基于剩余能量熵的供水管网可靠性优化设计

针对供水管网(WDS)的可靠性优化设计问题, 提出将剩余能量熵作为可靠性度量指标,建立以剩余能量熵最大化、以管网建造年费用和运行费用最小化为设计目标的多目标优化模型.结合一典型管网算例,应用非支配排序遗传算法-II（NSGA-II）并引入诱导变异算子求解该模型,给出设计目标间的Pareto前沿面.优化结果表明,成本和采用剩余能量熵描述的可靠性指标得到了显著的优化,诱导变异算子的引入大大加快了种群向目标解域的收敛速度.在解集中,将剩余能量熵与Vaabel提出的剩余能量因子和Todini提出的恢复力指标进行比较.比较结果显示,剩余能量熵与剩余能量因子、恢复力指标均存在很好的正相关关系,证实了以剩余能量熵作为可靠性指标的可行性.通过比较管网在各管段依次发生故障时的剩余能量熵和流量熵,发现剩余能量比流量熵更能够灵敏地反映故障工况,表明基于剩余能量熵指标设计的管网更能够提高管网应对故障的能力.

Reliability optimization design of water distribution system based on surplus energy entropy

For reliability optimization design in water distribution system (WDS), a multi-objective optimal design model was proposed using surplus power entropy (SPE) as the capacity reliability index. In this model, three design objectives were considered, including maximizing the SPE, minimizing the present value of construction capital cost and minimizing the operating cost of WDS. A typical network case was introduced and solved by the non-dominated sorted genetic algorithm-II (NSGA-II) with inducement mutation operator. Pareto fronts of the model were plotted among design objectives. The optimization results show that there was significant trade-off among costs and capacity reliability index represented by SPE. The introduction of inducement mutation operator greatly accelerates the convergence speed of population toward the target solution domain. The SPE was compared with the surplus power factor developed by Vaabel and the resilience index developed by Todini respectively. The comparison results show that a positive relationship between the SPE and the latter two, which confirms the feasibility of the SPE being used as an indicator of capacity reliability. A comparison between SPE and flow entropy of WDS under a range of pipe failures demonstrates that SPE is more sensitive to failure conditions than flow entropy index. The network designed by SPE can increase the capacity of the WDS to respond to failure problems．