Modeling triangular, rectangular, and parabolic weirs using weighted robust extreme learning machine

Abstract

Abstract In this study, dimensionless parameters influencing the coefficient of discharge (COD) are found and four different WRELM models are developed. After that, a dataset is created for verifying the WRELM models in which 70% of the data are employed to train learning machine models and the remaining 30% to test them. For the mentioned algorithm, the optimal number of hidden layer neurons along with the best activation function is chosen. Additionally, the best value for the regularization parameter of the WRELM algorithm is computed. By analyzing the simulation results, the superior WRELM model and the variables impacting the COD are detected. The superior WRELM model approximates COD values with the minimum error and the highest correlation with laboratory values. For the superior model, the values of the R, MAE and VAF statistical indices are computed to be 0.994, 0.0004 and 98.662, respectively. The analysis of the simulation results indicates that the dimensionless parameters α and T/B are the most influencing input parameters. The superior WRELM model results are compared with the algorithm, and it is concluded that the WRELM model is noticeably more efficient. For the superior WRELM model, a partial derivative sensitivity analysis (PDSA) is conducted in which as the input parameter α increases, the PSDA value increases as well. Finally, an equation is suggested for estimating COD values.

Keywords

• Coefficient of discharge
• Triangular weir
• Rectangular weir
• Parabolic weir
• Weighted robust extreme learning machine
• Modeling