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Application of Computational Intelligence Techniques to an Environmental Flow Formula
Int. J. Fuzzy Log. Intell. Syst. 2018;18(4):237-244
Published online December 25, 2018
© 2018 Korean Institute of Intelligent Systems.

Zong Woo Geem1 and Jin-Hong Kim2

1Department of Energy IT, Gachon University, Seongnam, Korea 2Department of Civil & Environmental Engineering, Chung-Ang University, Seoul, Korea
Correspondence to: Jin-Hong Kim (
Received November 20, 2018; Revised December 15, 2018; Accepted December 21, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords : Computational intelligence, Manning equation, Hydraulics, Curve fitting, Genetic algorithm, Artificial neural network