Análise da secagem de grãos de milho por modelos não lineares: abordagem bayesiana e estudo dos pontos influentes

Abstract

The analysis of grain drying kinetics is widely used in applied studies, as it is an essential step to ensure grain quality and reduce post-harvest losses. Statistical models are employed to describe this process, representing moisture loss over time. In this thesis, two articles were developed with the aim of analyzing the drying of corn grains, focusing on the estimation of parameters in nonlinear models using both frequentist and Bayesian inference approaches, as well as the identification of influential points on the decreasing curves associated with drying. In the first article, the main original contribution is the application of Bayesian inference with prior distributions based on the principle of maximum entropy,an innovative approach in food drying aimed at estimating the parameters of three nonlinear models (Lewis, Henderson and Pabis, and Overhults). This choice allows for the objective incorporation of available prior knowledge, maximizing the impartiality of prior information. The posterior distributions were obtained using the Markov Chain Monte Carlo (MCMC) method, enabling inference even in scenarios of high computational complexity. The Kullback-Leibler (KL) divergence was used to select the model that best represented the data. In the second article, in addition to the frequentist estimation of the parameters of five nonlinear models (Lewis, Overhults, Page, Simple Exponential with Three Parameters, and Midilli), an in-depth analysis was carried out to identify and interpret influential points on the decreasing curves. As the main contribution of this study, a new influential point, named P1, is proposed based on technical criteria related to the desired final moisture content. Moreover, critical points such as the inflection point, maximum acceleration point, and asymptotic deceleration point were identified through the analysis of derivatives of the fitted functions. The uncertainty associated with the location of these points was quantified using confidence intervals constructed via the bootstrap method. In this case, model selection was based on the adjusted coefficient of determination (R²adj) and the Akaike Information Criterion (AIC). The results of this thesis demonstrate that the application of nonlinear models, combined with robust and innovative statistical methods such as the use of maximum entropy priors and the definition of new critical points provides a more accurate and informative description of the drying process. These advances offer valuable support for decision-making in the control and optimization of this process in applied contexts.