Skip to main content
Log in

The Patterns of the Power Spectral Density Distribution of Fractal and Multifractal Processes

  • Mechanics of Machines
  • Published:
Journal of Machinery Manufacture and Reliability Aims and scope Submit manuscript

Abstract

This article deals with characteristic differences between the power spectral densities of monofractal and multifractal dynamical processes. The differences are analyzed from the point of view of determining the damage to the components of an engineering system by fractal analysis of the diagnostic data. As an example, the rolling bearing of a centrifugal pump is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Akhmetkhanov, R.S., Effect of damage to structural elements on the dynamic characteristics of the system, J. Mach. Manuf. Reliab., 2015, vol. 44, no. 6, pp. 539–544.

    Article  Google Scholar 

  2. http://masters.donntu.org/2012/fknt/kovalenko/library/article8.pdf. Accessed February 20, 2017.

  3. Akhmetkhanov, R.S., Application of fractal theory and wavelet analysis for identification of time series specific features in system diagnosis, Vestn. Nauch.-Tekh. Razvit., 2009, no. 1, pp. 26–31.

    Google Scholar 

  4. Akhmetkhanov, R.S., Numerical-analytical analysis methods of dynamic properties of mechanic systems, Probl. Mashinostr. Nadezhnosti Mash., 2003, no. 5, pp. 10–18.

    Google Scholar 

  5. Akhmetkhanov, R.S., Application of fractal theory in study of dynamic properties of mechanic systems, Probl. Mashinostr. Avtomatiz., 2003, no. 3, pp. 47–53.

    Google Scholar 

  6. Pavlov, A.N. and Anishchenko, V.S., Multifractal analysis of complex signals, Phys. Usp., 2007, vol. 50, no. 8, pp. 819–834.

    Article  Google Scholar 

  7. Baranowski, P., Krzyszczak, J., Slawinski, C., et al., Multifractal analysis of meteorological time series to assess climate impacts, Climate Res., 2015, vol. 65, pp. 39–52.

    Article  Google Scholar 

  8. Schroeder, M., Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, New York: W.H. Freeman, 1991.

    MATH  Google Scholar 

  9. Baikov, I.R., Kostareva, S.N., and Kitaev, S.V., Estimation of the technical condition of a gas compressor unit using fractal characteristics of vibrospectra, in Tr. 51-i nauchno-tekhnicheskoi konferentsii UGNTU (Proceedings of the 51st Conference of Ufa State Petrol. Technol. Univ.), Ufa: UGNTU, 2000, p. 78.

    Google Scholar 

  10. Popova, I.A., Gun’kin, V.N., Cherenkova, M.V., and Gridnev, A.E., Mesostructure of failure surface of silicon carbide in multifractal representation, Vestn. VGU, Ser.: Fiz., Mat., 2013, no. 2, pp. 90–95.

    Google Scholar 

  11. Pavlov, A.N., Metody analiza slozhnykh signalov (Analysis Methods for Complex Singals, The School-Book), Saratov: Nauchnaya Kniga, 2008.

    Google Scholar 

  12. Korolenko, P.V., Maganova, M.S., and Mesnyankin, A.V., Novatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike (Novation Methods for Analysis for Stochastic Processes and Structures in Optics), Moscow: Mosk. Gos. Univ. im. M.V.Lomonosova, 2004.

    Google Scholar 

  13. Filimonov, V.A., Mul’tifraktal’nye modeli vremennykh ryadov (Multifractal Models of Time Series), Nizh. Novgorod: NF GU VShE, 2010.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. S. Akhmetkhanov.

Additional information

Original Russian Text © R.S. Akhmetkhanov, 2018, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2018, No. 3, pp. 37–43.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akhmetkhanov, R.S. The Patterns of the Power Spectral Density Distribution of Fractal and Multifractal Processes. J. Mach. Manuf. Reliab. 47, 235–240 (2018). https://doi.org/10.3103/S1052618818030020

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1052618818030020

Navigation