清华大学 工程物理系, 公共安全研究院, 北京 100084
收稿日期:2023-02-06
基金项目:国家自然科学基金重大项目(72091512)
作者简介:史政一(1999-), 男, 博士研究生
通讯作者:黄弘, 教授, E-mail: hhong@tsinghua.edu.cn
摘要:许多事故和灾害事件表明, 城市基础设施系统之间的关联性可能会逐级放大事故或灾害的初始影响, 对城市、地区乃至国家产生非常大的危害, 因此研究在外界影响下城市基础设施系统之间关联性的表现和特征非常重要。该文以风险容忍度框架为基础, 对某城市区域的供水和供电网络的关联性开展研究, 根据若干网络参数的演化和分布特点, 分析了供水和供电网络面临外界随机冲击下的风险容忍度。随后对供水和供电网络间的地理关联性进行分析, 识别出了断电场景下供水网络中的关键组分。该研究为城市基础设施防护、规划、应急处置和韧性提升提供了支撑和参考。
关键词:城市基础设施供水网络供电网络风险容忍度地理关联性
Interdependencies between city water and electricity supply networks based on attack tolerance
SHI Zhengyi, HUANG Hong, ZHOU Shiwei
Institute of Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing 100084, China
Abstract: [Objective] Historical events suggest that infrastructure interdependencies exhibit negative influence in an amplifying or cascading way, leading to remarkably outcomes on an urban, regional, or even national scale. Therefore, studies on infrastructure interdependencies play a vital role. The interdependency-caused vulnerability of water and electricity supply networks, as components of city lifeline, generally poses risks to people's life safety, daily life, and industry functioning. [Methods] A case study of water and electricity supply networks of a district was conducted to measure their interdependencies in the frame of attack tolerance, thus innovatively advancing from its usual use in studies on the World Wide Web and social networks. Infrastructure systems tend to possess certain spatial structures, especially network-like ones such as water and electricity supply networks, rendering topological methods effective and straightforward. An attack tolerance framework based on graph theory was applied in this research. Two graph models were established using the Python NetworkX library prior to checking the correctness of the modeling. The degree of each vertex was calculated, and its frequency density curve was drawn to match the network characteristics with those of an exponential network, such as a water or electricity supply network. Subsequently, the fragmentation of the networks was studied. When the vertices were removed to simulate a random external attack, the original network as a whole disintegrated into multiple disconnected small components known as vertex clusters. This process is called fragmentation. The quantitative characteristics of vertex clusters, together with the basic network index called network diameter, served as indices of attack tolerance. The curves of the indices above the proportion of removed vertices and the distribution scatters of cluster size at a certain removed proportion were drawn to measure and compare the attack tolerance between the two networks. In addition, the distribution scatters were fit to an exponential form including two parameters and the curve of the parameters to the removed proportion was drawn. Finally, this study introduced a measure of geographical interdependency between water and electricity networks based on a previous attack tolerance study. The two networks were placed in the same coordination system that had been gridded rectangularly with a certain fineness. The hypothesis was that the electricity of each water vertex was provided by the nearest electricity vertex; the former was removed when the latter malfunctions. Vertices in each rectangle of the grid were completely removed to simulate a blackout of a district, and a geographical interdependency index was defined for every grid reference in accordance with the fragmentation indices. This research visualized the spatial distribution of the interdependency index at a certain grid fineness, through which the critical sections could be identified. [Results] The attack tolerance of the water supply network was slightly remarkable, and the southeast region of the water supply network of this district was the most dependent on the electricity supply network. [Conclusions] This work introduced an interdependency analysis method based on the framework of attack tolerance of a topological network and provided guidelines for the protection of infrastructure systems, urban planning, contingency plans, and resilience enhancements.
