Conditional cyclic random process as mathematical model of vibrational signals and processes with double stochasticity

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Lupenko S. A., Lutsyk N. S., Stadnyk N. B., Sverstiuk A. S., Zozulia A. M. № 1 (71) 147-159 Image Image

In this study the new mathematical model of the vibrational signals and processes in the form of conditional random process has been defined, which unlike their known models, make it possible to take into account their double stochasticity, that is, take into account stochasticity of the morphological and rhythmic structures of the cyclical signals at the same time. This model eliminates the discrepancy between the model of cyclic random processes and the stochastic models of the rhythm and significantly expands simulation tools and analysis rhythmic structure of the vibrational processes within the framework the stochastic approach, providing additional features for increasing the accuracy and informativeness of processing of the different physical nature and structure cyclical signals

Keywords: mathematical model, cyclical signal, random process, rhythm function.


  • 1. Lupenko, S. (2005). Tsyklichni funktsii ta yikh klasyfikatsiia v zadachakh modeliuvannia tsyklichnykh syhnaliv ta kolyvnykh system. Vymiriuvalna ta obchysliuvalna tekhnika v tekhnolohichnykh protsesakh, 1 (p. 177–185). Khmelnitsky: Navchalna knyha (in Ukrainian).
  • 2. Lupenko, S. (2006). Determnirovannye i sluchainye tciklicheskie funktcii kak modeli kolebatelnykh iavlenii i signalov: opredelenie i klassifikatciia. Elektronnoe modelirovanie, 28, 4 (in Russian).
  • 3. Lupenko, S. (2007). Tsyklichne funktsionalne vidnoshennia yak osnova matematychnoho formalizmu teorii modeliuvannia ta analizu tsyklichnykh syhnaliv. Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu. — Vol. 12, 3, 183–195(in Ukrainian).
  • 4. Lupenko, S., Studena, Iu. (2006). Matematychne modeliuvannia syhnaliv sertsia v zadachakh tekhnichnoi kardiometrii na bazi yikh modeli u vyhliadi tsyklichnoho vypadkovoho protsesu. VisnykTernopilskoho derzhavnoho tekhnichnoho universytetu. Vol. 11, 1, 134–142 (in Ukrainian).
  • 5. Horkunenko, A. B., Lupenko, S. A., & Lutskiv, A. M. (2010). Matematychne modeliuvannia ekonomichnykh tsyklichnykh protsesiv dlia yikh avtomatyzovanoho analizu ta prohnozu. Visnyk Khmelnytskoho natsionalnoho universytetu, 3 (in Ukrainian).
  • 6. Litvinenko, Ia. V., Lupenko, S. A., & Marushchak, P. O. (2013). Analiz mnozhestvennogo rastreskivaniia nanopokrytiia kak tciklicheskogo sluchainogo protcessa. Avtometriia, 2 (in Russian).
  • 7. Maruschak, P. O., Panin, S. V., Ignatovich, S. R., Zakiev, I. M., Konovalenko, & Lytvynenko, I. V. et. al. (2012). Influence of deformation process in material at multiple cracking and fragmentation of nanocoating. Theoretical and Applied Fracture Mechanics, 57 (in English).
  • 8. Lytvynenkom, I. V., Maruschak, P. O., & Lupenko, S. A. (2014). Processing and modeling of ordered relief at the surface of heat-resistant steels after laser irradiation as a cyclic random process. Automatic Control and Computer Sciences, 48 (1) (in English).
  • 9. Lytvynenko, I., Maruschak, P., Lupenko, S., & Panin, S. (2015). Segmentation and Statistical Processing of Geometric and Spatial Data on Self-Organized Surface Relief of Statically Deformed Aluminum Alloy. Applied Mechanics & Materials, 770 (in English).
  • 10. Lupenko, S. (2007). Operator peretvorennia shkaly v zadachakh modeliuvannia ta analizu tsyklichnykh syhnaliv. Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu. Vol. 12, 4 (in Ukrainian).