基于NSGA-Ⅱ算法的有压重力流输水系统水锤防护方案优化OA

[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,es-tablishes 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 pro-tection 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 mod-el 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.A-mong 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 in-dicators challenging.Pressure envelope comparisons confirmed that all optimized schemes restricted negative pres-sure 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 deci-sion-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 de-sign 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 com-bination 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 ref-erence for the design of water hammer protection in similar complex water transmission systems.