基于代理指标的供水管网抗震改造优化∗

Seismic Retrofit Optimization of Water Distribution System Based on Proxy Indicators

摘要:

基于水力模型计算的管网供水量满足率（SSIQ）指标，是评估供水管网震后性能的常用指标。在供水管网抗震改造优化模型中，若采用SSIQ 表示优化目标函数，优化求解需进行大量水力模型计算，计算耗时很长。为减小管网抗震改造优化模型的计算量，对节点流量韧性指标（FR）进行了改进，增加了管道破坏漏水能量损失的影响项，提出了一种管网能量指标（Energy Resilience， ER）表示震后管网性能；以ER 指标作为SSIQ 的代理指标，用于量化抗震改造优化模型的目标函数。仅通过管道地震失效概率、管网震前正常运行工况的水力参数计算ER 指标，不必进行震后管网水力模型计算，以期提升优化模型计算效率。以供水管网震后性能最大化和改造费用最小化为目标，以管道抗震改造措施为优化变量，建立了管网抗震改造多目标优化模型，并比较了ER 指标、FR 指标以及两个拓扑代理指标的替代效果。案例管网应用结果表明，ER 指标与SSIQ 指标相关系数呈现强相关性，基于ER 指标的优化方案与基于SSIQ 指标的优化方案的差异小于3%，ER 指标优化模型计算时间不足SSIQ 指标优化模型计算时间的1%。

Abstract:

The system serviceability index of quantity (SSIQ), calculated based on hydraulic models,is a widely used indicator to evaluate the post-seismic performance of water distribution systems(WDS). However, using SSIQ as the objective function in seismic retrofit optimization models forWDS requires extensive hydraulic calculations, leading to time-consuming computational burden. Toreduce this burden, the node flow resilience (FR) indicator was improved by incorporating the impactof pipeline breakage and leakage energy loss, and a network energy indicator, energy resilience (ER),was proposed to represent the post-seismic performance of WDS. ER served as a proxy for SSIQ toquantify the objective function of a seismic retrofit optimization model. This indicator could be calculat-ed without the need for post-seismic hydraulic model calculations, which was achieved by using onlythe seismic failure probability of pipelines and the hydraulic parameters of WDS under normal opera-tions, thereby improving the computational efficiency of the optimization model. With the objectivesof maximizing the post-seismic performance and minimizing the retrofit costs of WDS, a multi-objec-tive optimization model for pipeline seismic retrofitting was established, with pipeline seismic retrofitmeasures as optimization variables. The performance of ER, FR, and two topological proxy indica-tors were compared. Network application results in the case study indicated that ER showed strongcorrelation with SSIQ, with the difference between the optimization schemes based on ER and thatbased on SSIQ being less than 3%. The computation time for the ER optimization model was lessthan 1% of that for SSIQ optimization model.