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.

RESUMO Diferentes tipos de modelos matemáticos têm sido usados para prever o comportamento dinâmico do novo coronavírus (COVID-19). Muitos deles envolvem a formulação e solução de problemas inversos. Esse tipo de problema geralmente considera que o modelo, o vetor de variáveis de projeto e os parâmetros do sistema são todos valores determinísticos. Nesta contribuição, uma metodologia baseada em um processo de iteração de loop duplo é considerada para avaliar a influência de incertezas durante a resolução do problema inverso, proposto para estimar os parâmetros do modelo. No loop intermo, a solução associada ao maior valor de probabilidade associada as variáveis que apresentam incerteza é determinada. Já no loop externo, os valores das variáveis determinísticas é obtida. Para essa finalidade, a Análise de Confiabilidade Inversa é considerada como ferramenta de confiabilidade e o algoritmo de Evolução Diferencial é usado como ferramenta de otimização. Para fins de ilustração, a metodologia proposta é aplicada para estimar os parâmetros do modelo SIRD (SusceptívelInfeccioso-Recuperado-Morto) associado ao comportamento dinâmico da pandemia de COVID-19, considerando dados reais da epidemia da China e incertezas no número básico de reprodução (ℛ0). Os resultados obtidos demonstram que o aumento da confiabilidade implica no aumento do valor da função objetivo.

ABSTRACT Different types of mathematical models have been used to predict the dynamic behavior of the novel coronavirus (COVID-19). Many of them involve the formulation and solution of inverse problems. This kind of problem is generally carried out by considering the model, the vector of design variables, and system parameters as deterministic values. In this contribution, a methodology based on a double loop iteration process and devoted to evaluate the influence of uncertainties on inverse problem is evaluated. The inner optimization loop is used to find the solution associated with the highest probability value, and the outer loop is the regular optimization loop used to determine the vector of design variables. For this task, we use an inverse reliability approach and Differential Evolution algorithm. For illustration purposes, the proposed methodology is applied to estimate the parameters of SIRD (Susceptible-Infectious-RecoveryDead) model associated with dynamic behavior of COVID-19 pandemic considering real data from China’s epidemic and uncertainties in the basic reproduction number (ℛ0). The obtained results demonstrate, as expected, that the increase of reliability implies the increase of the objective function value.

As técnicas inversas são ferramentas muito utilizadas na determinação dos parâmetros envolvidos na modelagem de processos industriais. Neste trabalho o método Random, Restricted Window (R2W) é empregado na estimação dos parâmetros de transferência de massa envolvidos na cromatografia da separação da glicose e frutose a partir do suco de caju. O R2W é um método estocástico simples, que analisa a função custo a partir de estimativas aleatórias pertencentes a um domínio definido para os parâmetros que se deseja ajustar, assumindo novas buscas aleatórias através de uma janela de domínio restrito próxima aos melhores candidatos à solução do problema de interesse. Na modelagem do processo cromatográfico foi utilizada uma nova abordagem fenomenológica, chamada de "velocidade da frente de convecção", a qual mostrou potencial na caracterização da coluna cromatográfica. Nesta, a velocidade da fase móvel (líquida) é considerada o fator dominante no transporte das moléculas ao longo da coluna. O método R2W mostrou-se eficaz na obtenção dos parâmetros do modelo fornecendo uma ótima concordância entre os resultados da simulação computacional e os dados experimentais.

Inverse techniques are tools widely used in the determination of parameters involved in the modelling of industrial processes. In the present work the method Restricted Random Window (R2W) is employed to estimate the parameters of mass transfer involved in the chromatographic separation of glucose and fructose from cashew apple juice. The R2W is a simple stochastic method, that evaluates the cost function for random estimates within the domain for the parameters to be adjusted, with new random searches performed within a restricted domain in the vicinity of the best solution candidates for the problem of interest. In the chromatographic process a new approach phenomenological is used, called "front velocity", which considers as the dominant factor in the molecules transfer in chromatographic columns the liquid phase velocity. The R2W method has shown to be effective in the model parameters determination yielding a good agreement between the computational simulation and experimental data.