Estimation of scour depth around submerged weirs using self-adaptive extreme learning machine

In this study, the equilibrium scour depth downstream of the weir (ds-a), the maximum scour depth downstream of the weir (ds-max), the equilibrium scour depth upstream of the weir (dus-a) and the maximum scour depth upstream of the weir (dus-max) were simulated around the submerged weirs using the self-adaptive extreme learning machine (SAELM) model. In other words, the SAELM was utilized for the simulation of the scour depths around submerged weirs for the first time. In addition, Monte Carlo simulations (MCSs) were used to increase the accuracy of the artificial intelligence model. The results of modeling were validated using k-fold cross validation. At first, all effective parameters on the scour depth were determined and five distinct SAELM models were defined. Then, the optimal activation function of the SAELM model was obtained. By analyzing the results of modeling, the best models were identified to estimate ds-a/ht, ds-max/ht, dus-a/ht, and dus-max/ht, and the ratio of the average inflow velocity to the critical velocity (U0/Uc) was determined as the most effective input parameter. In the following, the results of superior models were compared with the artificial neural network (ANN) and support vector machine (SVM). The results showed that SAELM models were more accurate. The uncertainty analysis was performed for these models, some of them were overestimated and others were underestimated. In addition, some equations were presented for equilibrium models for calculation of scour depth around the submerged weirs, which are used by environmental and hydraulic engineers without previous knowledge about the artificial intelligence models. Finally, a partial derivative sensitivity analysis (PDSA) was performed for all input parameters of the superior models.