Ponente
Descripción
Estimation of Manning Coefficients with Nonlinear Least Squares
- $\underline{\text{Fabio Augusto Fortunato Filho}}$ - f235849@dac.unicamp.br;
- José Mario Martínez;
- Rodolfo Gotardi Begiato.
1,2 Institute of Mathematics, Statistics and Scientific Computing - University of Campinas (IMECC - UNICAMP), Campinas, São Paulo, Brazil;
3 Academic Department of Mathematics at the Technological University of Paraná (DAMAT-UTFPR), Curitiba, Paraná, Brazil.
Keywords: Hydraulic coefficient. Saint-Venant's equations. Derivative-free optimization.
The study of hydraulics is fundamental for understanding the behavior of fluids in natural and artificial systems, such as canals, rivers and streams. The Saint-Venant equations, a one-dimensional model, are widely used for this purpose. However, so that the equations can represent reality more accurately, it is necessary to estimate the Manning roughness coefficient, which takes into account the friction of the fluid with the different surfaces. Furthermore, due to the complexity of the channel geometry, the Manning coefficient can vary at each point, which makes the task of finding exact values even more challenging. In this context, we will adopt the Nelder-Mead method with space reduction based on interpolation to obtain the Manning coefficient. This approach will be applied to the problem of minimizing the sum of squares of the residuals, which is a widely used approach to modeling optimization problems. The proposed methodology was applied to data from the East Fork River and, using 1 day of training data, it was possible to make estimates about the depth of the channel for the next 27 days, being a relevant approach to describe the behavior of this river.
