Interpretable Machine Learning for Predicting and Optimizing Pressure Extremes in Pipeline Water Hammer Effects Based on the Method of Characteristics

This study seeks to address the joint optimization of placements, quantities, size parameters, and operating rules of multiple water hammer protection devices. An intelligent, explainable prediction and optimization framework is introduced to control water hammer effects during pump shutdown in water transmission pipelines. Leveraging Method of Characteristics (MOC) simulation data, the explainable machine learning (ML) model captures the relationships between pipeline operational parameters and protective device configurations. Moreover, an optimization model for water hammer protection measures has been established. Key findings include: (1) Among the evaluated ML models, XGBoost consistently achieved the highest performance, achieving R2 values of 0.92, 0.93, and 0.91 for Pmin, Hmax, and vmax. (2) Air vessel volume and preset pressure most strongly influence water hammer mitigation, significantly reducing both peak pressures and negative-pressure magnitudes while inhibiting excessive pump reversal. (3) A threshold effect emerges for air vessel parameters, beyond which additional increases offer diminishing returns due to nonlinear system constraints. (4) The optimized scheme improves hydraulic stability, raising the negative pressure by 6.07 m H2O relative to the measured vapor limit (− 9.80 m H2O), while maintaining Hmax and vmax within safe operational bounds. Overall, this research advances water hammer protection design, offering quantifiable improvements in safety, reliability, and cost efficiency for small- and medium-scale water conveyance systems prone to severe negative pressure. By integrating explainable ML insights in both the predictive and optimization phases, the proposed framework delivers a comprehensive approach to safeguarding pipelines against critical transient conditions.