Estimating the effect of sand-roughened bed on hydraulic jump characteristics using heuristic models

The hydraulic jump occurs in open channels and downstream of hydraulic structures because these features change the flow regime from super-critical to sub-critical. To prevent downstream channel erosion and guarantee the construction of a hydraulic jump, a stilling basin is utilized. The effect of sand-roughened beds on hydraulic jump characteristics was investigated using an experimental study. After that, new machine learning models including Emotional neural network (EANN), Hammerstein Weiner model (HWM), Elman neural networks ENN, and Extreme learning neural networks (ELNN) were adopted to estimate the ratio of hydraulic jump length to initial water depth. Different evaluation criteria such as determination Coefficient (R2), Mean Square Error (MSE), Correlation Coefficient (R), and Rout Mean Square Error (RMSE), scatter plots, time series comparison, and Spiral plots have been used to evaluate the models' performance. The results revealed that the Elman NN model outperformed the other models in estimating the ratio of hydraulic jump length to the initial depth (Lj/ y1), while the HWM model has a weaker performance than other models in estimating Lj/y1.