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

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

Boris Pospelov, Olekcii Krainiukov, Alexander Savchenko, Serhii Harbuz, Oleksandr Cherkashyn, Sergey Shcherbak, Ihor Rolin, Viktor Temnikov

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

Keywords


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

References


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

Marwan, N., Webber, C. L., Macau, E. E. N., Viana, R. L. (2018). Introduction to focus issue: Recurrence quantification analysis for understanding complex systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28 (8), 085601. doi: https://doi.org/10.1063/1.5050929

Oya, S., Aihara, K., Hirata, Y. (2014). Forecasting abrupt changes in foreign exchange markets: method using dynamical network marker. New Journal of Physics, 16 (11), 115015. doi: https://doi.org/10.1088/1367-2630/16/11/115015

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

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

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

Adeniji, A. E., Olusola, O. I., Njah, A. N. (2018). Comparative study of chaotic features in hourly wind speed using recurrence quantification analysis. AIP Advances, 8 (2), 025102. doi: https://doi.org/10.1063/1.4998674

Wendi, D., Marwan, N., Merz, B. (2018). In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots. International Journal of Bifurcation and Chaos, 28 (01), 1850007. doi: https://doi.org/10.1142/s0218127418500074

Donner, R. V., Balasis, G., Stolbova, V., Georgiou, M., Wiedermann, M., Kurths, J. (2019). Recurrence‐Based Quantification of Dynamical Complexity in the Earth's Magnetosphere at Geospace Storm Timescales. Journal of Geophysical Research: Space Physics, 124 (1), 90–108. doi: https://doi.org/10.1029/2018ja025318

Garcia-Ceja, E., Uddin, M. Z., Torresen, J. (2018). Classification of Recurrence Plots’ Distance Matrices with a Convolutional Neural Network for Activity Recognition. Procedia Computer Science, 130, 157–163. doi: https://doi.org/10.1016/j.procs.2018.04.025

Neves, F. M., Viana, R. L., Pie, M. R. (2017). Recurrence analysis of ant activity patterns. PLOS ONE, 12 (10), e0185968. doi: https://doi.org/10.1371/journal.pone.0185968

Ozken, I., Eroglu, D., Breitenbach, S. F. M., Marwan, N., Tan, L., Tirnakli, U., Kurths, J. (2018). Recurrence plot analysis of irregularly sampled data. Physical Review E, 98 (5). doi: https://doi.org/10.1103/physreve.98.052215

Souza, E. G., Viana, R. L., Lopes, S. R. (2008). Using recurrences to characterize the hyperchaos-chaos transition. Physical Review E, 78 (6). doi: https://doi.org/10.1103/physreve.78.066206

Schinkel, S., Dimigen, O., Marwan, N. (2008). Selection of recurrence threshold for signal detection. The European Physical Journal Special Topics, 164 (1), 45–53. doi: https://doi.org/10.1140/epjst/e2008-00833-5

Eroglu, D., Marwan, N., Stebich, M., Kurths, J. (2018). Multiplex recurrence networks. Physical Review E, 97 (1). doi: https://doi.org/10.1103/physreve.97.012312

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

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

Pospelov, B., Rybka, E., Togobytska, V., Meleshchenko, R., Danchenko, Y., Butenko, T. et. al. (2019). Construction of the method for semi-adaptive threshold scaling transformation when computing recurrent plots. Eastern-European Journal of Enterprise Technologies, 4 (10 (100)), 22–29. doi: https://doi.org/10.15587/1729-4061.2019.176579

Mindlin, G. M., Gilmore, R. (1992). Topological analysis and synthesis of chaotic time series. Physica D: Nonlinear Phenomena, 58 (1-4), 229–242. doi: https://doi.org/10.1016/0167-2789(92)90111-y

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

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

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.

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


GOST Style Citations








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

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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