Probabilistic Prediction and Reliability Analysis of Abutment Scour Depth Using Natural Gradient Boosting

Reliable prediction of abutment scour requires accurate point estimates and quantification of predictive uncertainty. This study developed a NGBoost (Natural Gradient Boosting) framework using 297 laboratory observations under clear-water conditions across three abutment geometries. Hyperparameters were optimized using Optuna, with separate training, validation, calibration, and test sets. The model achieved a test-set R2 of 0.980 and a root mean square error of 0.094. At the 95% nominal level, prediction-interval coverage was 96.67%, and the mean interval width was 26.69% smaller than that of split conformal prediction. Feature analyses identified the abutment Froude number and abutment geometry as important predictors. Monte Carlo simulation was used for a distribution-level reliability analysis based on independent sampling from measured and predictive scour-depth distributions. A design correction factor of 2.04 corresponded to a target reliability index of 1.5. The results demonstrate the potential of NGBoost for probabilistic abutment-scour assessment, while indicating the need for field validation and reliability analyses that account for dependence between measurements and predictions.