JP2011158985A - Connectiveness evaluation method for supply facility - Google Patents
Connectiveness evaluation method for supply facility Download PDFInfo
- Publication number
- JP2011158985A JP2011158985A JP2010018272A JP2010018272A JP2011158985A JP 2011158985 A JP2011158985 A JP 2011158985A JP 2010018272 A JP2010018272 A JP 2010018272A JP 2010018272 A JP2010018272 A JP 2010018272A JP 2011158985 A JP2011158985 A JP 2011158985A
- Authority
- JP
- Japan
- Prior art keywords
- facility
- facilities
- supply
- connectivity
- supply facility
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000011156 evaluation Methods 0.000 title claims abstract description 66
- 239000011159 matrix material Substances 0.000 claims abstract description 58
- 238000010586 diagram Methods 0.000 claims abstract description 22
- 239000000470 constituent Substances 0.000 claims description 28
- 238000000034 method Methods 0.000 claims description 20
- 238000004088 simulation Methods 0.000 claims description 17
- 238000004364 calculation method Methods 0.000 claims description 10
- 239000008399 tap water Substances 0.000 description 31
- 235000020679 tap water Nutrition 0.000 description 31
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 31
- 238000000746 purification Methods 0.000 description 10
- 238000009826 distribution Methods 0.000 description 6
- 230000001133 acceleration Effects 0.000 description 3
- 238000004891 communication Methods 0.000 description 2
- 238000012937 correction Methods 0.000 description 2
- 230000005611 electricity Effects 0.000 description 2
- 238000012502 risk assessment Methods 0.000 description 2
- 229910001018 Cast iron Inorganic materials 0.000 description 1
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- -1 electricity Substances 0.000 description 1
- 238000007429 general method Methods 0.000 description 1
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
Description
本発明は、地震による被災時における、供給物の供給元と被供給施設とを繋ぐ供給施設の連結性評価方法に関する。 The present invention relates to a connectivity evaluation method for a supply facility that connects a supply source and a supply facility at the time of a disaster caused by an earthquake.
地震によるリスク評価方法として、個々の施設における地震リスクを考慮して事業中断リスクを評価する方法は知られており、例えば、複数のサプライチェーンからの供給を受けつつ事業を継続する企業の地震によって生じる各サプライチェーンからの影響を算出する方法が知られている（例えば、特許文献１参照）。 As a risk assessment method for earthquakes, there is a known method for assessing the risk of business interruption taking into account the seismic risk at individual facilities. For example, by the earthquake of a company that continues its business while receiving supply from multiple supply chains. A method of calculating the influence from each supply chain that occurs is known (for example, see Patent Document 1).
しかしながら、地震によるリスク評価は、事業の中断リスクのみならず、例えば、電気・ガス・水道等の公共設備や電話やインターネット等の通信設備等、供給物の供給元と被供給施設とを繋ぐ供給施設における地震のリスクを評価することが求められている。すなわち、地震による被災時に、供給物の供給元から使用する被供給施設等までの連結が確保されるか否かという、供給施設の連結性の評価が求められている。 However, the risk assessment due to earthquakes is not only the risk of business interruption, but also the supply that connects the supply source and the supplied facility, such as public facilities such as electricity, gas, and water, and communication facilities such as the telephone and the Internet. There is a need to assess the risk of earthquakes at the facility. That is, there is a demand for evaluation of connectivity of a supply facility, such as whether or not a connection from a supply source of a supply to a supply facility to be used is secured in the event of a disaster caused by an earthquake.
本発明は、上記課題に鑑みてなされたものであり、その目的とするところは、地震による被災時における供給施設の連結性を評価する供給施設の連結性評価方法を提供することにある。 This invention is made | formed in view of the said subject, The place made into the objective is providing the connectivity evaluation method of the supply facility which evaluates the connectivity of the supply facility at the time of the disaster by an earthquake.
かかる目的を達成するために本発明の供給施設の連結性評価方法は、供給物の供給元と被供給施設とを繋ぐ供給施設の、地震による被災時の連結状態を評価する供給施設の連結性評価方法であって、評価対象が含まれる地域における、前記供給物の前記供給施設を構成し前記供給元と前記被供給施設とを含む各構成施設の繋がりが示された構成図から、平常時における前記供給施設の平常時供給施設モデルを生成する平常時モデル生成ステップと、想定するシナリオ地震の規模を決定するシナリオ地震決定ステップと、決定した前記シナリオ地震に対する各々の前記構成施設の被害率を評価する被害率評価ステップと、生成した前記平常時供給施設モデル及び評価した前記構成施設の前記被害率に基づいて前記供給施設を構成する複数の構成施設のうちの隣接する２つの構成施設毎に連結又は非連結を示す隣接行列を生成する隣接行列生成ステップと、生成された前記隣接行列からブール代数演算則に従って前記供給施設を構成する複数の前記構成施設のうちの２つの構成施設毎に連結又は非連結を示す可到達行列を求める可到達行列算出ステップと、を有することを特徴とする供給施設の連結性評価方法である。 In order to achieve this object, the connectivity evaluation method for a supply facility according to the present invention is a connectivity assessment of a supply facility that evaluates the connection state of a supply facility that connects a supply source and a supply facility at the time of an earthquake disaster. It is an evaluation method, and in a region where an evaluation target is included, from the configuration diagram showing the connection of each component facility that configures the supply facility of the supply and includes the supply source and the supplied facility, A normal model generation step for generating a normal supply facility model of the supply facility in FIG. 5, a scenario earthquake determination step for determining the magnitude of an assumed scenario earthquake, and a damage rate of each of the component facilities for the determined scenario earthquake A plurality of configurations constituting the supply facility based on the damage rate evaluation step to be evaluated, the generated normal supply facility model, and the damage rate of the evaluated configuration facility An adjacent matrix generation step for generating an adjacency matrix indicating connection or non-connection for every two adjacent constituent facilities in the configuration, and a plurality of the supply facilities that constitute the supply facility according to a Boolean algebra operation rule from the generated adjacency matrix And a reachability matrix calculation step of obtaining a reachability matrix indicating connection or non-connection for each of the two constituent facilities of the constituent facilities.
