Application of an evolutionary technique (PSO–SVM) and ANFIS in clear-water scour depth prediction around bridge piers

The mechanism of the local scour around bridge pier is so complicated that it is hard to predict the scour accurately using a traditional method frequently by considering all the governing variables and boundary conditions. The present study aims to investigate the application of different hybrid soft computing algorithms, such as particle swarm optimization (PSO)-tuned support vector machine (SVM) and a hybrid artificial neural network-based fuzzy inference system to predict the scour depth around different shapes of the pier using experimental data. The important independent input parameters used in developing the soft computing models are sediment particle size, a velocity of the flow and the time taken in the prediction of the scour depth around the bridge pier. Different pier shapes used in the present study are circular, round-nosed, rectangular and sharp-nosed piers. The accuracy and efficiency of the two hybrid models are analyzed and compared with reference to experimental results using model performance indices (MPI) such as correlation coefficient (CC), normalized root-mean-squared error (NRMSE), normalized mean bias (NMB) and Nash–Sutcliffe efficiency (NSE). The ANFIS model with Gbell membership and the PSO–SVM model with polynomial kernel function yield good results in terms of MPI. The performance of PSO–SVM with polynomial kernel function with CC of 0.949, NRMSE of 7.47, NMB of − 0.009 and NSE of 0.90 reveals that the hybrid ANFIS model with Gbell membership function yields slightly better than that of the PSO–SVM model with CC of 0.950, NRMSE of 6.92, NMB of − 0.002 and NSE of 0.91 for the optimum bridge pier with circular shape, whereas the performance of PSO–SVM model is better than that of ANFIS model for optimum bridge piers with rectangular and sharp nose shape. The PSO–SVM model can be adopted as accurate and efficient alternative approach in predicting scour depth of the pier.