DEVELOPMENT OF A SELF-ADJUSTING METHOD FOR CALCULATING RECURRENT DIAGRAMS IN A SPACE WITH A SCALAR PRODUCT

  • Boris Pospelov National University of Civil Defence of Ukraine, Ukraine
  • Ruslan Meleshchenko National University of Civil Defence of Ukraine, Ukraine
  • Vitalii Asotskyi Scientific-methodical Center of Educational Institutions in the Sphere of Civil Defence, Ukraine
  • Olena Petukhova National University of Civil Defence of Ukraine, Ukraine
  • Stella Gornostal National University of Civil Defence of Ukraine, Ukraine
  • Serhii Harbuz National University of Civil Defence of Ukraine, Ukraine
Keywords: metric-threshold uncertainty, recurrence diagram, self-adjusting method, metric, metric space, scalar product of vectors

Abstract

A self-adjusting method for calculating recurrence diagrams has been developed. The proposed method is aimed at overcoming the metric-threshold uncertainty inherent in the known methods for calculating recurrence diagrams. The method provides invariance to the nature of the measured data, and also allows to display the recurrence of states, adequate to real systems of various fields. A new scientific result consists in the theoretical justification of the method for calculating recurrence diagrams, which is capable of overcoming the existing metric-threshold uncertainty of known methods on the basis of self-adjusting by measurements by improving the topology of the metric space. The topology is improved due to the additional introduction of the scalar product of state vectors into the operation space. This allowed to develop a self-adjusting method for calculating recurrence diagrams with increased accuracy and adequacy of the display of recurrence states of real systems. Moreover, the method has a relatively low computational complexity, providing invariance with respect to the nature of the irregularity of measurements.

Verification of the proposed method was carried out on the basis of experimental measurements of concentrations of gas pollutants of atmospheric air for a typical industrial city. The main gas pollutants of the atmosphere are formaldehyde, ammonia and nitrogen dioxide, caused by stationary and mobile sources of urban pollution. The obtained experimental verification results confirm the increased accuracy and adequacy of the display of the recurrence of atmospheric pollution states, as well as the invariance of the method with respect to the nature of the irregularity of measurements. It has been established that the accuracy of the method is influenced by the a priori boundary angular dimensions of the recurrence cone. It was shown that with a decrease in the boundary angular dimensions of the recurrence cone, the accuracy of the recurrence mapping of the real states of dynamical systems in the calculated diagrams increases. It was experimentally established that the accuracy and adequacy of the mapping of the recurrence states of real dynamical systems acceptable for applications is provided for a boundary angular size of the recurrence cone of 10° or less.

Downloads

Download data is not yet available.

Author Biographies

Boris Pospelov, National University of Civil Defence of Ukraine

Research Center

Ruslan Meleshchenko, National University of Civil Defence of Ukraine

Department of Fire and Rescue Training

Vitalii Asotskyi, Scientific-methodical Center of Educational Institutions in the Sphere of Civil Defence

Department of organization and coordination of research activities

Olena Petukhova, National University of Civil Defence of Ukraine

Department of Fire Prevention in Settlements

Stella Gornostal, National University of Civil Defence of Ukraine

Department of Fire Prevention in Settlements

Serhii Harbuz, National University of Civil Defence of Ukraine

Department of Chair of Fire and Technogenic Safety of Facilities and Technologies

References

Webber,, C. L., Marwan, N. (Eds.) (2015). Recurrence Quantification Analysis. Understanding Complex Systems. doi: https://doi.org/10.1007/978-3-319-07155-8

Pospelov, B., Andronov, V., Meleshchenko, R., Danchenko, Y., Artemenko, I., Romaniak, M. et. al. (2019). Construction of methods for computing recurrence plots in space with a scalar product. Eastern-European Journal of Enterprise Technologies, 3 (4 (99)), 37–44. doi: https://doi.org/10.15587/1729-4061.2019.169887

Pospelov, B., Rybka, E., Meleshchenko, R., Borodych, P., Gornostal, S. (2019). Development of the method for rapid detection of hazardous atmospheric pollution of cities with the help of recurrence measures. Eastern-European Journal of Enterprise Technologies, 1 (10 (97)), 29–35. doi: https://doi.org/10.15587/1729-4061.2019.155027

Pospelov, B., Andronov, V., Rybka, E., Meleshchenko, R., Gornostal, S. (2018). Analysis of correlation dimensionality of the state of a gas medium at early ignition of materials. Eastern-European Journal of Enterprise Technologies, 5 (10 (95)), 25–30. doi: https://doi.org/10.15587/1729-4061.2018.142995

Javorka, M., Trunkvalterova, Z., Tonhajzerova, I., Lazarova, Z., Javorkova, J., Javorka, K. (2008). Recurrences in heart rate dynamics are changed in patients with diabetes mellitus. Clinical Physiology and Functional Imaging, 28 (5), 326–331. doi: https://doi.org/10.1111/j.1475-097x.2008.00813.x

Takens, F. (1981). Detecting strange attractors in turbulence. Lecture Notes in Mathematics, 366–381. doi: https://doi.org/10.1007/bfb0091924

Pospelov, B., Andronov, V., Rybka, E., Popov, V., Semkiv, O. (2018). Development of the method of frequency­temporal representation of fluctuations of gaseous medium parameters at fire. Eastern-European Journal of Enterprise Technologies, 2 (10 (92)), 44–49. doi: https://doi.org/10.15587/1729-4061.2018.125926

