Existen situaciones en donde se requiere el conocimiento de propiedades termodinámicas como la conductividad térmica para el presente caso. En algunas de ellas aparece una exigencia adicional, al tener que hacerse la medición a lo largo de los tres ejes espaciales perpendiculares. En el presente artículo, se propone predecir estas tres conductividades térmicas que aparecen en materiales ortotrópicos, mediante la solución de un problema inverso de transferencia de calor. El problema inverso se resolvió mediante el algoritmo Cuckoo, el determinístico de Levenberg-Marquardt, y con el nuevo híbrido entre estos dos. Se encontró que estas tres estrategias producen excelentes resultados al compararse entre ellas. Sin embargo, el algoritmo híbrido resultó ser más eficiente que sus precursores al resolver el presente problema. El algoritmo híbrido consumió en promedio menos tiempo de cómputo en comparación con el algoritmo metaheurístico y amplió el rango de búsqueda en comparación con el determinístico, manteniendo siempre precisión en sus resultados.
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.
<p class="MsoNormal"><span lang="EN-US">This work considers the prediction in real time of physicochemical parameters of a sample heated in a uniform electromagnetic field. The thermal conductivity (K)</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>K</m:r><m:r>) </m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><!--[endif]--><span lang="EN-US">and the </span><span lang="EN">combination of density and heat capacity terms (pc)</span><span lang="EN"> were estimated as a demonstrative example.</span><span lang="EN-US">The sample (with known geometry) was subjected to electromagnetic radiation, generating a uniform and time constant volumetric heat flow within it. Real temperature profile was simulated adding white Gaussian noise to the original data, obtained from the theoretical model. For solving the objective function, simulated annealing and genetic algorithms, along with the traditional Levenberg-Marquardt method were used for comparative purposes. Results show similar findings of all algorithms for three simulation scenarios, as long as the signal to noise ratio sits at least at 30 dB. It means for practical purposes, that the estimation procedure presented here requires both, a good experimental design and an electronic instrumentation correctly specified.</span><span lang="EN-US">If both requirements are satisfied simultaneously, it is possible to estimate these type of parameters on-line, without need for an additional experimental setup.</span></p><p class="MsoNormal"><span lang="EN-US">This work considers the prediction in real time of physicochemical parameters of a sample heated in a uniform electromagnetic field. The thermal conductivity </span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-family:"Cambria Math","serif"'><m:r>(</m:r><m:r>K</m:r><m:r>) </m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><!--[endif]--><span lang="EN-US">and the </span><span lang="EN">combination of density and heat capacity terms (</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span lang=EN style='font-family:"Cambria Math","serif"; mso-ansi-language:EN'><m:r>ρc</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><!--[endif]--><span lang="EN"> were estimated as a demonstrative example.</span><span lang="EN-US">The sample (with known geometry) was subjected to electromagnetic radiation, generating a uniform and time constant volumetric heat flow within it. Real temperature profile was simulated adding white Gaussian noise to the original data, obtained from the theoretical model. For solving the objective function, simulated annealing and genetic algorithms, along with the traditional Levenberg-Marquardt method were used for comparative purposes. Results show similar findings of all algorithms for three simulation scenarios, as long as the signal to noise ratio sits at least at 30 dB. It means for practical purposes, that the estimation procedure presented here requires both, a good experimental design and an electronic instrumentation correctly specified.</span><span lang="EN-US">If both requirements are satisfied simultaneously, it is possible to estimate these type of parameters on-line, without need for an additional experimental setup.</span></p>
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