DOI: https://doi.org/10.15587/1729-4061.2019.187252

Development of the correlation method for operative detection of recurrent states

Boris Pospelov, Vladimir Andronov, Evgeniy Rybka, Olekcii Krainiukov, Kostiantyn Karpets, Oleksandr Pirohov, Iryna Semenyshyna, Ruslan Kapitan, Alona Promska, Oleksii Horbov

Abstract


The correlation method for operative detection of recurrent states in complex dynamical systems at irregular measurements was proposed. The concepts of correlation for the case of the vectors of states of the trajectory of dynamics of complex systems and estimates of vectors correlation for a fixed length fragment moving along the trajectory were generalized. The space with scalar product of states vectors is used to implement the method. Estimation of the magnitudes of correlations of state vectors makes it possible to interpret them as corresponding levels of energy interaction of states vectors and to detect degree of their recurrence. In this case, calculation of the magnitudes of correlation are carried out only based on the known measurements of the state vector and does not require determining the threshold and the method of distance calculation, traditionally used in the methods of recurrent plots. The efficiency of the proposed method was tested on a specific example of experimental data of the actual dynamics of the vector of states of pollution of the urban atmosphere. The following gas pollutants were considered as components of the vector of state: formaldehyde, ammonia and carbon dioxide. The obtained results in general indicate the efficiency of the proposed method. It was established experimentally that the correlation method in case of irregular measurements of atmospheric contaminations ensures the authenticity of detection of recurrent states, corresponding to maximum correlation of states. In this case, the correlation assessment should be conducted for a movable fragment of a trajectory of the states vector. The length of the fragment should not be more than 10 responses

Keywords


correlation of states; energy interaction; fragment of trajectory of states; recurrent states; complex dynamical systems; gas atmospheric pollution

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Cited-by:

1. A method for preventing the emergency resulting from fires in the premises through operative control over a gas medium
Boris Pospelov, Ruslan Meleshchenko, Olekcii Krainiukov, Kostiantyn Karpets, Olena Petukhova, Yuliia Bezuhla, Tetiana Butenko, Viktoriia Horinova, Pavlo Borodych, Eduard Kochanov
Eastern-European Journal of Enterprise Technologies  Vol: 1  Issue: 10 (103)  First page: 6  Year: 2020  
doi: 10.15587/1729-4061.2020.194009





Copyright (c) 2019 Boris Pospelov, Vladimir Andronov, Evgeniy Rybka, Olekcii Krainiukov, Kostiantyn Karpets, Oleksandr Pirohov, Iryna Semenyshyna, Ruslan Kapitan, Alona Promska, Oleksii Horbov

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061