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

Abstract 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 (RF) and nondominated sorting genetic algorithm II (NSGA- 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 quantitatively verifies that connecting pipe diameter and local resistance coefficient of the downstream air vessel are the dominant parameters governing transient pressure behavior. The nonlinear interaction of the two parameters is quantitatively characterized, showing that the increase in positive-pressure peaks induced by a larger connecting pipe diameter can be counterbalanced by a corresponding rise in local resistance coefficient, reflecting a codependent mechanism between flow inertia and local head loss. This data-driven interpretation provides quantitative insight into parameter coupling and offers practical guidance for optimizing water-hammer protection device design.