Estudo da concentração da poluição do ar com parâmetro Fuzzy em Uberlândia

Abstract

Several of our daily occurring phenomena may be modeled by means of differential equations. In general, there are some difficulties in modeling such phenomena through those equations since they depend on the precision of the estimates of the parameters. The objective of this research is to study the numerical approximation to the solution for some types of differential equations through the use of the finite elements method, such as: a uni-dimensional, a stationary bi-dimensional and a non stationary bi-dimensional equation. We also present the estimates for the numerical errors committed when the approximations of the solutions are determined. More specifically, by means of an advective-diffusive partial differential equation with evolution in time, we model a pollution source that we consider as the chimney of a plant with constant parameters and with a homogeneous Dirichlet boundary condition in the city of Uberlândia. Finally, we were able to perform this modeling by merging the advective-diffusive partial differential equation with evolution in time with the fuzzy set theory, on the grounds that three parameters of this equation are determined by Fuzzy Rule-Based Systems. The diffusion parameter depends on temperature and concentration of the pollutants and the velocity towards x and y depends on the friction force presented in the city. This friction force is due to buildings, vegetation, terrain profile and other factors. We utilized satellite images in order to determine the temperatures in the city and the intervals of variation for diffusion whereas velocities were obtained through literature. The merge of those two types of theory provided the means to determine which is the best localization of an industrial district amongst the five points studied within different regional sectors of the city of Uberlândia.