このような供給施設の連結性評価方法によれば、評価対象が含まれる地域において供給物を供給するための各供給元から各被供給施設までの各構成施設の繋がりが示された構成図から生成した平常時供給施設モデルと、決定したシナリオ地震による構成施設の被災率とに基づいて隣接行列を生成するので、対象となる地域の各構成施設間の被災率を加味して、より正確に評価することが可能である。また、生成された隣接行列からブール代数演算則に従って可到達行列を求めるので、すべての構成施設に対し、供給元からの連結性を容易に評価することが可能である。 According to the connectivity evaluation method of such a supply facility, from the configuration diagram showing the connection of each component facility from each supply source to each supplied facility for supplying supplies in the area where the evaluation target is included Since the adjacency matrix is generated based on the generated normal supply facility model and the damage rate of the constituent facilities due to the determined scenario earthquake, more accurately considering the damage rate between each constituent facility in the target area It is possible to evaluate. In addition, since the reachability matrix is obtained from the generated adjacency matrix according to the Boolean algebra operation rule, it is possible to easily evaluate the connectivity from the supplier for all the constituent facilities.
ここで、供給施設は、供給元から、供給物が供給される末端に位置する需要施設までを繋ぐ配管やそれらの間に設けられている施設を含む施設全体を示しており、供給施設を構成する供給元の施設、需要施設、供給元と需要施設との間に設けられている施設、が各々構成施設である。供給元の施設以外の施設は、いずれも被供給施設となり得る。 Here, the supply facility indicates the entire facility including the piping connecting the supply source to the demand facility located at the terminal to which the supply is supplied and the facilities provided between them. The supply facility, the demand facility, and the facility provided between the supply source and the demand facility are the constituent facilities. Any facility other than the source facility can be a supplied facility.
かかる供給施設の連結性評価方法であって、前記シナリオ地震決定ステップから前記可到達行列算出ステップまでを繰り返しシミュレーションするシミュレーションステップと、実行された複数回の前記シミュレーションの結果に基づいて前記２つの構成施設間の連結性を評価する連結性評価ステップと、を有することが望ましい。
このような供給施設の連結性評価方法によれば、シナリオ地震決定ステップから可到達行列算出ステップまでを繰り返しシミュレーションした複数回のシミュレーションの結果に基づいて２つの構成施設間の連結性を評価するので、より信頼性が高い連結性を評価することが可能である。
A method for evaluating connectivity of such a supply facility, wherein the two configurations are based on a simulation step for repeatedly simulating the scenario earthquake determination step to the reachability matrix calculation step, and a result of the simulation performed a plurality of times. It is desirable to have a connectivity evaluation step for evaluating connectivity between facilities.
According to the connectivity evaluation method of such a supply facility, the connectivity between two constituent facilities is evaluated based on the results of a plurality of simulations in which simulation is repeatedly performed from the scenario earthquake determination step to the reachable matrix calculation step. It is possible to evaluate connectivity with higher reliability.
かかる供給施設の連結性評価方法であって、前記連結性評価ステップでは、複数回の前記シミュレーション結果となる前記可到達行列の各成分の平均値を求めることが望ましい。
このような供給施設の連結性評価方法によれば、連結性評価ステップにて、複数回のシミュレーション結果となる可到達行列の各成分の平均値を求めるので、単に連結しているか否かだけでなく、連結している確率を評価することが可能である。
In this connectivity evaluation method for a supply facility, in the connectivity evaluation step, it is desirable to obtain an average value of each component of the reachability matrix that is a result of the simulation multiple times.
According to the connectivity evaluation method of such a supply facility, in the connectivity evaluation step, the average value of each component of the reachability matrix that is the result of a plurality of simulations is obtained. It is possible to evaluate the probability of being connected.
かかる供給施設の連結性評価方法であって、前記連結性の評価結果を前記構成図上に図示する評価結果図示ステップを有することが望ましい。
このような供給施設の連結性評価方法によれば、連結性の評価結果が供給施設の構成図上に図示されるので、評価結果をより明確にわかりやすく表現することが可能である。
It is desirable that the method for evaluating connectivity of a supply facility includes an evaluation result display step of displaying the evaluation result of the connectivity on the configuration diagram.
According to such a connectivity evaluation method of the supply facility, the evaluation result of the connectivity is illustrated on the configuration diagram of the supply facility, so that the evaluation result can be expressed more clearly and easily.
本発明によれば、地震による被災時における供給施設の連結性を評価する供給施設の連結性評価方法を提供することにある。 According to the present invention, there is provided a connectivity evaluation method for a supply facility that evaluates the connectivity of the supply facility during a disaster caused by an earthquake.
以下、本実施形態の供給施設の連結性評価方法の一例について図を用いて詳細に説明する。
図１は、本発明に係る供給施設の連結性評価方法の評価フローを示す図である。
Hereinafter, an example of the connectivity evaluation method of the supply facility according to the present embodiment will be described in detail with reference to the drawings.
FIG. 1 is a diagram showing an evaluation flow of a connectivity evaluation method for a supply facility according to the present invention.
本実施形態においては、供給施設にて供給される種々の供給物のうち上水道を例に挙げ、地震発生時における水道水供給施設の連結性評価方法について説明する。ここで、水道水以外の供給物としては、例えば、電気、ガスや、通信データ等が挙げられる。 In this embodiment, a water supply system is taken as an example of various supplies supplied at a supply facility, and a method for evaluating connectivity of a tap water supply facility at the time of an earthquake will be described. Here, as supplies other than tap water, electricity, gas, communication data, etc. are mentioned, for example.
上水道は水道水の供給元である浄水場から配管を通り、また、配水池を経由して所定の地域の需要節点に供給され、需要節点から個々の需要施設、すなわち、ビルや工場、住戸などに水道水が供給されている。このため、地震により浄水場から個々の施設までの間の配管や配水池に亀裂が生じたり、配管等が損傷した場合には、水道水が個々の施設に供給されなくなる。すなわち、供給施設の連結が途絶えることになる。 The water supply is supplied from the water purification plant, which is the source of tap water, to the demand node in the specified area through the distribution reservoir, and from the demand node to individual demand facilities, that is, buildings, factories, dwelling units, etc. Tap water is supplied to For this reason, when a pipe or a distribution reservoir from a water purification plant to an individual facility is cracked or damaged by an earthquake, tap water is not supplied to the individual facility. In other words, the supply facilities will be disconnected.
