Evolutionary Pareto optimization of an ANFIS network for modeling scour at pile groups in clear water condition

The existence of waves and currents around the foundations of pile groups causes scour and reduces the stability of structures in coastal environments and rivers. In this study, a new hybrid multi-objective technique is developed to predict scour at pile groups in clear water condition. Singular Decomposition Value (SVD) and the Differential Evolution (DE) algorithm are used to determine the linear consequent parameters and nonlinear antecedent parameters, respectively, in an Adaptive Neuro-Fuzzy Inference System (ANFIS). Furthermore, the Pareto curve is used to select the tradeoff between two different objective functions, namely training error (TE) and prediction error (PE) to consider the flexibility of modeling and to optimally design the proposed method (ANFIS-DE/SVD). First, the most effective parameters on predicting scour at pile groups are determined and modeled by ANFIS-DE/SVD. Subsequently, sensitivity analysis is carried out using ANFIS-DE/SVD to identify the effect of each parameter on predicting scour at pile groups. The results indicate that the best input combination for estimating scour at pile groups includes critical velocity due to the incipient motion of sediment on the bed, mean particle diameter, flow depth, pile diameter, center-to-center distance between adjacent piles in line with the flow, center-to-center distance between adjacent piles perpendicular to the flow, number of piles parallel to the flow and number of piles normal to the flow. According to the sensitivity analysis results, the pile diameter and number of piles normal to the flow are the most effective parameters for predicting scour at pile groups in clear water condition. Furthermore, the ANFIS-DE/SVD results for the superior input combination are compared with the genetic algorithm and empirical equations. The results indicate that ANFIS-DE/SVD outperforms the other techniques. (C) 2016 Elsevier B.V. All rights reserved.