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.
Issue Section:
Friction and Wear
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
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