Methods of fractal analysis and phase trajectories for the improvement of identification of complex technical systems

• Autorzy: Chovnyuk Y. V. , Gumenyuk Y. O. , Djachenko L. A. , Ivanov E. A. , Kravchyuk V. T.

Identyfikatory

DOI

10.30657/qpi.2019.11.04

• Języki publikacji: EN

Abstrakty

EN

The procedure of the qualitative analysis of complex technical systems is discussed. One may use such methods of analysis for time series characterized the functioning of such systems. These time serious aren’t confirmed the hypothesis of trend existence. One may use at this qualitative analysis the methods of nonlinear dynamics and the theory of chaos. The basis for similar researches is Takens’s theorem. The randomness of the studied dynamical system as the model of the complex technical system given by time realizations is established by means of Lyapunov’s indicator. The state stability is estimated by Hausdorf’s fractal dimension and the fractality index. Visual evaluation of the time series was carried out by means of the phase trajectory restoration procedure. As a result of the analysis of the phase points in the phase space the split attractor is indicated, which gives the chance to speak about its bifurcation.

Słowa kluczowe

EN

fractal analysis; improvement; methods; phase trajectories; qualitative analysis

PL

analiza fraktalna; trajektoria fazowa; analiza jakościowa

• Wydawca: Oficyna Wydawnicza Stowarzyszenia Menedżerów Jakości i Produkcji
• Czasopismo: Zeszyty Naukowe. Quality. Production. Improvement
• Rocznik: 2019
• Tom: No. 2 (11)
• Strony: 41--50
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Chovnyuk Y. V.

• National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine

autor

Gumenyuk Y. O.

• National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine

autor

Djachenko L. A.

• National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine

autor

Ivanov E. A.

• National Aviation University, Kyiv, Ukraine

autor

Kravchyuk V. T.

• Kyiv National University of Construction and Architecture, Kyiv, Ukraine

Bibliografia

• [1.] Bezruchko B.P., Smirnov D.A. Matematicheskoje modelirovanije i chaoticheskie vremennije rjadi. – Saratov: Gos UNC “Kolledge”, 2005. – p. 320.
• [2.] Delignieres D., Torre K. Fractal dynamics of human gait : a reassessment of the 1996 data of Hausdorff et al. // Journal of Applied Physiology. – 2009. – Vol. 106. - pp. 1772- 1279.
• [3.] Dobovukov M.M., Kranev A.V., Starchenko N.V. Razmernost minimalnogo pokritija i lokalniji analis fractalnich vremennich rjadov // Vestnik RUDN. – 2004. T. 3. – No. 1. – pp. 81-95.
• [4.] Feder E. Fractali. – Moskwa: Mir, 1991. – p. 262.
• [5.] Figliola A., Serrano E., Paccosi G. About the effectiveness of different methods for the estimation of the multifractal spectrum of natural series // International Journal of Bifurcation and chaos. -2010. -Vol.20(2). - pp. 331-339.
• [6.] Hausdorff F. Dimension und Assures Mass/F. Hausdorf //Matematishe Annalen - 1919. - Vol. 79. - P.157 - 179.
• [7.] Kronover R. Fractali i chaos v dynamicheskich sistemach. – Moskwa: Postmarket, 2000. – p. 352.
• [8.] Malinetskie G.G., Potapov A.B., Podlazov A.V. Nelinejnaja dinamika. Podchodi, rezultati, nadezdi. – Moskwa: Komkniga, 2006. – p. 216.
• [9.] Mjun F. Chaoticheskie kolebanija. Vvodnji kjurs dlja nauchnich rabotnikov i ingenerov. – Moskwa: Mir, 1990. – p. 312.
• [10.] Starchenko N.V. Lokalniji analis chaoticheskich vremennich rjadov s pomoschju indeksa fraktalnosti: avtoref. diss. na soiskanije uchjonoji stepeni kand. fiz. – mat. nauk/N.V. Starchenko. – Moskwa, 2005. – p. 22.
• [11.] Takens F., Rand D.A., Young L.S. Detecting strange attractors in turbulence II Dynamical systems and Turbulence .Lecture Notes in Mathematics. -Springer-Verlag, 1981.-Vol.898. – pp. 366-381.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).