Combined particle swarm optimization and fuzzy inference system model for estimation of current-induced scour beneath marine pipelines

In this paper the capability of Particle Swarm Optimization (PSO) is employed to deal with an Adaptive Network based Fuzzy Inference System (ANFIS) model's inherent shortcomings to extract optimum fuzzy if–then rules in noisy areas arising from the application of nondimensional variables to estimate scour depth. In the model, a PSO algorithm is employed to optimize the clustering parameters controlling fuzzy if–then rules in subtractive clustering while another PSO algorithm is employed to tune the fuzzy rule parameters associated with the fuzzy if–then rules. The PSO model's objective function is the Root Mean Square (RMSE), by which the model attempts to minimize the error in scour depth estimation with respect to its generalization capability. To evaluate the model's performance, the experimental datasets are used as training, checking and testing datasets. Two-dimensional and nondimensional models are developed such that in the dimensional model the mean current velocity, mean grain size, water depth, pipe diameter and shear boundary velocity are used as input variables while in the nondimensional model the pipe, boundary Reynolds numbers, Froude number and normalized depth of water are set as input variables. The results show that the model provides an alternative approach to the conventional empirical formulae. It is evident that the developed PSO–FIS–PSO is superior to the ANFIS model in the noisy area in which the input and output variables are slightly related to each other.