Published
Internal volumetric heat generation and heat capacity prediction during a material electromagnetic treatment process using hybrid algorithms
Predicción de la generación interna volumétrica de calor y la capacidad calorífica durante un tratamiento electromagnético del material usando algoritmos híbridos
Keywords:
Microwave heating, inverse problems, parameter estimation, electromagnetic field (en)Calentamiento por microondas, problemas inversos, estimación de parámetros, campo electromagnético (es)
This work considers the estimation of internal volumetric heat generation, as well as the heat capacity of a solid spherical sample, heated by a homogeneous, time-varying electromagnetic field. To that end, the numerical strategy solves the corresponding inverse problem. Three functional forms (linear, sinusoidal, and exponential) for the electromagnetic field were considered. White Gaussian noise was incorporated into the theoretical temperature profile (i.e. the solution of the direct problem) to simulate a more realistic situation. Temperature was pretended to be read through four sensors. The inverse problem was solved through three different kinds of approach: using a traditional optimizer, using modern techniques, and using a mixture of both. In the first case, we used a traditional, deterministic Levenberg-Marquardt (LM) algorithm. In the second one, we considered three stochastic algorithms: Spiral Optimization Algorithm (SOA), Vortex Search (VS), and Weighted Attraction Method (WAM). In the final case, we proposed a hybrid between LM and the metaheuristics algorithms. Results show that LM converges to the expected solutions only if the initial conditions (IC) are within a limited range. Oppositely, metaheuristics converge in a wide range of IC but exhibit low accuracy. The hybrid approaches converge and improve the accuracy obtained with the metaheuristics. The difference between expected and obtained values, as well as the RMS errors, are reported and compared for all three methods.
Este trabajo considera la estimación de la generación interna volumétrica de calor y la capacidad calorífica de una muestra esférica sólida calentada por un campo electromagnético homogéneo variante en el tiempo. Para tal fin, la estrategia numérica soluciona el correspondiente problema inverso. Tres formas funcionales (lineal, senoidal y exponencial) para el campo electromagnético fueron considerados. Ruido blanco fue agregado al perfil de temperatura teórica (i.e. la solución del problema directo) para simular una situación más realística. La temperatura se pretendió que fuera leída por cuatro sensores. El problema inverso fue solucionado a través de tres diferentes enfoques: usando un optimizador tradicional, usando técnicas modernas y usando una mezcla de ambos. En el primer caso, usamos un algoritmo determinístico tradicional como lo es el de Levenberg-Marquardt (LM). En el segundo, consideramos tres metaheurísticos estocásticos: El Algoritmo de optimización de la espiral (SOA), la Búsqueda en vórtice (VS), y el método de atracción ponderada (WAM). Para el caso final, proponemos híbridos entre el LM y los algoritmos metahehurísticos. Los resultados muestran que LM converge a la solución esperada solo si las condiciones iniciales (IC) están dentro de un rango limitado. Por otra parte, los metaheurísticos convergen en un amplio rango de IC pero muestra baja precisión. Los enfoques híbridos convergen y mejoran la precisión obtenida con los metaheurísticos. La diferencia entre los valores esperados y obtenidos, así como, los errores RMS son reportados y comparados para los tres métodos.
References
Bermeo, L. et al., 2015. Estimation of the particle size distribution of colloids from multiangle dynamic light scattering measurements with particle swarm optimization. Ingeniería e Investigación, 35(1), pp.49–54.
Bermeo Varon, L., Barreto Orlande, H. & Eliçabe, G., 2015. Estimation of state variables in the hyperthermia therapy of cancer with heating imposed by radiofrequency electromagnetic waves. International Journal of Thermal Sciences, 98, pp.228–236.
Carslaw, H.S. & Jaeger, J.C., 1959. The flow heat in a sphere and cone. In Conduction of heat in solids. London: Oxford University Press, pp. 230–244.
Cebo-Rudnicka, A., Malinowski, Z. & Buczek, A., 2016. The influence of selected parameters of spray cooling and thermal conductivity on heat transfer coefficient. International Journal of Thermal Sciences, 10, pp.52–64.
Chen, B. et al., 2016. Identification of the thermal conductivity coefficients of 3D anisotropic media by the singular boundary method. International Journal of Heat and Mass Transfer, 100, pp.24–33.
