Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions

• The NF-GMDH model was applied as a new soft computing tool for predicting the scour depth at pile groups.
• Two evolutionary algorithms of PSO and GSA developed the NF-GMDH network for the training stage.
• The NF-GMDH-PSO predicted the scour depth with relatively lower error than NF-GMDH-GSA.
• Performing the empirical equations indicated higher error in comparison with the NF-GMDH models.
• Sensitivity analysis indicated that D is the most important parameter in modeling of scour depth.

In this paper, neuro-fuzzy based group method of data handling (NF-GMDH) as an adaptive learning network was utilized to predict the local scour depth at pile groups under clear-water conditions. The NF-GMDH network was developed using particle swarm optimization (PSO) and gravitational search algorithm (GSA). Effective parameters on the scour depth include bed sediment size, geometric properties, piles spacing, arrangements of pile group, and flow characteristics in upstream of group piles and critical flow condition due to initiation of particles’ motion on bed surface. Nine dimensional parameters were considered to define a functional relationship between input and output variables. The NF-GMDH models were carried out using datasets collected from the literature. The efficiency of training stages for both NF-GMDH-PSO and NF-GMDH-GSA models was investigated. Testing results for the NF-GMDH networks were compared with the empirical equations. The NF-GMDH-PSO network produced more efficient performance (R=0.95 and RMSE=0.035) for scour depth prediction compared with the NF-GMDH-GSA model (R=0.94 and RMSE=0.036). The NF-GMDH models indicated quite higher accuracy of scour prediction, compared with the empirical equations (R=0.44 and RMSE=0.127). Also, the sensitivity analysis indicated that pier diameter was the most significant parameter on scour depth.

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