XGBoost-Based Prediction of Velocity Distribution in an Open-Channel Bend and Multilevel SHAP Interpretation of Hydrodynamic Mechanisms

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Abstract
Velocity distributions in curved open-channel flows exhibit strong three-dimensionality and nonlinear behavior, posing challenges to both accurate prediction and physical interpretation. Using measured velocity data from nine discharge–water-depth combinations in a laboratory 180° open-channel bend, this study developed an integrated eXtreme Gradient Boosting (XGBoost)–SHapley Additive exPlanations (SHAP) framework, with multiple linear regression (MLR), random forest (RF), and a back-propagation neural network (BPNN) used for comparison. Leave-one-condition-out cross-validation was used to evaluate the predictive accuracy and stability of the four models. A stratified sampling strategy was then adopted to construct the training dataset, allowing information from all flow regimes to contribute to robust parameter calibration; the two data-partitioning strategies yielded broadly comparable predictive performance. Using models trained with stratified sampling, multidimensional model evaluation was further conducted using global statistical metrics, segment-wise predictive performance, held-out extreme-condition tests, and measured–predicted agreement, among other criteria, with XGBoost consistently showing the best performance. Multilevel SHAP analyses quantified global feature importance, pairwise interactions, streamwise variations in feature contributions, SHAP–PDP dependence relationships, and condition-specific attribution. The SHAP results indicate a two-level attribution structure in the model: hydraulic variables jointly define the global velocity baseline, and their contribution signs can switch between positive and negative. Spatial variables characterize cross-sectional velocity redistribution. Strong discharge–depth interaction is associated with width-to-depth-ratio-dependent adjustment of the bend flow field. The proposed framework establishes a complete experiment-driven prediction–mechanism interpretation workflow for sharply curved open-channel flow and provides new quantitative insight into model-represented multifactor hydrodynamic interactions in open-channel bends.
Funding Information
  • Education Department of Ningxia Hui Autonomous Region (NYG2024085)
  • National Natural Science Foundation of China (12461084)
  • Science and Technology Department of Ningxia Province (2026AAC030138)

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