THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS
The article considers the issue of measurement of dynamic variables of open nonlinear dynamical systems. Most of real physical and biological systems in the surrounding world are the nonlinear dynamic systems. The spatial, temporal and spatio-temporal structures are formed in such systems because of...
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| Format: | Article |
| Language: | English |
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Belarusian National Technical University
2015-12-01
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| Series: | Приборы и методы измерений |
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| Online Access: | https://pimi.bntu.by/jour/article/view/231 |
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| author | Yu. P. Machekhin Yu. S. Kurskoy |
| author_facet | Yu. P. Machekhin Yu. S. Kurskoy |
| author_sort | Yu. P. Machekhin |
| collection | DOAJ |
| description | The article considers the issue of measurement of dynamic variables of open nonlinear dynamical systems. Most of real physical and biological systems in the surrounding world are the nonlinear dynamic systems. The spatial, temporal and spatio-temporal structures are formed in such systems because of dissipation. The collective effects that associated with the processes of self-organization and evolution are possible there too. The objective of this research is a compilation of the Shannon entropy measurement equations for case of nonlinear dynamical systems. It’s proposed to use the interval mathematics methods for this. It is shown that the measurement and measurement results analysis for variables with complex dynamics, as a rule, cannot be described by classical metrological approaches, that metrological documents, for example GUM, contain. The reason of this situation is the mismatch between the classical mathematical and physical approaches on the one hand and processes that occur in real dynamic systems on the other hand. For measurement of nonlinear dynamical systems variables the special measurement model and measurement results analysis model are created. They are based on Open systems theory, Dynamical chaos theory and Information theory. It’s proposed to use the fractal, entropic and temporal scales as tools for evaluation of a systems state. As a result of research the Shannon entropy measurement equations, based on interval representations of measurement results. are created, like for an individual dynamic variable as for nonlinear dynamic system. It is shown that the measurement equations, based on interval mathematics methods, contains the exact solutions and allows take into account full uncertainty. The new results will complement the measurement model and the measurement results analysis model for case of nonlinear dynamic systems. |
| format | Article |
| id | doaj-art-a4a99325c21b4ceaa36939e1b0c2eeb0 |
| institution | Kabale University |
| issn | 2220-9506 2414-0473 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Приборы и методы измерений |
| spelling | doaj-art-a4a99325c21b4ceaa36939e1b0c2eeb02025-02-03T11:37:43ZengBelarusian National Technical UniversityПриборы и методы измерений2220-95062414-04732015-12-0162257263223THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODSYu. P. Machekhin0Yu. S. Kurskoy1Kharkov National University of RadioelectronicsKharkov National University of RadioelectronicsThe article considers the issue of measurement of dynamic variables of open nonlinear dynamical systems. Most of real physical and biological systems in the surrounding world are the nonlinear dynamic systems. The spatial, temporal and spatio-temporal structures are formed in such systems because of dissipation. The collective effects that associated with the processes of self-organization and evolution are possible there too. The objective of this research is a compilation of the Shannon entropy measurement equations for case of nonlinear dynamical systems. It’s proposed to use the interval mathematics methods for this. It is shown that the measurement and measurement results analysis for variables with complex dynamics, as a rule, cannot be described by classical metrological approaches, that metrological documents, for example GUM, contain. The reason of this situation is the mismatch between the classical mathematical and physical approaches on the one hand and processes that occur in real dynamic systems on the other hand. For measurement of nonlinear dynamical systems variables the special measurement model and measurement results analysis model are created. They are based on Open systems theory, Dynamical chaos theory and Information theory. It’s proposed to use the fractal, entropic and temporal scales as tools for evaluation of a systems state. As a result of research the Shannon entropy measurement equations, based on interval representations of measurement results. are created, like for an individual dynamic variable as for nonlinear dynamic system. It is shown that the measurement equations, based on interval mathematics methods, contains the exact solutions and allows take into account full uncertainty. The new results will complement the measurement model and the measurement results analysis model for case of nonlinear dynamic systems.https://pimi.bntu.by/jour/article/view/231nonlinear dynamic systemmeasurement equationinterval variablesshannon entropy |
| spellingShingle | Yu. P. Machekhin Yu. S. Kurskoy THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS Приборы и методы измерений nonlinear dynamic system measurement equation interval variables shannon entropy |
| title | THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS |
| title_full | THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS |
| title_fullStr | THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS |
| title_full_unstemmed | THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS |
| title_short | THE COMPILATION OF SHANNON ENTROPY MEASUREMENT EQUATION FOR NONLINEAR DYNAMIC SYSTEMS BY USING THE INTERVAL ANALYSIS METHODS |
| title_sort | compilation of shannon entropy measurement equation for nonlinear dynamic systems by using the interval analysis methods |
| topic | nonlinear dynamic system measurement equation interval variables shannon entropy |
| url | https://pimi.bntu.by/jour/article/view/231 |
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