Key words: city infrastructurewater supply networkelectricity supply networkattack tolerancegeographical interdependency
城市基础设施的持续、稳定运行是维护国家安全、发展社会经济、维持社会稳定及保障人民生活的基础。20世纪末,美国关键基础设施保护总统委员会(PCCIP)和美国关键基础设施保障办公室(CIAO)提出了基础设施系统的定义,是指一个由许多独立运行、功能互通且协同运作的为了生产和分配必需商品和服务的人造系统组成的网络,除各类实体设施外,还包括社会产业、制度、分配关系等非实体设施[1]。随着社会经济和科学技术的发展,基础设施系统的网络结构越来越复杂,高效率、大体量的运行增加了基础设施系统组分之间的相互关联程度,同时增加了系统的脆弱程度。施加在某一个或若干个组分上的破坏会通过关联性逐级放大,最终甚至可能扩大到整个地区、国家,乃至全球范围[2]。例如,2008年初,中国中南部遭受特大暴雪侵袭,大雪、结冰和低温对基础设施系统造成了严重的影响。暴雪直接造成电力短缺、交通阻塞,进而导致通信中断、应急系统停摆、经济受损、商业停滞,以及食物、油气、供水短缺等,整个基础设施系统出现了广泛的失效后果,造成经济损失1 111亿元[3]。
随着城市基础设施系统规模的不断扩大,认识、理解和分析其间的关联性变得越来越重要。国内外****开展了涉及多个维度、不同学科的研究。Rinaldi等[2]在2001年指出了基础设施系统相互关联的类型、反馈模式和失效影响,以及建模仿真工作面临的挑战。Zimmerman[4]、Dudenhoeffer等[5]、Wallace等[6]、Zhang等[7]从不同的角度解释基础设施系统关联性,并按不同的标准进行分类。基于智能体、系统动力学、经济学和拓扑学等多种方法模型被应用到基础设施关联性分析研究中[8-13]。
在城市关键基础设施系统中,供水和供电系统作为城市的“生命线”,影响着居民的生命安全、正常起居,以及工业部门的运转[14]。2011年,日本东部发生里氏9.0级地震,供水和供电系统均遭受不同程度的破坏,当日造成70万户居民供水短缺、474万户停电。供水和供电系统恢复90%的供应水平分别花费了41和7 d,对居民的正常生活造成了巨大影响[15]。供水和供电系统不但功能关键,而且关联紧密。供水系统中的水泵、阀门和控制系统均依赖于供电系统,供电系统组分的失效也会相继造成供水系统中地理位置邻近的相关联组分失效[16]。郑艺婷等[17]采用图论和Monte Carlo模拟的方法,定量地分析了地震灾害下供电系统对供水节点可靠性的影响。张超等[18]对供水和供电系统建立异质网络模型,以节点间物质和能量的传输关系为基础,采用关联失效动力学的方法,分析研究了网络失效的动力学传播的特性,并基于级联失效模式给出了对应的修复策略。
基础设施关联性可以用韧性[19]、脆弱性[20]、可靠性[21]等衡量,但在网络规模较大,包含上千个节点时,往往需要进行大量的计算[22]。
本文使用某城市区域供水和供电系统的管线测绘数据,分别建立2个基础设施系统的网络模型。之后以拓扑学为基础,基于网络风险容忍度分析框架,定量分析供水和供电网络在外部随机攻击下的风险容忍度。最后,模拟一个供电网络失效导致供水网络受影响的场景,结合供水网络的连通性和风险容忍度,定量给出2个系统间的地理位置关联性。本方法可以通过分析网络的整体拓扑特性,直观地体现网络抵抗外部冲击的能力。
1 研究方法本文提出的关联性分析框架如图 1所示。
图 1 供水和供电网络关联性分析框架 |
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1.1 基于网络的建模方法基础设施系统往往具有一定的地理位置和空间结构,尤其是供水管线、供电线路等网络状系统,所以拓扑学工具是直观地研究网络状基础设施系统关联性的有效手段,其中基于网络的建模方法应用广泛[8]。该方法以图论为理论依据。可记网络状基础设施系统为网络
在供水和供电网络中,水流和电流沿确定的方向在输水管道和输电线中流动,有向网络能很好地反映这种定向关系,但若只需要考察2个网络的拓扑关联特性且不涉及流、系统控制[9]或模拟仿真[23],则使用无向网络对结果没有影响。本文将建立无向有权网络, 即网络中任意2个节点间仅有最多1条边相连, 且所有的边都没有确定的方向。设权重的集合为
建立网络后, 本文将检验建模的合理性。网络分为指数网络与无标度网络, 绝大多数供水和供电网络都是指数网络。对一个连通网络, 定义与节点
1.2 网络的风险容忍度分析方法本文通过网络直径
1)
$d=\sum\limits_{u, v \in V} \frac{l_{u v}}{n(n-1)} .$ | (1) |
