RESUMO Neste artigo é realizada a estimativa de parâmetros e solução de um problema de transferência de calor, onde os resultados numéricos são comparados com dados experimentais obtidos na literatura. O modelo matemático é resolvido numericamente utilizando o Método das Diferenças Finitas (MDF) com formulação implícita. Já a estimativa dos parâmetros é feita utilizando os métodos de otimização estocástica Luus-Jaakola (LJ) e Algoritmo de Colisão de Partículas (do inglês, Particle Collision Algorithm PCA), bem como modificações propostas nos referidos métodos. Os resultados obtidos foram satisfatórios tendo as modificações apresentado uma redução do número de avaliações da função objetivo (NAF) necessários para encontrar os parâmetros de interesse, bem como possibilitou um bom ajuste entre as temperaturas obtidas experimentalmente e resultados numéricos, motivando novas aplicações em problemas de mesma natureza.

ABSTRACT In this article, the estimation of parameters and the solution of a heat transfer problem is performed, where the numerical results are compared with experimental data obtained in the literature. The mathematical model is solved numerically using the Finite Difference Method (MDF) with implicit formulation. The parameters are estimated using the Luus-Jaakola (LJ) and Particle Collision Algorithm (PCA) stochastic optimization methods, as well as proposed modifications to the referred methods. The results obtained were satisfactory and the modifications presented a reduction in the number of objective function evaluations (NAF) necessary to find the parameters of interest, as well as allowing a good adjustment between the temperatures obtained experimentally and numerical results, motivating new applications in problems of same nature.

ABSTRACT In academia, the study of the movement of water in the ground has been widespread since the last century. The same can be determined using the Richards equation. This is a nonlinear parabolic partial differential equation that requires parameters to generate the results of the problem. Some authors have proposed equations that represent the relationship between volumetric moisture and soil water potential, such as Haverkamp and van Genuchten. As main objective of this work, the inverse modeling was implemented to obtain the Richards equation parameters, applying the Luus-Jaakola method. To verify the mathematical model, a sensitivity analysis was performed, which allowed the observation of the effect that each parameter has on the output data, implying a linear dependence. The results produced proved to be satisfactory for the problem analyzed in our research.

ABSTRACT The simulation of terrestrial ecosystem processes, using numerical biosphere-atmosphere models that can be coupled to the Atmospheric Models, assist in a better diagnosis and forecast of climate and weather. To be able to represent a particular region, biome or ecosystem, the model parameters need to be fitted for local conditions. This work aims to assess the Luus-Jaakola (LJ) method in the optimization of the parameters in a two-stream radiative transfer model applied to a vegetation canopy. Solar radiation components (incident, S ↓, and reflected, S ↑) were measured above a sugarcane crop in a Tropical region from February 17 to 24, 2006. Among the combinations of internal and external iterations evaluated for Luss-Jaakola method, 60/30 (external/internal) iterations presented more precise albedo ( α = S ↑ / S ↓ ) simulated ( r 2 = 0 . 7386 ) and, for the accuracy of the simulated α, even though the 60/40 combination had the smallest percentual error (6.40%), the 60/30 combination was 0.03% higher. The precision and accuracy of S ↑ was greater with the parameters obtained by the inverse problem with the combination of 60/30 (external/internal) iterations respectively. In general, the behavior of simulated S ↑ at the top of the canopy was underestimated compared to the observed S ↑, especially in the early morning. For the simulated α at the top of the canopy, the model’s overestimation was observed at the lowest values of albedo. When the largest albedos are observed, only at the beginning of the day the model underestimated the values. As shown by the tests result, the parameters optimized by Luus-Jaakola method have an adequate representation of the observed data.