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Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model

Author

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  • Krzysztof Oprzędkiewicz

    (Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, Poland
    These authors contributed equally to this work.)

  • Maciej Rosół

    (Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, Poland
    These authors contributed equally to this work.)

  • Wojciech Mitkowski

    (Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30059 Krakow, Poland
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Krzysztof Oprzędkiewicz & Maciej Rosół & Wojciech Mitkowski, 2022. "Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model," Energies, MDPI, vol. 15(6), pages 1-13, March.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:6:p:2257-:d:774948
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    References listed on IDEAS

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    1. Rafał Stanisławski & Krzysztof J. Latawiec & Marian Łukaniszyn, 2015. "A Comparative Analysis of Laguerre-Based Approximators to the Grünwald-Letnikov Fractional-Order Difference," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, March.
    2. Krzysztof Oprzędkiewicz & Wojciech Mitkowski & Maciej Rosół, 2021. "Fractional Order Model of the Two Dimensional Heat Transfer Process," Energies, MDPI, vol. 14(19), pages 1-16, October.
    3. Raseelo J. Moitsheki & Atish Rowjee, 2011. "Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-13, April.
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    Cited by:

    1. Victor Busher & Vadim Zakharchenko & Anatoliy Shestaka & Valeriy Kuznetsov & Vitalii Kuznetsov & Stanislaw Nader, 2022. "Optimization of the Control of Electromagnetic Brakes in the Stand for Tuning Internal Combustion Engines Using ID Regulators of Fractional Order," Energies, MDPI, vol. 15(24), pages 1-19, December.

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