Comparison of Different Relationships for Estimating Longitudinal Velocity Depth Profile Based on The Optimization Method Using Genetic Algorithm

Depth distribution of longitudinal velocity in rivers and open canals is required for modeling many hydraulic processes. Therefore, introducing the most appropriate relation to estimating the velocity distribution has always been of interest to researchers and is constantly evolving. With the development of entropy theory and genetic programming based on the principle of natural evolution, these methods have been applied in a wide range of engineering sciences including fluid mechanics and hydraulics. The purpose of this study was to calculate the unknown parameters of velocity distribution relationships and estimate the longitudinal velocity profile using binary genetic algorithm optimization. For this purpose, the unknown parameters of Yang, Julian, Chiu, and Tsallis models, which are 4, 5, 3, and 5 respectively, were optimized using a genetic algorithm. After determining the unknown parameters of each model, a statistical comparison was performed between the measured and estimated velocity values ​​with the optimized relationships. The results showed that the one-dimensional velocity distribution estimated by all four models is accurate related to the experimental data. Root Mean Square Error (RMSE) for all one-dimensional velocity distribution simulations in the Yang model is 0.054, for the Julian model is 0.052, for the Chiu model is 0.042, and for the Tsallis model is 0.035m/s. However, considering the number of optimal parameters extracted by the Julian and the Thessalian models, it is recommended the use of these models to alluvial rivers.