Webber, C. L., Ioana, C., Marwan, N. (Eds.) (2016). Recurrence Plots and Their Quantifications: Expanding Horizons. Springer Proceedings in Physics. doi: https://doi.org/10.1007/978-3-319-29922-8

Ioana, C., Digulescu, A., Serbanescu, A., Candel, I., Birleanu, F.-M. (2014). Recent Advances in Non-stationary Signal Processing Based on the Concept of Recurrence Plot Analysis. Translational Recurrences, 75–93. doi: https://doi.org/10.1007/978-3-319-09531-8_5

Pospelov, B., Andronov, V., Rybka, E., Meleshchenko, R., Borodych, P. (2018). Studying the recurrent diagrams of carbon monoxide concentration at early ignitions in premises. Eastern-European Journal of Enterprise Technologies, 3 (9 (93)), 34–40. doi: https://doi.org/10.15587/1729-4061.2018.133127

Pospelov, B., Andronov, V., Rybka, E., Skliarov, S. (2017). Design of fire detectors capable of self-adjusting by ignition. Eastern-European Journal of Enterprise Technologies, 4 (9 (88)), 53–59. doi: https://doi.org/10.15587/1729-4061.2017.108448

Pospelov, B., Andronov, V., Rybka, E., Skliarov, S. (2017). Research into dynamics of setting the threshold and a probability of ignition detection by self­adjusting fire detectors. Eastern-European Journal of Enterprise Technologies, 5 (9 (89)), 43–48. doi: https://doi.org/10.15587/1729-4061.2017.110092

Marwan, N. (2011). How to avoid potential pitfalls in recurrence plot based data analysis. International Journal of Bifurcation and Chaos, 21 (04), 1003–1017. doi: https://doi.org/10.1142/s0218127411029008

Carrión, A., Miralles, R., Lara, G. (2014). Measuring predictability in ultrasonic signals: An application to scattering material characterization. Ultrasonics, 54 (7), 1904–1911. doi: https://doi.org/10.1016/j.ultras.2014.05.008

Beim Graben, P., Hutt, A. (2015). Detecting event-related recurrences by symbolic analysis: applications to human language processing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373 (2034), 20140089. doi: https://doi.org/10.1098/rsta.2014.0089

Graben, P. beim, Hutt, A. (2013). Detecting Recurrence Domains of Dynamical Systems by Symbolic Dynamics. Physical Review Letters, 110 (15). doi: https://doi.org/10.1103/physrevlett.110.154101

Thiel, M., Romano, M. C., Kurths, J., Meucci, R., Allaria, E., Arecchi, F. T. (2002). Influence of observational noise on the recurrence quantification analysis. Physica D: Nonlinear Phenomena, 171(3), 138–152. doi: https://doi.org/10.1016/s0167-2789(02)00586-9

Zbilut, J. P., Zaldivar-Comenges, J.-M., Strozzi, F. (2002). Recurrence quantification based Liapunov exponents for monitoring divergence in experimental data. Physics Letters A, 297 (3-4), 173–181. doi: https://doi.org/10.1016/s0375-9601(02)00436-x

Kondratenko, O. M., Vambol, S. O., Strokov, O. P., Avramenko, A. M. (2015). Mathematical model of the efficiency of diesel particulate matter filter. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 6, 55–61.

Vasiliev, M. I., Movchan, I. O., Koval, O. M. (2014). Diminishing of ecological risk via optimization of fire-extinguishing system projects in timber-yards. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 5, 106–113.

Dubinin, D., Korytchenko, K., Lisnyak, A., Hrytsyna, I., Trigub, V. (2017). Numerical simulation of the creation of a fire fighting barrier using an explosion of a combustible charge. Eastern-European Journal of Enterprise Technologies, 6 (10 (90)), 11–16. doi: https://doi.org/10.15587/1729-4061.2017.114504

Semko, A., Rusanova, O., Kazak, O., Beskrovnaya, M., Vinogradov, S., Gricina, I. (2015). The use of pulsed high-speed liquid jet for putting out gas blow-out. The International Journal of Multiphysics, 9 (1), 9–20. doi: https://doi.org/10.1260/1750-9548.9.1.9

Kustov, M. V., Kalugin, V. D., Tutunik, V. V., Tarakhno, E. V. (2019). Physicochemical principles of the technology of modified pyrotechnic compositions to reduce the chemical pollution of the atmosphere. Voprosy khimii i khimicheskoi tekhnologii, 1, 92–99. doi: https://doi.org/10.32434/0321-4095-2019-122-1-92-99

Vasyukov, A., Loboichenko, V., Bushtec, S. (2016). Identification of bottled natural waters by using direct conductometry Ecology. Environment and Conservation, 22 (3), 1171–1176.


👁 492
⬇ 280
Published
2019-09-16
How to Cite
Pospelov, B., Meleshchenko, R., Asotskyi, V., Petukhova, O., Gornostal, S., & Harbuz, S. (2019). DEVELOPMENT OF A SELF-ADJUSTING METHOD FOR CALCULATING RECURRENT DIAGRAMS IN A SPACE WITH A SCALAR PRODUCT. EUREKA: Physics and Engineering, (5), 10-18. https://doi.org/10.21303/2461-4262.2019.00981
Section
Computer Science

Most read articles by the same author(s)