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Abstrakty
In the paper the fractional order, state space model of a temperature field in a two-dimensional metallic surface is addressed. The proposed model is the two dimensional generalization of the one dimensional, fractional order, state space of model of the heat transfer process. It uses fractional derivatives along time and length. The proposed model assures better accuracy with lower order than models using integer order derivatives. Elementary properties of the proposed model are analysed. Theoretical results are experimentally verifed using data from industrial thermal camera.
Czasopismo
Rocznik
Tom
Strony
180--187
Opis fizyczny
Bibliogr. 34 poz., rys., tab., wykr.
Twórcy
autor
- Faculty of Electrical Engineering Automatic Control Informatics and Biomedical Engineering, Department of Automatic Control and Robotics, AGH University of Science and Technology, al. A Mickiewicza 30, 30-059 Kraków, Poland
autor
- Faculty of Electrical Engineering Automatic Control Informatics and Biomedical Engineering, Department of Automatic Control and Robotics, AGH University of Science and Technology, al. A Mickiewicza 30, 30-059 Kraków, Poland
autor
- Faculty of Electrical Engineering Automatic Control Informatics and Biomedical Engineering, Department of Automatic Control and Robotics, AGH University of Science and Technology, al. A Mickiewicza 30, 30-059 Kraków, Poland
Bibliografia
- 1. Podlubny I. Fractional Differential Equations San Diego: Academic Press; 1999.
- 2. Dzieliński A, Sierociuk D, Sarwas G. Some applications of fractional order calculus. Bulletin of the Polish Academy of Sciences, Technical Sciences. 2010.
- 3. Caponetto R, Dongola G, Fortuna L, Petra I. Fractional order sys-tems: Modelling and Control Applications. University of California ed. Chua LO, editor. Berkeley: World Scientific Series on Nonlinear Science; 2010.
- 4. Das S. Functional Fractional Calculus for System Identification and Controls Berlin: Springer; 2010.
- 5. Gal CG, Warma M. Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory. 2016.
- 6. Popescu E. On the fractional Cauchy problem associated with a feller semigroup. Mathematical Reports. ; 2010.
- 7. Sierociuk D, Skovranek T, Macias M, Podlubny I. Diffusion process modelling by using fractional-order models. Applied Mathematics and Computation. 2015.
- 8. Gómez JF, Torres L, Escobar RF. Fractional derivatives with Mittag-Leffler kernel. Trends and applications in science and engineering Kacprzyk J, editor. Switzerland: Springer; 2019.
- 9. Boudaoui A, El hadj Moussa Y, Hammouch , Ullah S. A fractional-order model describing the dynamics of the novel coronavirus (covid-19) with nonsingular kernel. Chaos, Solitons and Fractals. 2021; 146(110859):111.
- 10. Muhammad Farman M, Akgül A, Askar S, Botmart T. Modelling and analysis of fractional order zika model. AIMS Mathematics. 2022.
- 11. Oprzędkiewicz K, Gawin E, Mitkowski W. Modeling heat distribution with the use of a non-integer order, state space model. International Journal of Applied Mathematics and Com-puter Science. 2016.
- 12. Oprzędkiewicz K, Gawin E, Mitkowski W. Parameter identification for non-integer order, state space models of heat plant. In MMAR 2016 : 21th international conference on Methods and Models in Automation and Robotics; 2016; Międzyzdroje, Poland. p. 184-188.
- 13. Oprzędkiewicz K, Stanisławski R, Gawin E, Mitkowski W. A new algorithm for a cfe approximated solution of a discrete-time non inte-ger-order state equation. Bulletin of the Polish Academy of Sciences. Technical Sciences. 2017; 65(4):429-437.
- 14. Oprzędkiewicz K, Mitkowski W, Gawin E. An accuracy estimation for a non-integer order, discrete, state space model of heat transfer pro-cess. In Automation 2017 : innovations in automation, robotics and measurement techniques; 2017; Warsaw, Poland. p. 86-98.
