Application of Computational Intelligence Techniques to an Environmental Flow Formula

Abstract

Manning formula is one of the most famous functions used in hydraulics and hydrology, which calculates the average flow velocity based on roughness coefficient, hydraulic radius, and slope. This study intends to improve the original formula by minimizing the deviation error between calculated flow velocity and observed one. The first improvement approach was to estimate the exponent values of hydraulic radius and slope, instead of using current 2/3 and 1/2, while fixing the roughness value. When logarithm-converted multiple linear regression, calculus-based BFGS technique, and meta-heuristic genetic algorithm were applied to the problem, genetic algorithm found the best exponent values in terms of sum of squares error and coefficient of determination. The second approach was to estimate the individual roughness value, instead of a constant one, which is the function of hydraulic radius and slope. When multiple linear regression, artificial neural network with BFGS, and artificial neural network with genetic algorithm tackled the problem, the latter found the best solution. We hope these approaches will be utilized more practically in the future.