Predicting local scour depth of bridge piers using hybrid particle swarm optimization and gray wolf optimizer

Construction of bridge piers is expensive, and scouring near them can lead to instability. Without a suitable solution, it can ultimately result in the structure’s destruction. Therefore, a detailed study is required to understand this phenomenon and the factors affecting it. This research entails utilizing extensive field data to measure the local scour depth around bridge piers. It proposes an equation comprising scour-affecting parameters and defines an optimization model to establish this relationship. The decision variables of this model were determined using a meta-heuristic algorithm called the hybrid gray wolf-particle swarm (HPSGWO). For this purpose, various relationships were established to ascertain scour depth, and subsequently, the local scour depth of the bridge piers was calculated, based on these equations. Root Mean Square Error (RMSE), Relative Square Root (RSR), Nash-Sutcliffe Efficiency (NSE), Percent Bias (PBIAS), and Correlation Coefficient (CC) were employed as error measurement indices to evaluate the relationships. Upon comparison of the error measurement indices for the obtained relationships, the best input parameter combination and mathematical relationship for calculating scour depth were determined. These indices for the superior model are equal to 0.504 m, 0.52, 0.73, 7.7%, and 0.734 for RMSE, RSR, NSE, PBIAS, and CC, respectively. These values show that the equation presented in this research is suitable for calculating scour depth and is more reliable than the presented experimental methods. In the proposed relationship, scour depth is directly proportional to the Froude number and the ratio of base width to water depth while inversely proportional to the average size of bed particles to water depth.