Mathematical model of gas consumption process in the form of cyclic random process

Lytvynenko, Iaroslav; Lupenko, Serhii; Nazarevych, Oleg; Shymchuk, Grigorii; Hotovych, Volodymyr

doi:10.1109/csit52700.2021.9648621

Cited by 3 publications

(1 citation statement)

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“…In the dissertation of [47], a new approach to mathematical modeling, computer simulation and the processing of cyclic signals was created. This approach has been widely used for modeling cyclic signals of various natures [48][49][50][51][52]. As part of this approach, a conditional cyclic random process was developed, which enabled a consistent mathematical description of cyclic signals with double stochasticity, namely, with simultaneous stochasticity of their cyclic and rhythmic structures [53].…”

Section: Introductionmentioning

confidence: 99%

Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms

Lupenko,

Butsiy

2024

Fractal Fract

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This paper is devoted to the research of the isomorphic multidimensional cyclic structure and multidimensional phase structure of the cyclic random process (CRP) and to its formation method, which enables a rigorous formalization of intuitive ideas concerning cyclic stochastic motion. The fundamental properties of the cyclic random process and analytical dependencies between the multidimensional cyclic structure, multidimensional phase structure and rhythm structure of the CRP have been established. This work shows that the CRP is able to take into account the cyclicity of multidimensional distribution functions of cyclic signals as well as the variability in the rhythm of the investigated signals. A subclass of the CRP is the periodic random process, which allows for the use of classical processing methods of cyclic signals with a regular rhythm. Based on a series of experiments, significant advantages of the CRP as a mathematical model of electrocardiographic signals (ECG) compared to the periodic random process are shown.

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Section: Introductionmentioning

confidence: 99%

Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms

Lupenko,

Butsiy

2024

Fractal Fract

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Information Technology for Estimating City Gas Consumption During the Year

Kozlovskyi

Balanyuk

Martyniuk

et al. 2022

2022 International Conference on Smart Information Systems and Technologies (SIST)

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The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process

Lupenko

2022

Mathematics

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This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation.

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Mathematical model of gas consumption process in the form of cyclic random process

Cited by 3 publications

References 9 publications

Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms

Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms

Information Technology for Estimating City Gas Consumption During the Year

The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process

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