Estudo da incerteza do escoamento de rios através das Equações de Saint Venant

Abstract

The differential equations are present in the modeling of countless scientific phenomena, in several fields of knowledge. Many of these equations depend on parameters of difficult obtainment, which display uncertainties or imprecisions in their determination. In this respect, the general purpose of this research is to study the uncertainty surrounding the process of an open-channel flow, specifically that of rivers, using the Saint Venant equations. This uncertainty is approached in two aspects: through a parameter modeled by the Fuzzy Logic and by considering the slope of a river channel as random. For this purpose, we have initially studied concepts related to the differential equations, as well as analytical and numerical methods for solving them. To model this uncertainty mathematically in the river flow phenomenon, we have used the Fuzzy Set Theory. Thus, we have studied basic concepts related to this theory and Zadeh’s Extension Principle, which extends nonfuzzy mathematical concepts to fuzzy concepts. We have built the fuzzy solution for the Saint Venant Equations from the analytical solution and from due consideration about the contribution of lateral flow rate to the total river flow as a triangular fuzzy number. Additionally, we have solved the equations numerically, for specific boundary conditions, regarding one of the parameters as deterministic at one time and at another as an output variable of a Fuzzy Rule-Based System, built with expert knowledge. Finally, we have assessed the influence of the river channel slope on the flow, regarding this slope as a variable along the channel. This study presents, thus, an approach of the problem of river flow, which enables to find different solutions for several situations in a quick and dynamic way, with a possible saving in financial resources.