Cui, M. et al., 2016. A modified Levenberg–Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems. International Journal of Heat and Mass Transfer, 97, pp.908–916. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0017931015317932.
Dogan, B. & Olmez, T., 2015. A new metaheuristic for numerical function optimization: Vortex Search algorithm. Information Sciences, 293, pp.125–145.
Friedl, G. & Kuczmann, M., 2015. A New Metaheuristic Optimization Algorithm, the Weighted Attraction Method. Acta Technica Jaurinensis, 8(3), pp.257–266. Available at: http://acta.sze.hu/index.php/acta/article/view/381.
Giraldo, E., Peluffo, D. & Castellanos, G., 2012. Weighted time series analysis for electroencephalographic source location. DYNA, 79(176), pp.64–70.
Grup d’Innovació per la Millora de la Docència en Estructura Propietats i Processat de Materials, Materials - Silicom Carbide. Available at: http://www.ub.edu/cmematerials/es/content/carburo-de-silicio-sic [Accessed June 16, 2016].
Hào, D. et al., 2017. Determination of a term in the right-hand side of parabolic equations. Journal of Computational and Applied Mathematics, 309, pp.28–43.
Hussein, M.S. & Lesnic, D., 2014. Determination of the time-dependent thermal conductivity in the heat equation with spacewise dependent heat capacity. In 6th International Conference on Finite Difference Methods, FDM. pp. 217–224.
Kvasov, D.E. & Mukhametzhanov, M.S., 2017. Metaheuristic vs. deterministic global optimization algorithms: The univariate case. Applied Mathematics and Computation.
Kvasov, D.E. & Sergeyev, Y.D., 2014. Deterministic approaches for solving practical black-box global optimization problems. Advances in Engineering Software.
Mohebbi, F. & Sellier, M., 2016. Estimation of thermal conductivity, heat transfer coefficient, and heat flux using a three dimensional inverse analysis. International Journal of Thermal Sciences, 99, pp.258–270.
Mohebbi, F. & Sellier, M., 2016. Parameter estimation in heat conduction using a two-dimensional inverse analysis. In International Journal of Computational Methods in Engineering Science and Mechanics. pp. 1–14.
Necati Ozisik & Orlande, H., 2000. Techniques for solving inverse heat transfer problems. In Inverse Heat Transfer - Fundamentals and applications. New York: Taylor&Francis, pp. 35–58.
Nedin, R., Nesterov, S. & Vatulyan, A., 2016. Identification of thermal conductivity coefficient and volumetric heat capacity of functionally graded materials. International Journal of Heat and Mass Transfer, 102, pp.213–218.
Sergeyev, Y.D. & Kvasov, D.E., 2017. Deterministic Global Optimization: An Introduction to the Diagonal Approach, Springer-Verlag New York.
Strongin, R.G. & Sergeyev, Y.D., 2000. Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms 1st ed., Springer US.
Tamura, K. & Yasuda, K., 2011. Spiral Multipoint Search for Global Optimization. In 2011 10th International Conference on Machine Learning and Applications and Workshops. Anchorage, AK: IEEE, pp. 470–475. Available at: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6147022.
Tutcuoglu, A., Majidi, C. & Shan, W., 2016. Nonlinear thermal parameter estimation for embedded internal Joule heaters. International Journal of Heat and Mass Transfer, 97, pp.412–421.
Vere Beck, J. & Kenneth, A., 1977. Introduction To Linear Estimation. In Parameter Estimation in Engineering and Science. New York: John Wiley & Sons, pp. 130–212.
Wang, B. & Liu, J., 2016. Recovery of thermal conductivity in two-dimensional media with nonlinear source by optimizations. Applied Mathematics Letters, 60, pp.73–80.
Wang, L. et al., 2017. Identification of the boundary heat transfer coefficient from interior measurement of temperature field. Applied Mathematics Letters, 63, pp.6–13.
Yang, Y., Chen, W. & Lee, H., 2011. A nonlinear inverse problem in estimating the heat generation in rotary friction welding. Numerical Heat Transfer; Part A: Applications, 59(2), pp.130–149.
Zhigljavsky, A. & Žilinskas, A., 2008. Stochastic Global Optimization, Springer US.
How to Cite
License
Copyright (c) 2018 Edgar García-Morantes, Iván Amaya-Contreras, Rodrigo Correa-Cely
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.
