Estimating discharge coefficient of the sluice gate including, the semi-cylindrical sill utilizing multiple model strategy

Sluice gates with a semi-cylindrical sill are flow control structures that are used in irrigation canals to regulate water level and flow discharge. To estimate the flow discharge through these structures, it is necessary to accurately estimate the discharge coefficient. The aim of this study is to present a new approach based on data-mining to accurately estimate the C_d based on experimental data. First, standalone data-mining models such as Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) were developed. Then, to improve the performance of the standalone models, a multiple model (MM) strategy was used to develop new multiple models handled by ANN (MM-ANN) and GPR (MM-GPR). Next, an ensemble model (EM) strategy was developed. A total of 107 experiments were conducted to investigate the effect of the semi-cylindrical sill geometry on the discharge coefficient. 70 % of the data was reserved for the training phase, and the remaining 30 % for the testing phase. The ratio of energy head to sill width (h/b) and approach energy head to wetted parameter (h/P) were as input variables and the discharge coefficient (C_d) was an output variable. The outcomes of the multiple models and ensemble model were compared to the standalone methods using statistical metrics (R², RE%, RMSE, and MAE) and graphical tools (Taylor, Violin, RE%, and scatter plots). The MM-ANN model with R = 0.951, R² = 0.904, SI = 0.012, RE% = 0.891, MAE = 0.005, and RMSE = 0.007 outperformed the ANN, GPR, MM-GPR, and EM models in accuracy. The h/p variable had the greatest effect on the target variable of MM-ANN evidenced by a SHAP value of 0.45. The MM-ANN model provided reasonable estimates the experimental results. It is recommended to implement the multiple model strategy in order to improve the calculation accuracy of the models in this field.