Predicting maximum scour depth at sluice outlet: a comparative study of machine learning models and empirical equations

Estimating the maximum scour depth of sluice outlets is pivotal in hydrological engineering, directly influencing the safety and efficiency of water infrastructure. This research compared traditional empirical formulas with advanced machine learning (ML) algorithms, including RID, SVM, CAT, and XGB, utilizing experimental datasets from prior studies. Performance statistics highlighted the efficacy of the ML algorithms over empirical formulas, with CAT and XGB leading the way. Specifically, XGB demonstrated superiority with a correlation coefficient (CORR) of 0.944 and a root mean square error (RMSE) of 0.439. Following closely, the CAT model achieved a CORR of 0.940, and SVM achieved 0.898. For empirical formulas, although CORR values up to 0.816 and RMSE values of 0.799 can be obtained, these numbers are still lower than most ML algorithms. Furthermore, a sensitivity analysis underscored the densimetric Froude number (Fd) as the most crucial factor in ML models, with influences ranging from 0.839 in RID to 0.627 in SVM. Uncertainty in ML model estimates was further quantified using the Monte Carlo technique with 1,000 simulations on testing datasets. CAT and XGB have shown more stability than the other models in providing estimates with mean CORRs of 0.937 and 0.946, respectively. Their 95% confidence intervals (CIs) are [0.929-0.944] for CAT and [0.933-0.954] for XGB. These results demonstrated the potential of ML algorithms, particularly CAT and XGB, in predicting the maximum scour depth. Although these models offer high accuracy and higher 95% CI than others, the empirical formulas retain their relevance due to their simplicity and quick computation, which may still make them favored in certain scenarios.