LAUSR

In this paper, a novel weighted regularized extreme learning machine (WRELM) was used for the first time to simulate the scour depth around J‐, I‐ and W‐shaped stone weirs in curved canals. In the first step, dimensionless parameters affecting the scour depth around stone weirs were detected. Then, six WRELM models were developed using these parameters. It is worth mentioning that three different experimental models were utilized for verifying the WRELM models. Moreover, 70% of the experimental data were used to train the models and the remaining 30% to test them. After that, the number of neurons existing within the hidden layer was chosen to be 13. Then the best activation function of the WRELM model was selected. The optimal regularization parameter was also found for this activation function. Conducting a comprehensive sensitivity analysis in the next step detected the best WRELM model, as well as the most influencing input variables. The results of the superior model were compared with the regularized extreme learning machine (RELM) and extreme learning machine (ELM) models to prove the noticeable superiority of the WRELM. Furthermore, a formula was proposed to compute the scour gap around stone weirs with different shapes situated in curved canals. Finally, the sensitivity of the input variables on scour values was examined.