以下の説明では、供給元となる浄水場から、供給物が供給される末端に位置する需要施設としての個々の施設までを繋ぐ配管やそれらの間に設けられている施設としての需要節点や配水池等を含む施設全体が供給施設に相当し、供給施設を構成する浄水場、需要施設、浄水場と需要施設との間に設けられている需要節点や配水池、配管が各々構成施設の一例に相当する。そして、浄水場以外の施設は、いずれも被供給施設となり得る。 In the following explanation, the pipes that connect from the water purification plant that is the supply source to the individual facilities as demand facilities located at the end to which the supplies are supplied, and the demand nodes and distributions that are provided between them. The entire facility including water ponds, etc. corresponds to the supply facility, and water supply plants, demand facilities, demand nodes, water reservoirs, and pipes that are provided between the water treatment plant and the demand facility are examples of component facilities. It corresponds to. And all the facilities other than the water purification plant can be supplied facilities.
本実施形態の水道水供給施設の連結性評価方法では、地震が発生した際に、いずれかの浄水場から評価対象となる被供給施設に水道水を供給するための供給施設に亀裂等が生じることなく、水道水の供給経路が確保できるか否かを連結性としている。そして、連結性の評価とは、地震後に個々の被供給施設と浄水場とを繋ぐ配水施設が存在するか否かの評価を示している。 In the method for evaluating connectivity of tap water supply facilities according to the present embodiment, when an earthquake occurs, a crack or the like occurs in a supply facility for supplying tap water from one of the water purification plants to a supply target facility to be evaluated. Without being connected, whether or not a supply route for tap water can be secured is defined as connectivity. The connectivity evaluation indicates an evaluation of whether or not there is a water distribution facility that connects each supplied facility and the water treatment plant after the earthquake.
本実施形態の水道水供給施設の連結性評価方法は、図１に示すように、評価対象が含まれる地域の各構成施設間の繋がりが示された構成図としての配管図から、平常時において水道水を供給する供給施設の平常時供給施設モデルを生成する平常時モデル生成ステップ（ＳＴＥＰ１）と、想定する地震の規模を決定するシナリオ地震決定ステップ（ＳＴＥＰ２）と、決定したシナリオ地震に対する各々の構成施設の被害率を評価する被害率評価ステップ（ＳＴＥＰ３）と、生成した上水道の平常時供給施設モデル及び評価した構成施設の被害率に基づいて、地震により損失した後の上水道の被災後供給施設モデルを生成し、複数の構成施設のうちの隣接する２つの構成施設毎に連結又は非連結を示す隣接行列を生成する隣接行列生成ステップ（ＳＴＥＰ４）と、生成された隣接行列からブール代数演算則に従って可到達行列を求める可到達行列算出ステップ（ＳＴＥＰ５）と、シナリオ地震決定ステップから可到達行列算出ステップまでを繰り返しシミュレーションするシミュレーションステップ（ＳＴＥＰ６）と、実行された複数回のシミュレーション結果に基づいて２つの構成施設間の連結性を評価する連結性評価ステップ（ＳＴＥＰ７）と、連結性の評価結果を地域の配管図上に図示する評価結果図示ステップ（ＳＴＥＰ８）と、を有する。 As shown in FIG. 1, the connectivity evaluation method for a tap water supply facility according to the present embodiment is based on a piping diagram as a configuration diagram showing a connection between each component facility in an area where an evaluation target is included. A normal model generation step (STEP 1) for generating a normal supply facility model of a supply facility for supplying tap water, a scenario earthquake determination step (STEP 2) for determining the magnitude of an assumed earthquake, and each scenario earthquake determined Damage rate evaluation step (STEP 3) for evaluating the damage rate of the component facilities, the normal supply facility model of the generated water supply, and the supply facility after the disaster of the water supply after loss due to the earthquake based on the damage rate of the evaluated component facility An adjacency matrix generation step of generating a model and generating an adjacency matrix indicating connection or non-connection for every two adjacent configuration facilities among a plurality of configuration facilities ( TEP 4), a reachability matrix calculation step (STEP 5) for obtaining a reachability matrix from the generated adjacent matrix according to a Boolean algebra operation rule, and a simulation step (STEP 6) for repeatedly simulating the scenario earthquake determination step to the reachability matrix calculation step And a connectivity evaluation step (STEP 7) for evaluating the connectivity between the two constituent facilities based on the results of a plurality of simulations executed, and an evaluation result illustrating the connectivity evaluation result on a local piping diagram. Step (STEP 8).
図２は、評価対象の構成施設を含む地域の配管図である。図３は、平常時における配管の連結状態を示す平常時供給施設モデルの一例を示す図である。 FIG. 2 is a piping diagram of a region including the configuration facility to be evaluated. FIG. 3 is a diagram illustrating an example of a normal supply facility model showing a pipe connection state in a normal state.
平常時モデル生成ステップ（ＳＴＥＰ１）では、評価対象の被供給施設が連結されている需要節点と、この需要節点に水道水を供給する浄水場を含む地域の、図２に示すような配管図から、平常時における供給施設の連結状態を示す、図３に示すような平常時供給施設モデルを作成する。 In the normal model generation step (STEP 1), from the piping diagram as shown in FIG. 2 of the area including the demand node to which the supply facility to be evaluated is connected and the water purification plant that supplies tap water to this demand node. A normal supply facility model as shown in FIG. 3 showing the connection state of the supply facilities in the normal state is created.
