Prognostication of scour around twin and three piers using efficient outlier robust extreme learning machine

One of the most essential difficulties in the design and management of bridge piers is the estimation and modeling of scouring around the piers. The scour depth downstream of twin and three piers were simulated using a new outlier robust extreme learning machine (ORELM) model in this study. Furthermore, k-fold cross-validation with k = 4 was employed to validate the outcomes of numerical models. Four ORELM models with effective scouring parameters were first created to simulate scour depth. After then, the number of hidden layer neurons increased from two to thirty. The number of ideal hidden neurons was determined by examining the modeling results. The sigmoid activation function was also introduced as the best function. Furthermore, a sensitivity analysis was used to identify the superior model. The best model predicted scour depth as a function of the Froude number (Fr), the pier diameter to flow depth ratio (D/h), and the distance between the piers to flow depth ratio (d/h). The values of the objective function were accurately approximated by this model. As a result, using the ORELM model, the R², scatter index, and Nash-Sutcliffe efficiency coefficient were calculated to be 0.953, 0.146, and 0.949, respectively. The most efficient parameters for simulating the scour depth were Fr and D/h, according to the modeling results. It is worth noting that nearly half of the superior model's simulated outputs had an inaccuracy of less than 10%. The superior model's performance has been underestimated, according to uncertainty analysis. After that, a simple and practical equation for calculating the scour depth was established for the superior model. Additionally, the influence of each input parameter on the objective function was assessed using a partial derivative sensitivity analysis.