519.6

cyclic random process, gas consumption process, statistical processing, segmentation, cyclic random process.

The problem of construction of a new mathematical model of the gas consumption process is considered in this paper. The new mathematical model is presented as an additive mixture of three components: cyclic random process, trend component and stochastic residue. The process of obtaining three components is carried out on the basis of caterpillar method, thus obtaining ten components of singular decomposition. In this approach, the cyclic component is formed from the sum of nine components of the schedule, which have one thing in common – repeated deployment over time. The trend component of the new mathematical model is the second component of singular decomposition, and the stochastic residue is formed on the basis of the difference between the values of the studied gas consumption process and the sum of cyclic and trend components. Two approaches to stochastic processing of cyclic gas consumption process based on the known model of stochastic-periodic random process and cyclic random process as models of the cyclic component are used in this paper. Application of mathematical model of cyclic component in the form of cyclic random process with cyclic structure makes it possible to obtain estimation of variance on cycle of gas consumption process, provided segmentation of cyclic component on depressions, much less in comparison of obtained variance estimation for indicating greater accuracy in the study of the gas consumption process and will use the obtained stochastic estimates when modeling the gas consumption process in further studies.

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1. Pryymak M. V. Analiz elektronavantazhenʹ iz vykorystannyam liniynykh vypadkovykh protsesiv. Visnyk Ternopilʹsʹkoho derzh. tekhn. un-tu. 1999. Tom 4. Chyslo 1. Р. 84–87. [In Ukraine].
2. Marchenko B. H., Mulyk N. V., Fryz M. Y. Kharakterystychna funktsiya umovnoho liniynoho vypadkovoho protsesu yak matematychnoyi modeli hazospozhyvannya. Naukovi pratsi Natsionalʹnoho aviatsiynoho universytetu. Seriya: elektronika ta systemy upravlinnya. 2006. No. 3 (9). P. 40–46. [In Ukraine].
3. Maggio G., Cacciola G. (2009) A variant of the Hubbert curve for world oil production forecasts. Energy Policy 37 (11), 4761–4670.
4. Valero A. (2010) Physical geonomics: combining the exergy and Hubbert peak analysis for predicting mineral resources depletion. Resour. Conserv. Recycl. 54 (12), 1074–1083.
5. Szoplik J. (2015) Forecasting of natural gas consumption with artificial neural networks. Energy 85, 208–220.
6. Ardakani F. J., Ardehali M. M. (2014) Novel effects of demand side management data on accuracy of electrical energy consumption modeling and long-term forecasting. Energy Convers. Manage. 78, 745–752.
7. Demirel O. F., Zaim S., Caliskan A., Ozuyar P. (2012) Forecasting natural gas consumption in Istanbul using neural networks and multivariate time series methods. Turkish J. Electr. Eng. Comput. Sci. 20 (5), 695–711.
8. Gorucu F. B. (2010) Evaluation and forecasting of gas consumption by statistical analysis. Energy Sources 26, 267–276.
9. Khan M. A., (2015) Modelling and forecasting the demand for natural gas in Pakistan. Renewable Sustainable Energy Rev. 49, 1145–1159.
10. Zhang Wei; Yang, Jun (2015): Forecasting natural gas consumption in China by Bayesian Model Averaging, Energy Reports, ISSN 2352-4847, Elsevier, Amsterdam. Vol. 1. P. 216–220.
11. Lupenko S. Tsiklicheskiye funktsii i ikh klassy v zadachakh modelirovaniya tsiklicheskikh signalov i kolivnikh system. Vimíryuval'na i obchislyuval'na tekhnika v tekhnologíchnikh protsessakh. Khmel'nitskiy. 2005. No. 1. P. 177–185. [In Ukraine].
12. Lupenko S. A. Vypadkovyy protses iz zonnoyu chasovoyu strukturoyu ta simeystvo yoho funktsiy rozpodilu. Visnyk Ternopilʹsʹkoho derzhavnoho tekhnichnoho universytetu, 2005. Tom 14. P. 183–192. [In Ukraine].
13. Nazarevych O. Vydilennya richnoho trendu yak adytyvnoyi skladovoyi chasovoho ryadu hazospozhyvannya. Visnyk TNTU. 2011. Tom 16. No. 4. P. 201–209) [in Ukraine].
14. Golyandina N. E., Nekrutkin V. V., Zhigljavsky A. A. Analysis of Time Series Structure: SSA and Related Techniques. Boca Raton: Chapman&Hall. CRC, 2000. 305 p.
15. Lytvynenko I. V. The method of segmentation of stochastic cyclic signals for the problems of their processing and modeling. Journal of Hydrocarbon Power Engineering, Oil and Gas Measurement and Testing. 2017. Vol. 4.No. 2. P. 93–103.
16. Lytvynenko A. Horkunenko O. Kuchvara Y. Palaniza, Methods of processing cyclic signals in automated cardiodiagnostic complexes, in: Proceedings of the 1st International Workshop on Information-Communication Technologies and Embedded Systems. Mykolaiv, Ukraine, 2019. P. 116–127.
17. Lytvynenko I. V., Maruschak P. O., Lupenko S. A., Hats Yu. I., Menou A., Panin S. V. Software for segmentation, statistical analysis and modeling of surface ordered structures. Mechanics, resource and diagnostics of materials and structures (MRDMS–2016): Proceedings of the 10th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. AIP Publishing. 2016. Vol. 1785. No. 1, P. 030012-1-030012-7.
18. Lupenko S., Lytvynenko I., Stadnyk N., Osukhivska H., Kryvinska N. Modification of the Software System for the Automated Determination of Morphological and Rhythmic Diagnostic Signs by Electrocardio Signals. IntelITSIS-2020, Proceedings of the 1st International Workshop on Intelligent Information Technologies & Systems of Information Security. Khmelnytskyi, Ukraine, June 10–12. 2020. P. 36–46.
19. Priymak N. V. Guziy V. I. Issledovaniye vozmozhnosti izmereniya perioda korrelyatsii pereodicheski korrelirovanogo sluchaynogo protsesa po odnoy nablyudayemoy realizatsii. Vesnik Kiyevskogo politekhnicheskogo instituta „Yelektroakustika i zvukotekhnika” Kiyev: Vysshaya shkola, 1984. Vyp. 8. P. 31–33. [In Russian].