Scour at bridge piers in uniform and armored beds under steady and unsteady flow conditions using ANN-APSO and ANN-GA algorithms

Abstract

ABSTRACT Precise estimation of the local scour at bridge piers, considering flow unsteadiness and bed non-uniformity is crucial for economic and safe design of bridge piers. This study investigates scour at bridge piers in uniform and armored beds, under steady and unsteady flow conditions, applying feed-forward back-propagation (FFBP) artificial neural network (ANN) combined with evolutionary algorithms, using different data sets. ANN is well suited for complex pattern-sorting problems. However, their practical application is made difficult by the lack of a training algorithm, finding a global optimum weight in a relatively short time. Thus, evolutionary algorithms, including adaptive particle swarm optimization (APSO) and genetic algorithms (GA) are applied as exceptional tools for training and tuning the parameters of the proposed ANN models. Based on the available benchmark test data, the ANN-APSO model (with RMSE = 0.142 and 0.059 and R2 = 0.952 and 0.925 for steady and unsteady flow conditions, respectively) and ANN-GA model (with RMSE = 0.196 and 0.048 and R2 = 0.918 and 0.946 for steady and unsteady flow conditions, respectively) are shown to be superior to FFBP-ANN model (with RMSE = 0.214 and 0.106 and R2 = 0.891 and 0.838 for steady and unsteady flow conditions, respectively). Accordingly, the proposed ANN-APSO model is the best tool to evaluate the scour depth at bridge piers in uniform sediment beds under steady flow condition. It can be seen that the ANN-GA algorithm has the best fitness values compared to those of the ANN-APSO algorithm and the other reported approaches in uniform and armored sediment beds under unsteady flow condition. The developed models provide good approximations of the benefits of an FFBP-ANN combined with GA and APSO algorithms compared with a FFBP model, being superior in precision and time consumption.