この平常時供給施設モデルには、対象となる施設を含む地域に設けられている施設である需要節点１４、配水池１３、及び浄水場１２を構成施設１１として示し、配管図に基づいて各構成施設１１間を、配管と見なした線にて繋いで各構成施設１１が連結されている状態を示しておく。このとき、図３には示していないが、配管内を流れる水の方向も示しておく。また、水道水供給施設の連結性評価方法では、必ずしも浄水場から需要施設までの連結性を評価しなくとも、水道水が供給されている途中の施設を被供給施設として連結性も評価できるので、必ずしも全ての構成施設が平常時供給施設モデルに示されている必要はない。図３の例では、需要節点１４の先には当該需要節点１４と連結された各需要施設を示していないが、各需要節点１４と各需要施設との連結状態もモデル化しておくと、各需要施設を被供給施設とした上水道の連結性を評価することも可能である。 In this normal supply facility model, a demand node 14, a reservoir 13 and a water purification plant 12 which are facilities provided in an area including a target facility are shown as component facilities 11, and each component is configured based on a piping diagram. A state in which the constituent facilities 11 are connected by connecting the facilities 11 with a line regarded as a pipe will be described. At this time, although not shown in FIG. 3, the direction of water flowing in the pipe is also shown. In addition, the connectivity evaluation method for tap water supply facilities does not necessarily evaluate the connectivity from the water treatment plant to the demand facility, so the facility in the middle of which tap water is being supplied can be evaluated as the supplied facility. Not all component facilities need to be shown in the normal supply facility model. In the example of FIG. 3, each demand facility connected to the demand node 14 is not shown beyond the demand node 14, but if the connection state between each demand node 14 and each demand facility is also modeled, It is also possible to evaluate the connectivity of water supply with the demand facility as the supplied facility.
本実施形態においては、連結性の評価手法として、複数ある連結性評価法のうち、代表的なＩＳＭ（Interpretive Structural Modeling）法を用いている。ＩＳＭ法は、構成施設１１間の関係を明らかにしてシステムの構造特性を解析する手法である。 In the present embodiment, a representative ISM (Interpretive Structural Modeling) method among a plurality of connectivity evaluation methods is used as a connectivity evaluation method. The ISM method is a method for analyzing the structural characteristics of the system by clarifying the relationship between the constituent facilities 11.
以下では、説明の便宜上図４に示す簡略モデルのような上水道の平常時供給施設モデルを用いて説明する。 In the following, for the convenience of explanation, a normal water supply facility model such as the simplified model shown in FIG. 4 will be used.
図４は、供給経路の連結性評価方法を説明するための簡略モデルの一例である。図４（ａ）は、平常時供給施設モデルの簡略モデルの一例であり、図４（ｂ）は、平常時供給施設モデルの簡略モデルに示す供給施設のうちの一部が損傷を受けた場合を示す図であり、図４（ｃ）は、被災後供給施設モデルの簡略モデルの一例である。 FIG. 4 is an example of a simplified model for explaining a connectivity evaluation method for supply paths. 4A is an example of a simplified model of the normal supply facility model, and FIG. 4B is a case where a part of the supply facility shown in the simplified model of the normal supply facility model is damaged. FIG. 4C is an example of a simplified model of the post-disaster supply facility model.
図示するように、本上水道の平常時供給施設モデルは、４つの構成施設Ｓ１〜Ｓ４を有し、次のように連結されている。第１構成施設Ｓ１からは第２構成施設Ｓ２に水道水が流出し、第２構成施設Ｓ２と第３構成施設Ｓ３から水道水が流入するように連結されている。第２構成施設Ｓ２からは第１構成施設Ｓ１と第４構成施設Ｓ４に水道水が流出し、第１構成施設Ｓ１と第３構成施設Ｓ３から流入するように連結されている。第３構成施設Ｓ３からは第１構成施設Ｓ１と第２構成施設Ｓ２に水道水が流出し、他の構成施設からの流入はないように連結されている。第４構成施設Ｓ４からの水道水の流出はないが、第２構成施設Ｓ２から水道水が流入するように連結されている。 As shown in the figure, the normal water supply facility model of the main water supply system has four component facilities S1 to S4 and is connected as follows. The tap water flows from the first component facility S1 to the second component facility S2, and is connected so that the tap water flows from the second component facility S2 and the third component facility S3. The tap water flows from the second component facility S2 to the first component facility S1 and the fourth component facility S4, and is connected so as to flow from the first component facility S1 and the third component facility S3. From the third component facility S3, tap water flows out to the first component facility S1 and the second component facility S2, and is connected so that there is no inflow from other component facilities. Although there is no outflow of tap water from the fourth component facility S4, the tap water is connected so as to flow from the second component facility S2.
水道水供給施設の連結性評価方法では、作成した平常時供給施設モデル（図４（ａ））に基づいて、平常時の隣接行列Ａを作成する。平常時の隣接行列Ａは、平常時供給施設モデルが有する各構成施設のうちの隣接、すなわち直接連結されている２つの構成施設間の連結状態を示す行列であり、１回のステップにて２つの構成施設以外の他の構成施設を経由することなく直接的に連結されているか否かを示す行列である。図４（ａ）の平常時供給施設モデルの場合には、（式１）に示す平常時の隣接行列Ａにて表される。
平常時の隣接行列Ａでは、縦方向に供給経路の起点となる構成施設が配置され、横方向に到達点となる構成施設が配置されている。そして、構成施設Ｓｉから構成施設Ｓｊへ連結していれば”Ａｉ，ｊ＝１”、連結していなければ”Ａｉ，ｊ＝０”が示される。すなわち（式１）では、水道水が流出する第１構成施設Ｓ１からは第２構成施設Ｓ２の連結状態を示す成分Ａ１，２に「１」が与えられ、水道水が流出しない第３構成施設Ｓ３からは第４構成施設Ｓ４の連結状態を示す成分Ａ３，４に「０」が与えられる。また、平常時の隣接行列Ａは、連結の方向性を考慮するため、対称行列になるとは限らない。
In the tap water supply facility connectivity evaluation method, a normal adjacency matrix A is created based on the created normal supply facility model (FIG. 4A). The normal adjacency matrix A is a matrix indicating a connection state between two constituent facilities that are adjacent to each other, that is, directly connected among the constituent facilities of the normal supply facility model, and is 2 in one step. It is a matrix which shows whether it is connected directly, without passing through other composition facilities other than one composition facility. In the case of the normal supply facility model of FIG. 4A, it is represented by the normal adjacency matrix A shown in (Equation 1).
