长距离重力流输水工程中水锤易致管道振动破裂,严重威胁供水安全。以新疆某地区JK输水工程为研究对象,采用多目标遗传算法(NSGA-Ⅱ)和特征线法(MOC)构建输水系统水锤防护多目标优化模型,以安全性指标和经济性指标为目标函数对优化模型求解。实例分析表明,基于NSGA-Ⅱ的优化方法可生成一系列Pareto最优方案,既能显著降低最大水锤压力(降幅约13.21%),又能有效控制防护设备规模与成本(空气罐体积减少约28.6%);优化方案C作为最终实施方案:布置7个气囊式空气罐,空气罐体积为5 000 m³,预设压力为1.2H^*,连通管内径为600 mm。研究结果对长距离重力流输水系统的水锤防护设计具有理论指导意义与工程参考价值。

[Objective] Water hammer effect in long-distance gravity-flow water transmission projects threatens the safety and stability of system operation. Current research has predominantly focused either on pumped water supply systems or on the optimization of single-objective parameters. Focusing solely on either maximum-pressure control or cost minimization makes it difficult to balance safety and economy, which often leads to insufficient protection or overdesign in engineering practice. This study, based on the Xinjiang JK gravity-flow water transmission project, establishes a multi-objective optimization model for water hammer protection that integrates the multi-objective genetic algorithm with the method of characteristics (MOC). The study aims to identify the safest and most economical protection strategy. [Methods] This study employed an integrated approach combining the NSGA-II multi-objective genetic algorithm and MOC to construct a multi-objective optimization model for water hammer protection. The model incorporated 12 decision variables encompassing parameters of various protective devices and evaluated three combined protection strategies: Scheme A (air valve + unidirectional surge tank + water hammer relief valve), Scheme B (air valve + bidirectional surge tank), and Scheme C (air valve + air vessel). The maximum water hammer pressure was used as the safety indicator, while the total project cost served as the economic indicator. The multi-objective optimization model was configured with a population size of 50, a crossover probability of 0.8, and a mutation probability of 0.05. After 200 generations of iteration, the optimal Pareto front was obtained. Finally, the optimized parameters were validated through transient water hammer simulation using MOC to accurately assess maximum pressures, thereby enabling a comprehensive trade-off analysis between safety and economy across all schemes. [Results] All three protection schemes effectively reduced water hammer pressure and controlled costs.Among them,Scheme C (air valve+air vessel) delivered the best overall performance:the volume of the air vessel was reduced by 28.6%,significantly cutting project investment;the maximum water hammer pressure decreased from 135.82 m to 117.88 m,a 13.2% reduction,meeting all engineering safety requirements.Although Schemes A and B also showed improvements,Scheme A exhibited relatively weaker overall pressure control compared with Scheme C,because of the limited capability of air valves and unidirectional surge tanks to suppress positive pressure,rendering it more dependent on the relief valve.Scheme B,while demonstrating good regulatory performance,entailed higher construction costs due to the need to maintain a higher design water level,making further reduction of economic indicators challenging.Pressure envelope comparisons confirmed that all optimized schemes restricted negative pressure within the safe limit of -10 m,completely avoiding the risk of cavitation and column separation water hammer.The Pareto solution set was uniformly distributed and exhibited strong convergence,clearly revealing quantitative trade-offs between safety and economy under different preferences, thereby providing a rational and diverse decision-making framework for engineering applications. [Conclusion] The proposed model effectively reconciles the competing relationship between safety and economy, addressing a critical engineering challenge that traditional design methods have struggled to solve—simultaneous pressure control and cost optimization.Case study results show that the model generates a well-distributed and convergent Pareto-optimal solution set.Among all schemes,the combination of air valves and air vessels (Scheme C) exhibits the best comprehensive performance due to its effective regulation of both positive and negative pressures and relatively lower construction and operational costs.The model demonstrates strong generalizability and broad applicability, offering valuable theoretical guidance and practical reference for the design of water hammer protection in similar complex water transmission systems.