$f=\frac{\left|V_{\mathrm{r}}\right|}{n}, 0 <f<1 .$ | (2) |
$G^{\prime}=\bigcup\limits_{p=1}^{c} S_{p} .$ | (3) |
1.3 基于风险容忍度的地理位置关联性分析方法当供电网络某区域内的某些组分失效时,供水网络中的一些节点或边可能会因供电不足而失去部分或全部功能。供电与供水网络之间存在地理关联,即供电网络某个空间范围内组分的失效往往会导致供水网络相邻组分的失效[2]。
为模拟供水和供电网络间地理位置的失效关联性,把城市区域在东西、南北方向划分为(H×V)个矩形网格。假设供水节点需要的电力由距其最近的供电节点提供,当供电网络在某个网格涵盖的地理空间内发生故障时,将该网格内与故障供电节点相邻的供水节点去除[18, 25](见图 2,其中空心节点表示去除的节点),以模拟供水节点因断电而失去正常功能的情景。
图 2 按地理位置关联性移除节点的方法示意图 |
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之后, 计算移除网格
$r_{h v}=c_{h v} \frac{n}{\log \left\langle s_{h v}\right\rangle} .$ | (4) |
2 算例介绍本文研究的供水网络(见图 3a)和供电网络(见图 3b)包含的节点和边的数量如表 1所示。本文使用的计算工具是Python,其中与网络有关的计算用NetworkX库来处理。
图 3 某城市区域的供水和供电网络示意图 |
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表 1 网络所包含的节点和边的数量
网络 | n | m |
供水网络 | 4 000 | 4 063 |
供电网络 | 3 003 | 4 861 |
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3 结果与讨论本文用角标“w”和“e”分别表示供水和供电网络,以示区分。
3.1 供水和供电网络类型检验对图 3的供水和供电网络分别建立网络
图 4 供水和供电网络类型检验 |
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3.2 随机冲击下的供水和供电网络风险容忍度分析3.2.1 供水和供电网络节点簇特征参数分析如1.2节所述, 随着
图 5 |
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比较而言, 随着
3.2.2 供水和供电网络节点簇大小的分布特征本节讨论当
$L_{p}=\frac{s_{p}}{n} .$ | (5) |
图 6 f一定时Lp的分布情况(模拟200次) |
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记区间系列
$F_{t}=\left|\left\{S_{p} \mid D_{t, 1} \leqslant L_{p}<D_{t, 2}\right\}\right| .$ | (6) |
另外,随着f的增加,散点的分布越来越接近一个指数函数,设其表达式为
$L_{p}=a \exp \left(b \log F_{t}\right) .$ | (7) |
图 7 待定系数a和b随f的变化趋势 |
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用式(7)拟合的结果可以在f不太小时反映供水和供电网络遭受外界随机冲击后被破坏的程度,对灾后基础设施的功能评估有一定的参考价值。
3.3 供水和供电网络的地理位置关联性分析图 8展示了
图 8 不同网格数下rhv在网络中的空间分布 |
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因此, 对该城市区域而言,
4 结论本文在风险容忍度框架下定量研究了某城市区域的供水和供电网络的关联性。以供水和供电网络的网络模型为基础,基于该框架有关概念和若干参数如网络直径、节点簇数量、节点簇大小等,研究了供水和供电网络在外界随机冲击下的风险容忍度表现,并分析了节点簇大小的分布。以风险容忍度分析为基础,本文研究了供水与供电两基础设施网络间的地理位置关联性,指出了地理关联下供水网络易受断电影响的关键区域。本文的研究结果为有关部门进行基础设施防护、规划、应急处置和韧性提升等提供了支撑和参考。
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