Análise de sensibilidade global via método sobol aplicada à simplificação de um modelo matemático de fermentação com dois substratos

Abstract

This study aimed to generate a simplified model based on the mathematical model proposed by Tochampa et al. (2005) through the application of global sensitivity analysis using the Sobol method. The original model describes the fermentation process conducted by the yeast Candida mogii, in which xylose is converted into xylitol in the presence of glucose as a co-substrate. Initially, the full model was implemented and evaluated, reproducing the kinetic equations defined by Tochampa et al. (2005). Subsequently, global sensitivity analysis was applied, allowing the identification of the most relevant parameters for the process dynamics, as well as those with minimal influence on the analyzed variables. Based on these results, a model simplification was proposed, reducing the number of parameters from eleven to seven without significantly compromising the system's performance. Comparative results showed that the simplified model maintained high accuracy in predicting biomass production and glucose consumption, achieving R2 values of 0.977 and 0.941 respectively, with low statistical errors. However, for xylose consumption and xylitol formation, the differences from the complete model were more evident, with R2 values decreasing to 0.939 and 0.816, respectively, indicating lower accuracy for these variables. Nevertheless, the simplification represented a significant advancement, reducing both mathematical and computational complexity, while highlighting the robustness of the Sobol method as a tool to guide model simplification. It is concluded that the applied strategy proved effective in maintaining the system's representativeness with fewer parameters, contributing to a better understanding of the fermentation process dynamics and expanding the model’s potential applications in various biotechnological contexts.