Development of the method operative calculation the recurrent diagrams for non-regular measurements

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.181516

Keywords:

recurrence plot, complex dynamic systems, irregular measurements, atmospheric gas pollution

Abstract

Researchers widely use methods for calculation of recurrence plots based on measurement of dynamics of a vector of states in a phase space for visual and quantitative analysis of the behavior of complex dynamic systems in various fields. Such methods have high potential capabilities. However, one cannot use them directly for the operative calculation of recurrence plots at the real speed of measurements of a vector of states, taking into account irregularity of measurements. One of the reasons is the lack of a method, which would be capable of operative and reliable mapping of recurrence states of real systems in recurrence plots at irregular measurements of a vector of states.

We propose a method for the operative calculation of recurrence plots at irregular measurements. Its base is a scientific analysis of reasons for low reliability and impossibility of an operative calculation of recurrence plots, as well as search and substantiation of constructive methods for their elimination. Such methods include: current calculation of recurrence plots; improvement of a phase space by introduction of an operation of scalar product for vectors of states; adaptation of a recurrence threshold to measurement results. The base of a process of the current calculation of recurrence plots is a use of only current and previous measurements of a vector of states of the system. It is possible to reconcile two key factors of low reliability of mapping of recurrence states in diagrams related to uncertainty of a norm and a threshold of recurrence in the proposed improved phase space.

The above has made possible to propose a threshold adaptation method for conical regions of recurrence. It has been proposed to use two adaptive thresholds with different angular parameters of recurrence cones in the calculation to ensure reliable mapping of recurrence states in diagrams under conditions of irregular measurement of a vector of states. We confirmed the operability of the proposed operative method for calculation of recurrence plots and illustrated it by an example with irregular measurements of the real dynamics of a vector of states of dangerous pollution in the urban atmosphere

Author Biographies

Boris Pospelov, Scientific-Methodical Center of Educational Institutions in the Sphere of Civil Defence Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Professor

Department of Organization and Coordination of Research Activities

Olekcii Krainiukov, V. N. Karazin Kharkiv National University Svobody sq., 4, Kharkiv, Ukraine, 61022

Doctor of Geographical Sciences, Associate Professor

Department of Ecological Safety and Environmental Education

Alexander Savchenko, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD, Senior Research

Department of Prevention Activities and Monitoring

Serhii Harbuz, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD

Department of Fire and Technological Safety of Facilities and Technologies

Oleksandr Cherkashyn, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD

Department of Fire and Rescue Training

Sergey Shcherbak, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Department of Fire and Rescue Training

Ihor Rolin, Military Institute for Tank Troops National Technical University "Kharkiv Polytechnic Institute" Poltavskyi Shliakh str., 192, Kharkiv, Ukraina, 61000

Doctor of Military Sciences, Associate Professor

Viktor Temnikov, Military Institute for Tank Troops National Technical University "Kharkiv Polytechnic Institute" Poltavskyi Shliakh str., 192, Kharkiv, Ukraina, 61000

PhD

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Published

2019-10-24

How to Cite

Pospelov, B., Krainiukov, O., Savchenko, A., Harbuz, S., Cherkashyn, O., Shcherbak, S., Rolin, I., & Temnikov, V. (2019). Development of the method operative calculation the recurrent diagrams for non-regular measurements. Eastern-European Journal of Enterprise Technologies, 5(4 (101), 26–33. https://doi.org/10.15587/1729-4061.2019.181516

Issue

Vol. 5 No. 4 (101) (2019): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2019 Boris Pospelov, Olekcii Krainiukov, Alexander Savchenko, Serhii Harbuz, Oleksandr Cherkashyn, Sergey Shcherbak, Ihor Rolin, Viktor Temnikov

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