Pareto design of multiobjective evolutionary neuro-fuzzy system for predicting scour depth around bridge piers

Abstract A new multiobjective-based method is developed to predict the scour depth around bridge piers using a wide-ranging field dataset. The differential evolution (DE) algorithm and singular value decomposition (SVD) are utilized to optimize the parameters of nonlinear antecedent and linear consequent of the Gaussian membership function of adaptive neuro-fuzzy inference system (ANFIS) (ANFIS-DE/SVD). To attain a flexible model, the objective functions of training error and predicting error are formulated, and a Pareto curve is employed to choose the trade-off between these two objective functions as the optimal ANFIS design. The effect of every parameter on scour depth is surveyed through 26 combinations of input to identify the best model. Subsequent to finding the optimal combination, the performance of ANFIS-DE/SVD is compared with regression-based equations. The results indicate the superior performance of ANFIS-DE/SVD [R=0.95; mean absolute relative error (MARE)=0.25; root mean squared error (RMSE)=0.23; scatter index (SI)=0.38; BIAS=0.02)]. The estimation uncertainty of the developed ANFIS-DE/SVD was calculated and compared with classical regression-based and artificial intelligence-based techniques and found to be the least with a value of ±0.027. The results of the current study demonstrated that ANFIS-DE/SVD presented the highest accuracy with a remarkable enhancement of predicting accuracy. Generally, it can be deduced from the current study that (1) developed ANFIS-DE/SVD is appropriate for scour depth prediction around bridge piers with different pier shapes; (2) the optimization of the classical ANFIS is helpful capturing the complex 3D nature of the scour depth mechanism and improving the accuracy of prediction; (3) the proposed ANFIS-DE/SVD is a premier alternative, which can present reliable and precise predictions for optimal design.

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