Chapter 7 - Pareto Multiobjective Bioinspired Optimization of Neuro-Fuzzy Technique for Predicting Sediment Transport in Sewer Pipe

Abstract

One of the most important concerns in the open-channel project regards estimating the minimum velocity required to prevent sedimentation. The higher performances of the artificial intelligence (AI)-based techniques than classical regression-based models were proved in the sediment-transport modeling. One of the well-known AI-based methods is the adaptive neuro-fuzzy inference system (ANFIS). The main issues that should be considered in ANFIS are optimization of the linear consequent parameters and nonlinear antecedent parameters. To do that the individual ANFIS applied a hybrid algorithm (a combination of the backpropagation and least-square algorithms). To enhance the predictive performance of the ANFIS, the evolutionary algorithms, including differential evolution (DE) and genetic algorithm (GA) (ANFIS-DE and ANFIS-GA), were integrated with individual ANFIS as a single-objective optimization. In this study a new multiobjective evolutionary Pareto optimal design of an ANFIS model is developed to evaluate sediment transport in pipe channels. The singular value decomposition (SVD) and bioinspired evolutionary-based optimization algorithm (i.e., DE and GA) are used to optimally improve the Gaussian membership functions of the linear consequent and nonlinear antecedent parameters, respectively, in ANFIS. Two different target functions, which are known as prediction error and training error, are applied, and by using the Pareto curve, the trade-off between these functions is chosen as the optimum modeling point. The developed hybrid ANFIS models (ANFIS-DE/SVD and ANFIS-GA/SVD) and an extensive range of experimental datasets collected from literature are employed to predict the minimum velocity with different input combinations. An assessment of the developed multiobjective ANFIS-based method with single-objective optimization of ANFIS (ANFIS-DE and ANFIS-GA) and individual ANFIS indicates the higher performance of the developed multiobjective techniques (R = 0.99; mean average percentage error = 3.65; root-mean-square error = 0.04; scatter index = 0.01; bias = 0.03; ρ = 0.005). The prediction uncertainty of the developed multiobjective models is quantified and compared with other ones.