In the normal adjacency matrix A, the component facility that is the starting point of the supply path is arranged in the vertical direction, and the component facility that is the arrival point is arranged in the horizontal direction. If the component facility S i is connected to the component facility S j , “A i, j = 1” is indicated , and if not connected, “A i, j = 0” is indicated. That is, in (Formula 1), “1” is given to the components A 1 and 2 indicating the connection state of the second component facility S2 from the first component facility S1 from which the tap water flows out, and the third component in which the tap water does not flow out. From the facility S3, “0” is given to the components A 3 and 4 indicating the connection state of the fourth component facility S4. Further, the normal adjacency matrix A is not necessarily a symmetric matrix in order to consider the direction of connection.
シナリオ地震決定ステップ（ＳＴＥＰ２）ではシナリオ地震を決定する。シナリオ地震は、地震の位置や規模等の地震源情報を特定した地震であり、本実施形態の上水道の連結性を評価する際には、発生したと想定する地震の規模を、シナリオ地震による地表最大速度として設定する。 In the scenario earthquake determination step (STEP 2), a scenario earthquake is determined. A scenario earthquake is an earthquake that specifies earthquake source information such as the location and magnitude of the earthquake. When evaluating the connectivity of the water supply in this embodiment, the magnitude of the earthquake that is assumed to have occurred Set as maximum speed.
地表最大速度は、例えば、距離減衰式（司宏俊・翠川三郎：断層タイプ及び地盤条件を考慮した最大加速度・最大速度の距離減衰式，日本建築学会構造系論文集，Vol. 523, pp.63-70, 1999）に基づいて求められる。このとき、地震における地表最大速度のばらつきを考慮し、求められた地表最大速度を中央値として、中央値に対するばらつきを乱数にて与えたうえで各構成施設Ｓ１〜Ｓ４の地表最大速度を設定する。 The maximum surface velocity is, for example, the distance attenuation formula (Toshitoshi Tsuji, Saburo Sasakawa: Maximum acceleration / maximum velocity distance attenuation considering the fault type and ground conditions, Architectural Institute of Japan, Vol. 523, pp.63 -70, 1999). At this time, considering the variation of the maximum surface speed in the earthquake, the maximum surface speed obtained is set as the median, and the variation with respect to the median is given by a random number, and then the maximum surface speed of each component facility S1 to S4 is set. .
被害率評価ステップ（ＳＴＥＰ３）では、設定された各構成施設の地表最大速度に対する各構成施設Ｓ１〜Ｓ４の標準被害率を求める。標準被害率は、例えば、「Ｈ１９年度首都直下地震による東京の被害想定評価報告書」（東京都総務局）に示されており、例えば、送水管・配水管の被害想定にあたっては、過去の地震被害データから得られた地表加速度と鋳鉄管被害率（被害箇所／km）が用いられる。実際の被害想定には、この関係式に、管種係数、管径係数および液状化危険度から決定される地盤係数を考慮して被害箇所数を決定する方法が一般的である。数式（式２）に、代表的な送配水管の被害箇所数算定式を示す。
被害箇所数 ＝ 標準被害率（箇所／km）
×液状化危険度ランクによる補正係数
×管種・管径別の補正係数
×配水管延長（km） ・・・（式２）
ここで、
標準被害率（箇所／ｋｍ）＝２．２４＊１０−３*（ｖ−２０）１．５１
・・・（式３）
ｖ：地表最大速度
（式３）に、シナリオ地震の発生時における各構成施設Ｓ１〜Ｓ４の地表最大速度ｖとして設定した値を入力することにより、標準被害率が求められる。
In the damage rate evaluation step (STEP 3), the standard damage rates of the constituent facilities S1 to S4 with respect to the set maximum surface speed of the constituent facilities are obtained. The standard damage rate is shown, for example, in the “Evaluation Report for Damage Estimates in Tokyo due to the H19 Fiscal Year Earthquake” (General Affairs Bureau, Tokyo). The surface acceleration obtained from the damage data and the cast iron pipe damage rate (damage location / km) are used. For actual damage estimation, a general method is to determine the number of damage points in consideration of the ground coefficient determined from the pipe type coefficient, pipe diameter coefficient and liquefaction risk in this relational expression. Formula (Formula 2) shows the formula for calculating the number of damaged parts of typical water transmission and distribution pipes.
Number of damage points = standard damage rate (locations / km)
× Correction factor based on liquefaction risk rank
× Correction coefficient by pipe type and pipe diameter
× Water pipe extension (km) (Formula 2)
here,
Standard damage rate (location / km) = 2.24 * 10 −3 * (v−20) 1.51
... (Formula 3)
v: Maximum ground speed By inputting the value set as the maximum ground speed v of each constituent facility S1 to S4 at the time of occurrence of the scenario earthquake into the maximum ground speed, the standard damage rate is obtained.
隣接行列生成ステップ（ＳＴＥＰ４）では、所定の構成施設から他の所定の構成施設への連結部分において、（式３）により標準被害率が例えば６０％と算出された場合には、例えば０〜１の間の乱数を発生させて、０．６以上の数が発生した場合には、連結されていると評価して、平常時の隣接行列Ａの対応する成分を「１」に書き換えて被災後の隣接行列Ａ１を生成する。このとき、平常時の隣接行列Ａの各成分Ａｉ，ｊに対し、地表最大速度ｖの設定及び標準被害率の算出を行った結果、第１構成施設Ｓ１と第２構成施設Ｓ２との間の配管と、第２構成施設Ｓ２と第３構成施設Ｓ３との間の配管が被害を受けたという結果が得られた場合には、平常時供給施設モデルから機能を損失した構成施設を取り除いた図４（ｃ）に示すような、被災後供給施設モデルを生成する。 In the adjacency matrix generation step (STEP 4), when the standard damage rate is calculated to be 60%, for example, according to (Equation 3) in the connection portion from the predetermined configuration facility to another predetermined configuration facility, for example, 0-1 When a number of 0.6 or more is generated, it is evaluated that they are connected and the corresponding component of the normal adjacency matrix A is rewritten to “1” after the disaster. The adjacency matrix A1 is generated. At this time, as a result of setting the ground surface maximum speed v and calculating the standard damage rate for each component A i, j of the adjacency matrix A in the normal time, it is between the first component facility S1 and the second component facility S2. If the result was that the piping between the second component facility S2 and the third component facility S3 was damaged, the component facility that lost its function was removed from the normal supply facility model. A post-disaster supply facility model as shown in FIG. 4C is generated.
