Application of nature-inspired optimization algorithms to ANFIS model to predict wave-induced scour depth around pipelines

Wave-induced scour depth below pipelines is a physically complex phenomenon, whose reliable prediction may be challenging for pipeline designers. This study shows the application of adaptive neuro-fuzzy inference system (ANFIS) incorporated with particle swarm optimization (ANFIS-PSO), ant colony (ANFIS-ACO), differential evolution (ANFIS-DE) and genetic algorithm (ANFIS-GA) and assesses the scour depth prediction performance and associated uncertainty in different scour conditions including live-bed and clear-water. To this end, the non-dimensional parameters Shields number (θ), Keulegan–Carpenter number (KC) and embedded depth to diameter of pipe ratio (e=D) are considered as prediction variables. Results indicate that the ANFIS-PSO model (R ² _{live bed} ¼ 0:832 and R ² _{clear water} ¼ 0:984) is the most accurate predictive model in both scour conditions when all three mentioned non-dimensional input parameters are included. Besides, the ANFIS-PSO model shows a better prediction performance than recently developed models. Based on the uncertainty analysis results, the prediction of scour depth is characterized by larger uncertainty in the clear-water condition, associated with both model structure and input variable combination, than in live-bed condition. Furthermore, the uncertainty in scour depth prediction for both live-bed and clear-water conditions is due more to the input variable combination (R-factor _ave ¼ 4:3) than it is due to the model structure (R-factor _ave ¼ 2:2).