A Proposed Novel Hybrid Intelligent Model Based on ANFIS Integrated with Firefly Algorithm for Forecasting Discharge Coefficient of Side Weirs on Converging Canals^*

Abstract

Side weirs are widely used to measure and control flows passing through main canals. In this study, a hybrid model is developed to approximate the discharge coefficient of side weirs located on converging canals for the first time, meaning that the adaptive neuro-fuzzy inference system (ANFIS) network is optimized by means of the firefly algorithm. After that, six ANFIS and adaptive neuro-fuzzy inference system-firefly algorithm (ANFIS-FA) models are introduced using input parameters. In addition, in this study, Monte Carlo simulation is employed to study the modelling accuracy. Furthermore, the k-fold cross-validation approach is implemented to validate the modelling results. Analysing the modelled results demonstrates that the hybrid models are more accurate than the ANFIS ones. The superior model simulates the discharge coefficient values with reasonable accuracy. For example, the values of the determination coefficient (R 2), the mean absolute error (MAE) and the root mean square error (RMSE) for the superior model are calculated as 0.993, 0.011 and 0.015, respectively. Also, about 98% of the superior model results have errors less than 12%. According to the uncertainty analysis results, the superior model has an overestimated performance. A sensitivity analysis indicates that the flow Froude number at the side weir downstream is the most effective input parameter.