可到達行列算出ステップ（ＳＴＥＰ５）では、生成された被災後供給施設モデルに対して連結性の評価を行う。連結性の評価は、被災後供給施設モデルの被災後の隣接行列Ａ１から、ブール代数演算則に従って（式４）を用いて可到達行列Ｔを求める。
ここで、ｍは平常時供給施設モデルに含まれる構成施設の数を示している。可到達行列Ｔは、平常時供給施設モデルが有する各構成施設のうちの２つの構成施設間の連結を示す行列であり、２つの構成施設間が平常時供給施設モデル内にて直接的又は間接的に連結される経路を有しているか否かを示す行列である。図４（ｃ）の被災時供給施設モデルの場合には、（式５）に示すような可到達行列Ｔにて表される。
In the reachability matrix calculation step (STEP 5), connectivity is evaluated for the generated post-disaster supply facility model. For the evaluation of connectivity, the reachable matrix T is obtained from the adjacency matrix A1 after the disaster of the supply facility model after the disaster using (Equation 4) according to the Boolean algebra operation rule.
Here, m indicates the number of constituent facilities included in the normal supply facility model. The reachable matrix T is a matrix indicating a connection between two constituent facilities among the constituent facilities of the normal supply facility model, and the two constituent facilities are directly or indirectly in the normal supply facility model. It is a matrix which shows whether it has the path | route connected automatically. In the case of the disaster supply facility model of FIG. 4C, it is represented by a reachable matrix T as shown in (Equation 5).
本実施形態の説明に用いた平常時供給施設モデルは、４つの構成施設にて構成された簡略モデルであるが、実際のシステムは図２に示したような規模を有するため、非常に大きな行列となる。このため、可到達行列Ｔを効率よく高速に求める方法として、例えばネットワーク内の任意の２点の最短経路を求めるアルゴリズムであるWarshall-Floyd法を用いる。 The normal supply facility model used in the description of the present embodiment is a simplified model composed of four component facilities, but the actual system has a scale as shown in FIG. It becomes. For this reason, as a method for obtaining the reachable matrix T efficiently and at high speed, for example, the Warshall-Floyd method which is an algorithm for obtaining the shortest path of any two points in the network is used.
このようにして、可到達行列Ｔを求めることにより、各構成施設が各々個別の特定の地表最大速度ｖにて移動するような、あるシナリオ地震による、連結性が評価される。このような評価は、特定の地表最大速度ｖが生じた際の、連結性の評価の１つのデータであるため信頼性が低い。このため、シミュレーションステップ（ＳＴＥＰ６）にて、シナリオ地震を決定するシナリオ地震決定ステップ（ＳＴＥＰ２）から可到達行列Ｔを求める可到達行列算出ステップ（ＳＴＥＰ５）を、ベルヌーイ試行とモンテカルロ法を用い、複数回（ｎ）、例えば１０００回のシミュレーションを繰り返す。 In this way, by obtaining the reachable matrix T, connectivity due to a certain scenario earthquake in which each constituent facility moves at a specific specific maximum surface velocity v is evaluated. Such evaluation is low in reliability because it is one piece of data for evaluating connectivity when a specific surface maximum velocity v occurs. For this reason, in the simulation step (STEP 6), the reachability matrix calculation step (STEP 5) for obtaining the reachable matrix T from the scenario earthquake determination step (STEP 2) for determining the scenario earthquake is performed a plurality of times using the Bernoulli trial and the Monte Carlo method. (N) For example, 1000 simulations are repeated.
シミュレーションの結果からは、連結性評価ステップ（ＳＴＥＰ７）にて、求められた可到達行列Ｔの各成分における平均値が求められる。この平均値にて、シナリオ地震による各構成施設における非連結確率が表される。 From the result of the simulation, an average value in each component of the obtained reachability matrix T is obtained in the connectivity evaluation step (STEP 7). This average value represents the probability of disconnection at each component facility due to a scenario earthquake.
図５は、規模の小さなシナリオ地震における水道水供給施設の連結性の評価結果を示す図であり、図６は、規模の大きなシナリオ地震における水道水供給施設の連結性の評価結果を示す図である。 FIG. 5 is a diagram showing the evaluation result of the connectivity of the tap water supply facility in the small-scale scenario earthquake, and FIG. 6 is a diagram showing the evaluation result of the connectivity of the tap water supply facility in the large-scale scenario earthquake. is there.
求められたシナリオ地震による各構成施設１１における非連結確率を、評価結果図示ステップ（ＳＴＥＰ８）にて、事前に用意した構成図、すなわち評価対象の構成施設１１が連結されている需要節点１４と、この需要節点１４に水道水を供給する浄水場１２を含む地域の地図上の配管図に図示する。このとき、例えば、図５、図６に示すように、評価対象の需要節点１４上に非連結確率に対応させて面積を違えた円を描くことにより、地震により配管が損傷を受けて水道水が供給されなくなる可能性が高い構成施設１１を効果的に明示することが可能である。 In the evaluation result indicating step (STEP 8), the configuration diagram prepared in advance for the disconnection probability in each component facility 11 due to the obtained scenario earthquake, that is, the demand node 14 to which the component facility 11 to be evaluated is connected, This is shown in a piping diagram on a map of an area including a water purification plant 12 that supplies tap water to the demand node 14. At this time, for example, as shown in FIGS. 5 and 6, by drawing a circle with a different area corresponding to the disconnection probability on the demand node 14 to be evaluated, the pipe is damaged by the earthquake and the tap water It is possible to effectively specify the configuration facility 11 that has a high possibility of not being supplied.
本実施形態の水道水供給施設の連結性評価方法によれば、評価対象となる地域において水道水を供給するための各浄水場１２から各被供給施設となる各構成施設１１までの供給施設の構成図から生成した平常時供給施設モデルと、決定したシナリオ地震による各構成施設の被災率とに基づいて被災後供給施設モデルを生成するので、対象となる地域の各構成施設１１の被災率をより正確に評価することが可能である。 According to the connectivity evaluation method for tap water supply facilities of this embodiment, the supply facilities from each water purification plant 12 for supplying tap water to each component facility 11 serving as each supplied facility in the area to be evaluated. Since the supply facility model after the disaster is generated based on the normal supply facility model generated from the configuration diagram and the damage rate of each component facility caused by the determined scenario earthquake, the damage rate of each component facility 11 in the target area is calculated. It is possible to evaluate more accurately.
