Bayesian neural networks for prediction of equilibrium and time-dependent scour depth around bridge piers

The physical process of scour around bridge piers is complicated. Despite various models presented to predict the equilibrium scour depth and its time variation from the characteristics of the current and sediment, scope exists to improve the existing models or to provide alternatives to them. In this paper, a neural network technique within a Bayesian framework, is presented for the prediction of equilibrium scour depth around a bridge pier and the time variation of scour depth. The equilibrium scour depth was modeled as a function of five variables; flow depth and mean velocity, critical flow velocity, median grain diameter and pier diameter. The time variation of scour depth was also modeled in terms of equilibrium scour depth, equilibrium scour time, scour time, mean flow velocity and critical flow velocity. The Bayesian network predicted equilibrium and time-dependent scour depth much better when it was trained with the original (dimensional) scour data, rather than using a non-dimensional form of the data. The selection of water, sediment and time variables used in the models was based on conventional scour depth data analysis. The new models estimate equilibrium and time-dependent scour depth more accurately than the existing expressions. A committee model, developed by averaging the predictions of a number of individual neural network models, increased the reliability and accuracy of the predictions. A sensitivity analysis showed that pier diameter has a greater influence on equilibrium scour depth than the other independent parameters.