Discharge coefficient of side weirs on converging channels using extreme learning machine modeling method

Abstract

Generally, side weirs are utilized in main flumes to control and adjust the flow. In this study, for the first time, the discharge coefficient of side weirs installed on converging channels is simulated using proposed artificial intelligence (AI) measurement “Extreme Learning Machine” (ELM). To enhance the efficiency of the numerical model, the Monte Carlo simulations (MCs) are applied and the k-fold cross validation method is used for validating the yielded numerical results. Then, the most significant input parameters are detected for simulating the discharge coefficient. Subsequently, the number of the ELM hidden layer neurons is determined by trial and error process. Next, the most optimized activation function is also chosen. Then, using the input parameters, six ELM models are developed and the superior model and the most effective input parameter are identified through a sensitivity analysis. It is observed that the model estimates the discharge coefficient with acceptable accuracy. For instance, the coefficient of determination (R2) and the mean absolute percent error (MAPE) for this model are surmised to be 0.963 and 5.135, respectively. Also, the Froude number at the downstream of the side weir (Fd) is introduced as the most effective input parameter. Besides, a relationship is provided for calculating the discharge coefficient. Subsequently, through the conduction of an error analysis, it is concluded that the superior model has an overestimated performance. Furthermore, the partial derivative sensitivity analysis (PDSA) is carried out on the input parameters and it is proved that the PDSA value is obtained negative for all Froude numbers.