Assessment of Stochastic Approaches in Prediction of Wave-Induced Pipeline Scour Depth

Scouring phenomena below a pipeline exposed to waves is intrinsically a stochastic process. There is a huge level of uncertainty due to effective parameters on the scour depth prediction and mathematical shape of traditional equations for the scour depth prediction. With inspiration from previous investigations, Shields parameter ($\theta$), Keulegan–Carpenter number ($KC$), and ratio of embedded depth to pipe diameter ($e/D$) were considered as effective parameters governing on this process. Furthermore, effective parameters mentioned in this study were taken into account as random variables and the general structure of empirical equations extracted from the literature have been regarded to develop stochastic methods such as generalized likelihood uncertainty estimation (GLUE) and sequential uncertainty fitting (SUFI). Having obtained statistical error indices values such as root-mean square error (RMSE), mean absolute percentage of error (MAPE), and agreement coefficient ($d$) from the training and testing phases, it was found that both improved stochastic methods have provided adequate accuracy for predicting pipeline scour depth. Moreover, performance of the developed stochastic models and genetic programing (GP) approach were compared with those obtained using deterministic techniques using the total improvement ($I{M}_T$) index. Quantitative comparisons of the proposed stochastic models indicated that the GLUE method ($I{M}_T=21.5$ and 24.73%) was the most efficient model in clear-water and live-bed conditions with large values of $e/D$. In terms of various conditions of scouring process, the highest and least improvement occurred in the clear-water and live-bed conditions with small values of $e/D$, respectively. Ultimately, the developed stochastic methods were more efficient compared with the deterministic models in prediction of wave-induced pipeline scour depth with consideration of uncertainty.