Determination of the length of hydraulic jumps using artificial neural networks

Hydraulic jumps have many uses such as dissipation of energy while water is flowing over spillways, increasing the water surface channels for distribution, chlorinating of wastewater, and many other cases. The length of hydraulic jumps is one of the most important parameters in designing the stilling basin, however, it cannot be calculated by mathematical analyses only – experimental and laboratorial results should also be used. In this study, an artificial neural network (ANN) technique was developed to determine the length of the hydraulic jumps in a rectangular section with a horizontal apron. Two algorithms, namely Levenberg–Marquardt (LM) and gradient descent with momentum and adaptive learning rule back propagation (BP) are employed to reach optimum model. From the different model structures that were examined, an LM algorithm with a 3–4–1 structure was adapted as the final model. The selected model can predict the length of jumps with high accuracy and satisfy the evaluation criteria, with root mean square error RMSE = 0.01224, mean absolute percentage error MAPE = 2.59%, and coefficient of determination R2 = 0.9962. A comparison between the selected ANN model and empirical Silvester equation was also done and the results showed that the ANN method is more precise.