Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA

Chaos, Solitons and Fractals

Volumn 69, Issue , 2014, Pages 90-99

  Vitanov, Nikolay K ^a,b   Hoffmann, Norbert P ^c,d   Wernitz, Boris ^e  

^a INSTITUTE OF MECHANICS   (Bulgaria)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

^d HAMBURG UNIVERSITY OF TECHNOLOGY   (Germany)

^e Ferodo Friction   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BRAKES; FRACTALS; FRICTION; FRICTION MATERIALS; PRINCIPAL COMPONENT ANALYSIS; SPECTRUM ANALYSIS; STRUCTURAL DYNAMICS; TIME MEASUREMENT; TRIBOLOGY; VIBRATION ANALYSIS;

CHAOTIC ATTRACTORS; CHARACTERISTICS OF VIBRATIONS; DETRENDED FLUCTUATION ANALYSIS; DYNAMICAL PROCESS; FRICTION INTERFACES; LONG TIME SCALE DYNAMICS; NONLINEAR TIME-SERIES ANALYSIS; SINGULAR SPECTRUM ANALYSIS;

TIME SERIES ANALYSIS;

EID: 84952319217     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2014.09.010     Document Type: Article

References (56)

1. R. Vautard, and M. Ghil Singular spectrum analysis in nonlinear dynamics with application to paleoclimatic time series Physica D 35 1989 395 424
2. R. Vautard, P. Yiou, and M. Ghil Singular spectrum analysis - a toolkit for short noisy chaotic signals Physica D 58 1992 95 126
3. N.K. Vitanov, K. Sakai, and Z.I. Dimitrova SSA, PCA, TDPSC, ACFA: useful combination of methods for analysis of short and nonstationary time series Chaos Solitons Fract 37 2008 187 202
4. S. Panchev, T. Spassova, and N.K. Vitanov Analytical and numerical investigation of two Lorenz-like dynamical systems Chaos Solitons Fract 33 2007 1658 1671
5. M.E. Schlesinger, and N. Ramankutty An oscillation in the global climate system of period 65-75 years Nature 367 1994 723 726
6. Kravtsov S., Ghil M. Interdecadal variability in a hybrid coupled ocean-atmosphere-sea.
7. L. Marelli, R. Bilato, P. Franz, P. Martin, A. Murari, and M. O'Gorman Singular spectrum analysis as a tool for plasma fluctuations analysis Rev Sci Instrum 72 2001 499 502
8. C.M. Theobald, C.A. Glassey, G.W. Horgan, and C.D. Robinson Principal component analysis of landmarks from reversible images J R Stat Soc C - Appl Stat 53 2004 163 175
9. S. Wold, K. Esbensen, and P. Geladi Principal component analysis Chemometrics Intell Lab Syst 2 1987 37 52
10. J.L. Carland, and A.L. Mills Classification and characterization of heterothropic microbial communities on the basis of patterns of community-level sole-carbon-source utilization Appl Environ Microbiol 57 1991 2351 2359
11. E.L. Russell, L.H. Chiang, and R.D. Braatz Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis Chemometric Intell Lab Syst 51 2000 81 93
12. H. Kantz, and T. Schreiber Nonlinear time series analysis 1997 Cambridge University Press Cambridge
13. T. Böck, and N.K. Vitanov Low dimensional chaos in zero-Prandtl-number Benard Marangoni convection Phys Rev E 65 2002 [Article No. 037203]
14. H. Kantz, D. Holstein, M. Ragwitz, and N.K. Vitanov Markov chain model for turbulent wind speed data Physica A 342 2004 315 321
15. Z.I. Dimitrova, and N.K. Vitanov Chaotic pairwise competition Theor Popul Biol 66 2004 1 12
16. N.K. Vitanov, Z.I. Dimitrova, and H. Kantz On the trap of extinction and its elimination Phys Lett A 349 2006 350 355
17. N.M. Kinkaid, O.M. O'Reilly, and P. Papadopoulos Automotive disc brake squeal J Sound Vib 267 2003 105 166
18. F. Chen Automotive disk brake squeal: an overview Int J Vehicle Des 51 2009 39 72
19. Hoffmann N, Gaul L. Friction induced vibrations of brakes: research fields and activities. SAE Technical Paper Series 2008; 2008-01-2579: p. 1-8.
20. Diao K, Zhang L, Meng D. Study on statistical analysis of uncertainty of disc brake squeal. SAE Technical Paper 2014-01-0030.
21. Diao K, Zhang L, Meng D. Modeling and experimental investigation on time-varying characteristic of brake frictional squeal. SAE Technical Paper 2014-01-2517.
22. B.F. Feeny, and J.W. Liang Phase space reconstructions and stick-slip Nonlinear Dyn 13 1997 39 57
23. S. Oberst, and J.C.S. Lai Chaos in brake squeal noise J Sound Vib 330 2011 955 975
24. S. Oberst, and J.C.S. Lai Statistical analysis of brake squeal noise J Sound Vib 330 2011 2978 2994
25. B.A. Wernitz, and N.P. Hoffmann Recurrence analysis and phase space reconstruction of irregular vibration in friction brakes: signatures of chaos in steady sliding J Sound Vib 331 2012 3887 3896
