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.
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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.
http://masters.donntu.org/2012/fknt/kovalenko/library/article8.pdf. Accessed February 20, 2017.
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.
Akhmetkhanov, R.S., Numerical-analytical analysis methods of dynamic properties of mechanic systems, Probl. Mashinostr. Nadezhnosti Mash., 2003, no. 5, pp. 10–18.
Akhmetkhanov, R.S., Application of fractal theory in study of dynamic properties of mechanic systems, Probl. Mashinostr. Avtomatiz., 2003, no. 3, pp. 47–53.
Pavlov, A.N. and Anishchenko, V.S., Multifractal analysis of complex signals, Phys. Usp., 2007, vol. 50, no. 8, pp. 819–834.
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.
Schroeder, M., Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, New York: W.H. Freeman, 1991.
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.
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.
Pavlov, A.N., Metody analiza slozhnykh signalov (Analysis Methods for Complex Singals, The School-Book), Saratov: Nauchnaya Kniga, 2008.
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.
Filimonov, V.A., Mul’tifraktal’nye modeli vremennykh ryadov (Multifractal Models of Time Series), Nizh. Novgorod: NF GU VShE, 2010.
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Original Russian Text © R.S. Akhmetkhanov, 2018, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2018, No. 3, pp. 37–43.
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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
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DOI: https://doi.org/10.3103/S1052618818030020