.
154
177
.
24.
Pérez-Canales, D.
,
Álvarez-Ramírez, J.
,
Jáuregui-Correa, J. C.
,
Vela-Martínez, L.
, and
Herrera-Ruiz, G.
,
2011
, “
Identification of Dynamic Instabilities in Machining Process Using the Approximate Entropy Method
,”
Int. J. Mach. Tools Manuf.
,
51
(
6
), pp.
556
564
.
25.
An
,
X. L.
,
Li
,
C. S.
, and
Zhang
,
F.
,
2016
, “
Application of Adaptive Local Iterative Filtering and Approximate Entropy to Vibration Signal Denoising of Hydropower Unit
,”
J. Vib. Eng.
,
18
(
7
), pp.
4299
4311
.
26.
An
,
X. L.
, and
Yang
,
J. J.
,
2017
, “
A Method of Eliminating the Vibration Signal Noise of Hydropower Unit Based on NA-MEMD and Approximate Entropy
,”
J. Process Mech. Eng.
,
231
(
2
), pp.
317
328
.
27.
Lei
,
X. G.
,
Zeng
,
Y. C.
, and
Li
,
L.
,
2007
, “
Noisy Speech Endpoint Detection Based on Approximate Entropy
,”
Tech. Acoust.
,
1
(
26
), pp.
121
125
.
28.
Cheng, H. Y.
,
He, T.
,
He, W. P.
,
Wu, Q.
, and
Zhang, W.
,
2011
, “
A New Method to Detect Abrupt Change Based on Approximate Entropy
,”
Acta Phys. Sin.
,
60
(
4
), pp.
1
9
.
29.
Huang
,
N. E.
,
Shen
,
Z.
,
Steven
,
R. L.
,
Wu, M. C.
,
Shih, H. H.
,
Zheng, Q.
,
Yen, N.-C.
,
Tung, C. C.
, and
Liu, H. H.
,
1998
, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis
,”
Proc. R. Soc. London. Ser. A
,
454
(
1971
), pp.
903
995
.
30.
Guo
,
K. J.
,
Zhang
,
X. G.
,
Li
,
H. G.
, and
Meng
,
G.
,
2008
, “
Application of EMD Method to Friction Signal Processing
,”
Mech. Syst. Signal Process.
,
22
(
1
), pp.
248
259
.
31.
Kennel
,
M. B.
,
Brown
,
R.
, and
Abarbanel
,
H. D. I.
,
1992
, “
Determining Embedding Dimension for Phase Space Reconstruction Using a Geometrical Reconstruction
,”
Phys. Rev. A
,
45
(
6
), pp.
3403
3411
.
32.
Lorenz
,
E. N.
,
1963
, “
Deterministic Nonperiodic Flow
,”
J. Atmos. Sci.
,
20
(
2
), pp.
130
141
.
33.
Takens
,
F.
,
1981
, “
Detecting Strange Attractors in Turbulence
,”
Dynamical Systems and Turbulence, Warwick 1980
(Lecture Notes in Mathematics, Vol. 898), Springer, Berlin, pp.
366
381
.
34.
Ding
,
C.
,
Zhu
,
H.
,
Sun
,
G. D.
,
Zhou
,
Y. K.
, and
Zuo
,
X.
,
2017
, “
Chaotic Characteristics and Attractor Evolution of Friction Noise During Friction Process
,”
Friction
,
6
(1), pp. 47–61.
35.
Eckmann
,
J. P.
,
Kanphorst
,
O. S.
, and
Ruelle
,
D.
,
1987
, “
Recurrence Plots of Dynamical Systems
,”
Europhys. Lett.
,
4
(
9
), pp.
973
977
.
36.
Marwan
,
N.
,
Romano
,
M. C.
,
Theil
,
M.
, and
Kurths
,
J.
,
2007
, “
Recurrence Plots for the Analysis of Complex Systems
,”
Phys. Rep.
,
438
(
5–6
), pp.
237
329
.
37.
Fraser
,
A. M.
, and
Swinney
,
H. L.
,
1986
, “
Independent Coordinates for Strange Attractors From Mutual Information
,”
Phys. Rev. A
,
33
(
2
), pp.
1134
1140
.
You do not currently have access to this content.