また、平常時供給施設モデルと、各構成施設１１の被災率とに基づいて被災後の隣接行列Ａ１を生成し、生成された被災後の隣接行列Ａ１からブール代数演算則に従って可到達行列Ｔを求めるので、すべての構成施設１１に対し、供給元である浄水場１２からの連結性を容易に評価することが可能である。 In addition, a post-disaster adjacency matrix A1 is generated based on the normal supply facility model and the disaster rate of each constituent facility 11, and the reachable matrix T is calculated from the generated post-disaster adjacency matrix A1 according to the Boolean algebra. Therefore, it is possible to easily evaluate the connectivity from the water purification plant 12 as the supply source to all the constituent facilities 11.
また、シナリオ地震決定ステップから可到達行列算出ステップまでを繰り返しシミュレーションした複数回のシミュレーションの結果に基づいて２つの構成施設１１間の連結性を評価するので、より信頼性が高い連結性を評価することが可能である。 In addition, the connectivity between the two constituent facilities 11 is evaluated based on the results of a plurality of simulations in which the scenario earthquake determination step to the reachability matrix calculation step are repeatedly simulated, so that more reliable connectivity is evaluated. It is possible.
また、連結性評価ステップにて、複数回のシミュレーション結果となる可到達行列Ｔの各成分Ａｉ，ｊの平均値を求めるので、単に連結しているか否かだけでなく、連結している確率を評価することが可能である。 Further, in the connectivity evaluation step, the average value of each component A i, j of the reachable matrix T, which is a simulation result of a plurality of simulations, is obtained. Can be evaluated.
また、連結性の評価結果を供給施設の構成図に図示するので、実際の構成施設１１が設けられている位置に、当該構成施設１１の非連結確率が示されるので、知りたい構成施設１１が見付け易い情報を提供することが可能である。また、非連結確率を円の大きさにて示すように図形にて示したので、数値が羅列した情報より評価結果をより認識しやすい情報を提供することが可能である。ここで、連結性の評価結果の図示方法は、円に限るものではない。 In addition, since the connectivity evaluation result is shown in the configuration diagram of the supply facility, the probability of disconnection of the configuration facility 11 is shown at the position where the actual configuration facility 11 is provided. It is possible to provide easy-to-find information. In addition, since the non-connection probability is indicated by a graphic as indicated by the size of a circle, it is possible to provide information that makes it easier to recognize the evaluation result than information in which numerical values are listed. Here, the method for illustrating the connectivity evaluation result is not limited to a circle.
上記実施形態においては、地震の規模を地表最大速度にて示した例について説明したが、これに限らず、例えば地表最大加速度を用いても構わない。 In the said embodiment, although the example which showed the magnitude | size of the earthquake with the ground surface maximum speed was demonstrated, it is not restricted to this, For example, you may use a ground surface maximum acceleration.
また、上記実施形態においては、可到達行列Ｔを効率よく高速に求める方法として、Warshall-Floyd法を用いた例について説明したが、これに限るものではない。 In the above embodiment, an example using the Warshall-Floyd method has been described as a method for efficiently and rapidly obtaining the reachable matrix T. However, the present invention is not limited to this.
上記実施形態は、本発明の理解を容易にするためのものであり、本発明を限定して解釈するためのものではない。本発明は、その趣旨を逸脱することなく、変更、改良され得ると共に、本発明にはその等価物が含まれることはいうまでもない。 The above embodiment is for facilitating the understanding of the present invention, and is not intended to limit the present invention. The present invention can be changed and improved without departing from the gist thereof, and it is needless to say that the present invention includes equivalents thereof.
１０ 供給施設、１１ 構成施設、
１２ 浄水場、１３ 配水池、１４需要節点、
Ｓ１ 第１構成施設、Ｓ２ 第２構成施設、
Ｓ３ 第３構成施設、Ｓ４ 第４構成施設
10 supply facilities, 11 component facilities,
12 water treatment plants, 13 distribution reservoirs, 14 demand nodes,
S1 first component facility, S2 second component facility,
S3 3rd component facility, S4 4th component facility
Claims (4)
評価対象が含まれる地域における、前記供給物の前記供給施設を構成し前記供給元と前記被供給施設とを含む各構成施設間の繋がりが示された構成図から、平常時における前記供給施設の平常時供給施設モデルを生成する平常時モデル生成ステップと、
想定するシナリオ地震の規模を決定するシナリオ地震決定ステップと、
決定した前記シナリオ地震に対する各々の前記構成施設の被害率を評価する被害率評価ステップと、
生成した前記平常時供給施設モデル及び評価した前記構成施設の前記被害率に基づいて、前記供給施設を構成する複数の構成施設のうちの隣接する２つの構成施設毎に連結又は非連結を示す隣接行列を生成する隣接行列生成ステップと、
生成された前記隣接行列からブール代数演算則に従って前記供給施設を構成する複数の前記構成施設のうちの２つの構成施設毎に連結又は非連結を示す可到達行列を求める可到達行列算出ステップと、
を有することを特徴とする供給施設の連結性評価方法。 A supply facility connectivity evaluation method for evaluating a connection state of a supply facility connecting a supply source and a supply facility at the time of an earthquake disaster,
From the configuration diagram showing the connection between each component facility including the supply source and the supplied facility in the region where the evaluation target is included, A normal model generation step for generating a normal supply facility model;
A scenario earthquake determination step for determining the magnitude of the scenario earthquake to be assumed;
A damage rate evaluation step for evaluating a damage rate of each of the component facilities with respect to the determined scenario earthquake;
Based on the generated normal supply facility model and the damage rate of the evaluated component facility, adjacent ones of the plurality of component facilities constituting the supply facility are connected or disconnected. An adjacency matrix generation step for generating a matrix;
A reachability matrix calculation step for obtaining a reachable matrix indicating connection or non-connection for each of two constituent facilities of the plurality of constituent facilities that constitute the supply facility according to a Boolean algebra operation rule from the generated adjacent matrix;
A method for evaluating connectivity of a supply facility, comprising:
前記シナリオ地震決定ステップから前記可到達行列算出ステップまでを繰り返しシミュレーションするシミュレーションステップと、
実行された複数回の前記シミュレーションの結果に基づいて前記２つの構成施設間の連結性を評価する連結性評価ステップと、
を有することを特徴とする供給施設の連結性評価方法。 A method for evaluating connectivity of a supply facility according to claim 1,
A simulation step for repeatedly simulating the scenario earthquake determination step to the reachability matrix calculation step;
A connectivity evaluation step for evaluating connectivity between the two constituent facilities based on the results of the simulation performed a plurality of times;
A method for evaluating connectivity of a supply facility, comprising:
前記連結性評価ステップでは、複数回の前記シミュレーションの結果となる前記可到達行列の各成分の平均値を求めることを特徴とする供給施設の連結性評価方法。 A method for evaluating connectivity of a supply facility according to claim 2,
In the connectivity evaluation step, an average value of each component of the reachability matrix that is a result of the simulation multiple times is obtained.