26. Wernitz BA, Hoffmann NP. New Approaches to signal analysis of friction noise and vibration. In: Proceedings of the IMechE international conference of braking, York; 2009.
27. R.V. Kappagantu, and B.F. Feeny Part 1: Dynamical characterization of a frictionally excited beam Nonlinear Dyn 22 2000 317 333
28. R. Hegger, H. Kantz, and T. Schreiber Practical implementation of nonlinear time series methods: the TISEAN package Chaos 9 1999 413 435
29. T. Schreiber Interdisciplinary applications of nonlinear time series methods Phys Rep 308 1999 2 64
30. J.W. Kantelhard, E. Koscielny-Bunde, H.H.A. Rego, S. Havlin, and A. Bunde Detecting long-range correlations with detrended fluctuation analysis Physica A 295 2001 441 454
31. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H.E. Stanley Multifractal detrended fluctuation analysis of nonstationary time series Physica A 316 2002 87 114
32. P.C. Ivanov, L.A.N. Amaral, A.L. Goldberger, S. Havlin, M.G. Rosenblum, Z.R. Struzik, and H.E. Stanley Multifractality in human heartbeat dynamics Nature 399 1999 461 465
33. J.F. Muzy, E. Bacry, and A. Arneodo The multifractal formalism revisited with wavelets Int J Bifurcation Chaos 4 1994 245 302
34. N.K. Vitanov, and E.D. Yankulova Multifractal analysis of the long-range correlations of the heartbeat activity of Drosophila melanogaster Chaos Solitons Fract 28 2006 768 775
35. D.S. Broomhead, and G.P. King Extracting qualitative dynamics from experimental data Physica D 20 1986 217 236
36. A.M. Albano, J. Muench, C. Schwant, A.I. Mees, and P.E. Rapp Singular-value decomposition and the Grassberger-Procaccia algorithm Phys Rev A 38 1988 3017 3026
37. A.I. Mees, P.E. Rapp, and L.S. Jennings Singular-value decomposition and embedding dimension Phys Rev A 36 1987 340 346
38. T. Sauer, J.A. Yorke, and M. Casdagli Embedology J Stat Phys 65 1991 579 616
39. H.D.I. Abarbanel, R. Brown, J.J. Sidorowich, and L.S. Tsirming The analysis of observed chaotic data in physical systems Rev Mod Phys 65 1993 1331 1392
40. J.D. Farmer, and J.J. Sidorowich Predicting chaotic time series Phys Rev Lett 59 1987 845 848
41. H. Kantz, and T. Schreiber Dimension estimates and physiological data Chaos 5 1995 143 154
42. R. Hegger, H. Kantz, L. Matassini, and T. Schreiber Coping with nonstationarity by overembedding Phys Rev Lett 84 2000 4092 4095
43. J.B. Elsner, and A.A. Tsonis Singular spectrum analysis. A new tool in time series analysis 1996 Springer New York
44. A.M. Fraser, and H.L. Swinney Independent coordinates for strange attractors from mutual information Phys Rev A 33 1986 1134 1140
45. M.B. Kennel, R. Brown, and H.D.I. Abarabanel determining embedding dimension for phase-space reconstruction using a geometrical construction Phys Rev A 45 1992 3403 3411
46. P. Grassberger, and I. Procaccia Measuring the strangeness of strange attractors Physica D 9 1983 189 208
47. T. Sauer, and J. Yorke How many delay coordinates do you need? Int J Bifurcation Chaos 3 1993 737 744
48. M. Sano, and Y. Sawada Measurement of the Lyapunov spectrum from a chaotic time series Phys Rev Lett 55 1985 1082 1085
49. J.-P. Eckmann, S. Ollifson Kamphorst, D. Ruelle, and S. Ciliberto Lyapunov exponents from a time series Phys Rev A 34 1986 4971 4979
50. H.-L. Yang, G. Radons, and H. Kantz Covariant Lyapunov vectors from reconstructed dynamics: the geometry behind true and spurious Lyapunov exponents Phys Rev Lett 109 2012 [Article No. 244101]
51. H. Kantz, G. Radons, and H.-L. Yang The problem of spurious Lyapunov exponents in time series analysis and its solution by covariant Lyapunov vectors J Phys A: Math Theor 46 2013 [Article No. 254009]
52. F. Ginelli, P. Poggi, A. Turchi, H. Chate, R. Livi, and A. Politi Characterizing dynamics with covariant Lyapunov vectors Phys Rev Lett 99 2007 [Article No. 130601]
53. J.L. Lopez, L. Veleva, and D.A. Lopez-Sauri Multifractal detrended analysis of the corrosion potential fluctuations during copper patina formation on its first stages in sea water Int J Electrochem Sci 9 2014 1637 1649
54. J.S. Murgia, and H.S. Rosu Multifractal analysis of row sum signals of elementary cellular automata Physica A 391 2012 3638 3649
55. J.B. Bassingthwaighte, L.S. Liebovitch, and B.J. West Fractal psychology 1994 Oxford University Press New York
56. M.A. Sanchez Cranero, J.E. Trinidada Segovai, and J. Garzia Perez Some comments on Hurst exponent and the long memory processes on capital markets Physica A 387 2008 5543 5551