nach oben

Erschienen in:

2018 | OriginalPaper | Buchkapitel

Application of an Ant Colony Optimization Algorithm in Modeling the Heat Transfer in Porous Aluminum

verfasst von : Rafał Brociek, Damian Słota, Mariusz Król, Grzegorz Matula, Waldemar Kwaśny

Erschienen in: Information and Software Technologies

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper procedure for solving inverse heat conduction problem with fractional derivative is presented. Authors present time fractional heat conduction model with Caputo derivative and Neumann, Robin boundary conditions, which can be applied to describe process of heat conduction in porous media. Based on temperature measurements, functional describing error of approximate solution is created. Considered inverse problem is transform to find minimum of created functional. In order to solve inverse problem (find unknown parameters of model) authors applied an Ant Colony Optimization (ACO) algorithm. Finally, experiment with data from porous aluminum was carried out to check effectiveness of proposed algorithm. Goal of this paper is reconstruction unknown parameters in heat conduction model with fractional derivative and show that ACO is effective algorithm and works well in these type of problems.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel The Use of an Artificial Neural Network for a Sea Bottom Modelling

Nächstes Kapitel Application of the Taylor Transformation to the Systems of Ordinary Differential Equations

Socha, K., Dorigo, M.: Ant colony optimization in continuous domains. Eur. J. Oper. Res. 185, 1155–1173 (2008)CrossRef

Brociek, R., Słota, D.: Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation. Math. Model. Nat. Phenom. 13 (2018). Article no 5MathSciNetCrossRef

Brociek, R., Słota, D.: Application of real ant colony optimization algorithm to solve space fractional heat conduction inverse problem. In: Dregvaite, G., Damasevicius, R. (eds.) ICIST 2016. CCIS, vol. 639, pp. 369–379. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46254-7_29CrossRef

Brociek, R., Słota, D.: Reconstruction of the boundary condition for the heat conduction equation of fractional order. Therm. Sci. 19, 35–42 (2015)CrossRef

Chen, S., Liu, F., Jiang, X., Turner, I., Burrage, K.: Fast finite difference approximation for identifying parameters in a two-dimensional space-fractional nonlocal model with variable diffusivity coefficients. SIAM J. Numer. Anal. 56, 606–624 (2016)MathSciNetCrossRef

Dabiri, A., Moghaddam, P.B., Machado, J.A.T.: Optimal variable-order fractional PID controllers for dynamical systems. J. Comput. Appl. Math. 339, 40–48 (2018)MathSciNetCrossRef

Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-72703-3CrossRefMATH

Ionescu, C., Lopes, A., Copot, D., Machado, J.A.T., Bates, J.H.T.: The role of fractional calculus in modelling biological phenomena: a review. Commun. Nonlin. Sci. Numer. Simul. 51, 141–159 (2017)CrossRef

Ismailov, M.I., Cicek, M.: Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions. Appl. Math. Model. 40, 4891–4899 (2016)MathSciNetCrossRef

10.

Obrączka, A., Kowalski, J.: Modeling the distribution of heat in the ceramic materials using fractional differential equations. In: Szczygieł, M. (eds.) Materiały XV Jubileuszowego Sympozjum „Podstawowe Problemy Energoelektroniki, Elektromechaniki i Mechatroniki”, PPEEm 2012, Archiwum Konferencji PTETiS, Komitet Organizacyjny Sympozjum PPEE i Seminarium BSE, vol. 32, pp. 132–133 (2012). (in polish)

11.

Xiaoran, L., Shangbo, Z., Hua, L., Hongbin, T., Ying, Q.: Rhythm oscillation in fractional-order Relaxation oscillator and its application in image enhancement. J. Comput. Appl. Math. 339, 69–84 (2018)MathSciNetCrossRef

12.

Brociek, R.: Implicit finite difference method for time fractional diffusion equations with mixed boundary conditions. Zeszyty Naukowe Politechniki Śląskiej, Matematyka Stosowana 4, 73–87 (2014)

13.

Klafter, J., Lim, S., Metzler, R.: Fractional Dynamics: Resent Advances. World Scientific, New Jersey (2012)MATH

14.

Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH

15.

Cui, M., Zhao, Y., Xu, B., Gao, X.: A new approach for determining damping factors in Levenberg-Marquardt algorithm for solving an inverse heat conduction problem. Int. J. Heat Mass Transf. 107, 747–754 (2017)CrossRef

16.

Hetmaniok, E., Nowak, I., Słota, D., Wituła, R., Zielonka, A.: Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method. Therm. Sci. 17, 643–650 (2013)CrossRef

17.

Hetmaniok, E., Słota, D., Zielonka, A.: Parallel procedure based on the swarm intelligence for solving the two-dimensional inverse problem of binary alloy solidification. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds.) PPAM 2015. LNCS, vol. 9574, pp. 287–297. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32152-3_27CrossRef

18.

Hetmaniok, E.: Inverse problem for the solidification of binary alloy in the casting mould solved by using the bee optimization algorithm. Heat Mass Transf. 52, 1369–1379 (2016)CrossRef

19.

Murio, D.: Stable numerical solution of a fractional-diffusion inverse heat conduction problem. Comput. Math. Appl. 53, 1492–1501 (2007)MathSciNetCrossRef

20.

Birvinskas, D., Jusas, V., Martisius, I., Damasevicius, R.: Data compression of EEG signals for artificial neural network classification. Inf. Technol. Control 42, 238–241 (2013)

21.

Das, R., Akay, B., Singla, R.K., Singh, K.: Application of artificial bee colony algorithm for inverse modelling of a solar collector. Inverse Prob. Sci. Eng. 25, 887–908 (2017)MathSciNetCrossRef

22.

Jafrasteh, B., Fathianpour, N.: A hybrid simultaneous perturbation artificial bee colony and back-propagation algorithm for training a local linear radial basis neural network on ore grade estimation. Neurocomputing 235, 217–227 (2017)CrossRef

23.

Woźniak, M., Połap, D.: Hybrid neuro-heuristic methodology for simulation and control of dynamic systems over time interval. Neural Netw. 93, 45–56 (2017). https://doi.org/10.1016/j.neunet.2017.04.013CrossRef

24.

Karaboga, D., Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214, 108–132 (2009)MathSciNetMATH

25.

Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39, 459–471 (2007)MathSciNetCrossRef

26.

Połap, D., Woźniak, M.: Polar bear optimization algorithm: meta-heuristic with fast population movement and dynamic birth and death mechanism. Symmetry 9(10), 203:1–203:20 (2017). https://doi.org/10.3390/sym9100203CrossRef

27.

Woźniak, M., Połap, D.: Adaptive neuro-heuristic hybrid model for fruit peel defects detection. Neural Netw. 98, 16–33 (2018). https://doi.org/10.1016/j.neunet.2017.10.009CrossRef

28.

Połap, D., Kęsik, K., Woźniak, M., Damaševičius, R.: Parallel technique for the metaheuristic algorithms using devoted local search and manipulating the solutions space. Appl. Sci. 8(2), 293:1–293:25 (2018). https://doi.org/10.3390/app8020293CrossRef

Titel: Application of an Ant Colony Optimization Algorithm in Modeling the Heat Transfer in Porous Aluminum
verfasst von: Rafał Brociek
Damian Słota
Mariusz Król
Grzegorz Matula
Waldemar Kwaśny
Verlag: Springer International Publishing
Buch: Information and Software Technologies
Print ISBN: 978-3-319-99971-5

Electronic ISBN: 978-3-319-99972-2

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-99972-2_30

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"