Optimization of Protection Device Parameters for Pump-Stopping Water Hammer Protection in Long-Distance Water Conveyance Pipelines via Hybrid NSGA-II

Water hammer in long-distance pumped water transmission pipelines can cause severe safety incidents, making effective protection for pipelines and pump stations essential. However, optimizing parameters of water hammer protection devices remains challenging, as engineers often rely on time-consuming, experience-based trial-and-error methods. To address this, a multi-objective optimization framework combining Random Forest and Non-dominated Sorting Genetic Algorithm II is proposed. An RF model is trained to map relationships between device parameters and extreme water hammer pressures. A multi-objective optimization model is developed with unidirectional surge tower water level, maximum pressure, and minimum pressure as objectives. Furthermore, SHapley Additive exPlanations (SHAP), an interpretable machine learning method, is employed to reveal the importance and interactions of parameters. Results show that the approach rapidly identifies optimal device settings, achieving a 79% increase in minimum pressure, a 25% reduction in surge tower water level, and negligible change in maximum pressure compared with the original design. SHAP analysis indicates that connecting pipe diameter and local resistance coefficient of the downstream air vessel are the most influential factors; moreover, the rise in positive pressure peaks from larger connecting pipe diameters can be mitigated by increasing the local resistance coefficient. The findings provide practical guidance for similar engineering applications.