Minimal-Input Bridge Pier Scour Prediction with Critical-Velocity-Bounded Uncertainty Propagation in Data-Scarce Regions

Bridge-pier scour prediction with limited data requires parsimonious inputs, rigorous out-of-sample evaluation, and explicit treatment of hydraulic uncertainty. We developed a geometry-specific machine-learning framework with five dimensionless predictors. Nested cross-validation selected particle-swarm-optimized support vector regression (PSO-SVR) for circular piers and grid-search k-nearest neighbors (GS-KNN) for rectangular piers. Pooled out-of-fold root mean square error (RMSE)/Nash–Sutcliffe efficiency (NSE) values were 0.2614/0.6057 and 0.3395/0.6845, respectively. Across 564 common records, the models had lower RMSE than the canonical Sheppard/Melville (S/M) and Hydraulic Engineering Circular No. 18 (HEC-18) equations. Shapley additive explanations (SHAP) ranked pier Reynolds number highest for circular piers and relative flow depth highest for rectangular piers. Formulation-related critical-velocity uncertainty was propagated over a range defined by three formulations. The Qaidam cases showed substantial prediction–observation discrepancies and exceeded the circular training range in Froude number. They were therefore treated as extrapolative proof-of-concept applications. The framework supports reproducible, domain-aware minimal-input scour assessment.