Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model
In the paper, the problem of modeling of thermal traces is addressed. The proposed model allows prediction of the behaviour of a thermal mark left by a warm body on cooler ground. In the model, a fractional order (FO) approach is employed. This allows consideration of an inital function (not only a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/15/6/2257 |
| _version_ | 1827649162530783232 |
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| author | Krzysztof Oprzędkiewicz Maciej Rosół Wojciech Mitkowski |
| author_facet | Krzysztof Oprzędkiewicz Maciej Rosół Wojciech Mitkowski |
| author_sort | Krzysztof Oprzędkiewicz |
| collection | DOAJ |
| description | In the paper, the problem of modeling of thermal traces is addressed. The proposed model allows prediction of the behaviour of a thermal mark left by a warm body on cooler ground. In the model, a fractional order (FO) approach is employed. This allows consideration of an inital function (not only a condition in one, initial time instant). The proposed model uses a scalar FO differential equation approximated with the use of Continuous Fraction Expansion (CFE) approximation. This allows maintenance of a relatively small size of the model with good accuracy in the sense of a Mean Square Error (MSE) cost function. Experimental verification confirms good accuracy of the proposed model in modeling of thermal traces. |
| first_indexed | 2024-03-09T19:52:59Z |
| format | Article |
| id | doaj.art-477b03ee604241a790d980015a2f8062 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T19:52:59Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-477b03ee604241a790d980015a2f80622023-11-24T01:05:55ZengMDPI AGEnergies1996-10732022-03-01156225710.3390/en15062257Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient ModelKrzysztof Oprzędkiewicz0Maciej Rosół1Wojciech Mitkowski2Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, PolandDepartment of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, PolandDepartment of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, PolandIn the paper, the problem of modeling of thermal traces is addressed. The proposed model allows prediction of the behaviour of a thermal mark left by a warm body on cooler ground. In the model, a fractional order (FO) approach is employed. This allows consideration of an inital function (not only a condition in one, initial time instant). The proposed model uses a scalar FO differential equation approximated with the use of Continuous Fraction Expansion (CFE) approximation. This allows maintenance of a relatively small size of the model with good accuracy in the sense of a Mean Square Error (MSE) cost function. Experimental verification confirms good accuracy of the proposed model in modeling of thermal traces.https://www.mdpi.com/1996-1073/15/6/2257non integer order systems2D heat transferfractional order state equationinitial problemCFE approximationthermal camera |
| spellingShingle | Krzysztof Oprzędkiewicz Maciej Rosół Wojciech Mitkowski Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model Energies non integer order systems 2D heat transfer fractional order state equation initial problem CFE approximation thermal camera |
| title | Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model |
| title_full | Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model |
| title_fullStr | Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model |
| title_full_unstemmed | Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model |
| title_short | Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model |
| title_sort | modeling of thermal traces using fractional order a discrete memory efficient model |
| topic | non integer order systems 2D heat transfer fractional order state equation initial problem CFE approximation thermal camera |
| url | https://www.mdpi.com/1996-1073/15/6/2257 |
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