Robust Extreme Learning Machine for estimation of triangular, rectangular, and parabolic weirs

Abstract

In this paper, for the first time, the DC of triangular, rectangular, and parabolic weirs is simulated by a new learning machine called “Robust Extreme Learning Machine” (RELM). The used laboratory data are divided into two categories: training (70% data) and testing (30% data). In the next step, the number of neurons inside the hidden layer is examined. For the structure of the proposed RELM algorithm, 10 hidden layer neurons are embedded. For the learning machine used in the present study, six different activation functions are evaluated that the Sigmoid activation function has better performance and is used for the RELM structure. Next, the calibration parameter of the RELM algorithm is discussed. The optimal regularization parameter is selected for the present study equal to 0.0001. Then, using parameters affecting the DC, four RELM models are developed. By performing various analyzes, the superior RELM model and the most effective input parameters are identified. Also, comparing the performance of the RELM model with ELM shows the superiority of the RELM algorithm. For the superior model, a relative derivative sensitivity analysis is performed to investigate the behaviour of the input parameters on the DC. Finally, an equation for estimating the DCs of triangular, rectangular, and parabolic weirs is proposed.