- 15. Oprzędkiewicz K, Mitkowski W, Gawin E, Dziedzic K. The Caputo vs. Caputo-Fabrizio operators in modelling of heat transfer process. Bul-letin of the Polish Academy of Sciences. Technical Sciences. 2018; 66(4):501-507.
- 16. Oprzędkiewicz K, Gawin E. The practical stability of the discrete, fractional order, state space model of the heat transfer process. Ar-chives of Control Sciences. 2018.
- 17. Oprzędkiewicz K, Mitkowski W. A memory efficient non in-teger order discrete time state space model of a heat transfer process. Interna-tional Journal of Applied Mathematics and Computer Science. 2018.
- 18. Oprzędkiewicz K. Non integer order, state space model of heat transfer process using Atangana-Baleanu operator. Bulletin of the Polish Academy of Sciences. Technical Sciences. 2020; 68(1):43-50.
- 19. Długosz M, Skruch P. The application of fractional-order models for thermal process modelling inside buildings. Journal of Building Phys-ics. 2015; 1(1):1-13.
- 20. Ryms M, Tesch K, Lewandowski W. The use of thermal imaging camera to estimate velocity profiles based on tem-perature distribu-tion in a free convection boundary layer. International Journal of Heat and Mass Transfer. 2021.
- 21. Khan H, Shah R, Kumam P, Arif M. Analytical solutions of fractional order heat and wave equations by the natural transform decomposi-tion method. Entropy. 2019.
- 22. Olsen-Kettle L. Numerical solution of partial differential equa-tions Brisbane: The University of Queensland; 2011.
- 23. Al-Omari SK. A fractional Fourier integral operator and its extension to classes of function spaces. Advances in Difference Equations. 2018; 1(195):19.
- 24. Oprzędkiewicz K, Mitkowski W, Rosół M. Fractional order model of the two dimensional heat transfer process. Energies. 2021.
- 25. Kaczorek T. Singular fractional linear systems and electrical circuits. International Journal of Applied Mathematics and Computer Science. 2011.
- 26. Kaczorek T, Rogowski K. Fractional Linear Systems and Electrical Circuits Białystok: Publishing House of the Bialystok University of Technology; 2014.
- 27. Bandyopadhyay B, Kamal S. Solution, stability and realization of fractional order differential equation. In A Sliding Mode Approach, Lecture Notes in Electrical Engi-neering 317. Switzerland: Springer; 2015. p. 5590.
- 28. Wyrwas M, Mozyrska D, Girejko E. Comparison of h-difference fractional operators. In Mitkowski W, editor. Advances in the Theory and Applications of Non-integer Order Systems. Switzerland: Spring-er; 2013. p. 1-178.
- 29. Berger J, Gasparin S, Mazuroski W, Mende N. An effi-cient two-dimensional heat transfer model for building enve-lopes. An Interna-tional Journal of Computation and Methodology, Numerical Heat Transfer, Part A: Applications. 2021; 79(3):163194.
- 30. Moitsheki RJ, Rowjee A. Steady heat transfer through a two-dimensional rectangular straight fin. Mathematical Problems in Engi-neering. 2011.
- 31. Yang L, Sun B, Sun X. Inversion of thermal conductivity in two-dimensional unsteady-state heat transfer system based on finite dif-ference method and artificial bee colony. Applied Sciences. 2019.
- 32. Mitkowski W. Outline of Control Theory Kraków: Publishing House AGH; 2019.
- 33. Brzek M. Detection and localisation structural damage in selected geometric domains using spectral theory (in Polish). PhD thesis ed. Mitkowski W, editor. Kraków: AGH University of Science and Tech-nology; 2019.
- 34. Michlin SG, Smolicki CL. Approximate methods for solving differential and integral equations (in Polish) Warszawa: PWN; 1970.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fa114baa-5e4c-4560-8ae0-7951cd2ab68b
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