Development of more accurate discharge coefficient prediction equations for rectangular side weirs using adaptive neuro-fuzzy inference system and generalized group method of data handling

A rectangular side weir is a hydraulic structure commonly utilized all around the world in urban stormwater and wastewater sewer networks and in irrigation drainage systems to deviate excessive flow passing through the main channel. In this study, a genetic algorithm (GA) is employed to identify the best selection of adaptive neuro-fuzzy inference system (ANFIS) membership functions and the evolutionary design of a generalized group method of data handling (GMDH) structure for prediction of the side weir discharge coefficient. Moreover, the Singular Value Decomposition (SVD) method is applied to calculate the linear parameters of the ANFIS results and linear coefficient vectors in GMDH (ANFIS-GA/SVD and GMDH-GA/SVD). The side weir dimensionless length, Froude number, the ratio of weir height to upstream flow depth, and the ratio of weir length to upstream flow depth serve as inputs to the ANFIS-GA/SVD and GMDH-GA/SVD models to forecast the discharge coefficient. We compared the results of these multi-objective methods with the single-objective methods and found that the multi-objective methods are superior regarding accuracy. Sensitivity analysis is also carried out to determine the impact of each parameter on discharge coefficient estimation. ANFIS-GA/SVD outperformed ANFIS-GA, GMDH-GA/SVD, GMDH-GA and existing regression-based and machine learning-based equations. The uncertainty analysis is also carried out to assess the quantitative performance of all models. The results indicate that the uncertainty width for the best model (ANFIS-GA/SVD) is ±0.0067.