Predicting submerged hydraulic jump characteristics using machine learning methods

Abstract

Hydraulic jump typically occurs downstream of hydraulic structures by converting the supercritical to subcritical flow regimes. If the tail-water depth is greater than the secondary depth of the hydraulic jump, the jump will be submerged (SHJ). In these conditions, the momentum equations will not have an analytical solution and a new solution is required. In this study, after dimensional analysis, an experimental study was conducted in a rectangular flume with a length of 9 m, a width of 0.5 m and a depth of 0.45 m in a wide range of Froude numbers (Fr = 3.5 to 11.5) and submergence ratios (Sr = 0.1 to 4). The data were then normalized and divided into two parts of training and testing. A new technique, DGMDH, was used to predict the submerged hydraulic jump characteristics. The results were then compared with the GMDH model. The results showed that DGMDH model estimated the relative submergence depth, jump length, and relative energy loss with accuracy of R2 = 0.9944 and MAPE = 0.038, R2 = 0.9779 and MAPE = 0.0387, and R2 = 0.9932 and MAPE = 0.0192, respectively. While the accuracy of GMDH model for relative submergence depth, jump length, and relative energy loss was respectively R2 = 0.9923 and MAPE = 0.043, R2 = 0.9671 and MAPE = 0.0527, and R2 = 0.9932 and MAPE = 0.0192. Due to superiority of the DGMDH model over the GMDH model, it is recommended to use this model to estimate the submerged hydraulic jump characteristics. Highlight The results showed that DGMDH model have more accurate results than the GMDH model in predicting the relative submergence depth, jump length, and relative energy loss.

Sill Role Effect on the Flow Characteristics (Experimental and Regression Model Analytical)

“…Some of the parameters in the above relationship, such as channel width, thickness, and sill height, have assumed specific values and are not present in the research objectives, so the effects of these parameters have been ignored. In the present study, since the flow is turbulent, the Reynolds number can be ignored [17][18][19]. To make the parameters meaningful, the dimensional analysis of the present study was summarized and calculated in Equation ( 5) by dividing some of them by each other.…”

“…Using Solver in Excel and the regression technique, the equations were presented to obtain an appropriate form with the least error and a high correlation coefficient according to Equations (19) This study established equations to predict the relative energy dissipation and C d of the gate with and without sill conditions. First, the non-linear form of the proposed equations for relative energy dissipation as a function of the dimensionless parameters was determined.…”

“…Using Solver in Excel and the regression technique, the equations were presented to obtain an appropriate form with the least error and a high correlation coefficient according to Equations (19) and (20):…”

Estimating the permeability coefficient of soil using CART and GMDH approaches

“…Sihag et al (2021aSihag et al ( , 2021b predicted the aeration efficiency of the flume using GMDH. Nasrabadi et al (2021) used the GMDH method to predict submerged hydraulic jump characteristics such as jump length, relative energy loss and relative submergence depth. Zeinali et al (2021) showed that the GMDH model has best performance in estimating the hydro-socio-technology-knowledge indicators compared to those obtained via radial basis function and regression trees.…”

Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods

“…At the same time, Naseri and Othman [32] predicted the length of jump on the smooth beds using ANN. Nasrabadi et al [33] studied submerged hydraulic jump characteristics using machine learning methods. According to the evaluation, the Developed Group Method of Data Handling (DGMDH) model is more accurate than the Group Method Data Handling (GMDH) model and other previous research predicting the submergence depth and jump length relative energy dissipation.…”