Forecasting of time-dependent scour depth based on bagging and boosting machine learning approaches

Forecasting the time-dependent scour depth (d_st) is very important for the protection of bridge structures. Since scour is the result of a complicated interaction between structure, sediment, and flow velocity, empirical equations cannot guarantee an advanced accuracy, although they would preserve the merit of being straightforward and physically inspiring. In this article, we propose three ensemble machine learning methods to forecast the time-dependent scour depth at piers: extreme gradient boosting regressor (XGBR), random forest regressor (RFR), and extra trees regressor (ETR). These models predict the scour depth at a given time, d_st, based on the following main variables: the median grain size, d₅₀, the sediment gradation, σ_g, the approach flow velocity, U, the approach flow depth y, the pier diameter D_p, and the time t. A total of 555 data points from different studies have been taken for this research work. The results indicate that all the proposed models precisely estimate the time-dependent scour depth. However, the XGBR method performs better than the other methods with R = 0.97, NSE = 0.93, AI = 0.98, and CRMSE = 0.09 at the testing stage. Sensitivity analysis exhibits that the time-dependent scour depth is highly influenced by the time scale.