前記連結性の評価結果を前記構成図上に図示する評価結果図示ステップを有することを特徴とする供給施設の連結性評価方法。 A method for evaluating connectivity of a supply facility according to claim 2 or claim 3,
A connectivity evaluation method for a supply facility, comprising an evaluation result display step for displaying the connectivity evaluation result on the configuration diagram.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2010018272A JP2011158985A (en) | 2010-01-29 | 2010-01-29 | Connectiveness evaluation method for supply facility |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2010018272A JP2011158985A (en) | 2010-01-29 | 2010-01-29 | Connectiveness evaluation method for supply facility |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JP2011158985A true JP2011158985A (en) | 2011-08-18 |
Family
ID=44590907
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP2010018272A Pending JP2011158985A (en) | 2010-01-29 | 2010-01-29 | Connectiveness evaluation method for supply facility |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2011158985A (en) |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2016025549A (en) * | 2014-07-23 | 2016-02-08 | 日本電気株式会社 | Network management server, canalization determination method and program |
| JP2018205956A (en) * | 2017-06-01 | 2018-12-27 | 富士通株式会社 | Regional characteristic prediction method, regional characteristic prediction device, and regional characteristic prediction program |
| CN109560546A (en) * | 2018-12-10 | 2019-04-02 | 四川大学 | A kind of quick partition method of urban high voltage distribution network |
| CN110543615A (en) * | 2019-09-05 | 2019-12-06 | 国网湖南省电力有限公司 | Risk factor interaction analysis method based on SPSS explanation structure model |
| JP2019220106A (en) * | 2018-06-22 | 2019-12-26 | メタウォーター株式会社 | Information processing system, information processing device, and program |
| JP2021028842A (en) * | 2018-06-22 | 2021-02-25 | メタウォーター株式会社 | Information processing system, information processing device, and program |
-
2010
- 2010-01-29 JP JP2010018272A patent/JP2011158985A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2016025549A (en) * | 2014-07-23 | 2016-02-08 | 日本電気株式会社 | Network management server, canalization determination method and program |
| JP2018205956A (en) * | 2017-06-01 | 2018-12-27 | 富士通株式会社 | Regional characteristic prediction method, regional characteristic prediction device, and regional characteristic prediction program |
| JP2019220106A (en) * | 2018-06-22 | 2019-12-26 | メタウォーター株式会社 | Information processing system, information processing device, and program |
| JP2021028842A (en) * | 2018-06-22 | 2021-02-25 | メタウォーター株式会社 | Information processing system, information processing device, and program |
| CN109560546A (en) * | 2018-12-10 | 2019-04-02 | 四川大学 | A kind of quick partition method of urban high voltage distribution network |
| CN110543615A (en) * | 2019-09-05 | 2019-12-06 | 国网湖南省电力有限公司 | Risk factor interaction analysis method based on SPSS explanation structure model |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| JP2011158985A (en) | Connectiveness evaluation method for supply facility | |
| JP5756767B2 (en) | Water leak detection device | |
| Luna et al. | Postearthquake recovery of a water distribution system: Discrete event simulation using colored petri nets | |
| Jung et al. | Robustness-based design of water distribution systems | |
| Hernandez-Fajardo et al. | Probabilistic study of cascading failures in complex interdependent lifeline systems | |
| Tabesh et al. | Calibration of water distribution hydraulic models: A comparison between pressure dependent and demand driven analyses | |
| Qi et al. | A comprehensive framework to evaluate hydraulic and water quality impacts of pipe breaks on water distribution systems | |
| He et al. | Modeling the damage and recovery of interdependent civil infrastructure network using Dynamic Integrated Network model | |
| Ishido et al. | A new indicator for real-time leak detection in water distribution networks: design and simulation validation | |
| Tomar et al. | Hindcasting the functional loss and restoration of the Napa water system following the 2014 earthquake using discrete-event simulation | |
| Wang et al. | Modeling cascading failure of interdependent critical infrastructure systems using HLA-based co-simulation | |
| Liu et al. | Seismic functional reliability analysis of water distribution networks | |
| Wang et al. | Assessing the impact of systemic heterogeneity on failure propagation across interdependent critical infrastructure systems | |
| Wang et al. | Submarine cable path planning based on weight selection of design considerations | |
| Bata et al. | Urban water supply systems’ resilience under earthquake scenario | |
| Li et al. | Interdependent effects of critical infrastructure systems under different types of disruptions | |
| Kim et al. | A study on 3D safety state information platform architecture design for realistic disaster management based on spatial information | |
| Sweetapple et al. | A tool for global resilience analysis of water distribution systems | |
| Jun et al. | Valve distribution and impact analysis in water distribution systems | |
| Liu et al. | Seismic design of water distribution networks using auto-generation techniques | |
| Kiyan et al. | Smart dashboard of water distribution network operation: A case study of tehran | |
| Han et al. | Enabling state estimation for fault identification in water distribution systems under large disasters | |
| Christodoulou et al. | Urban water distribution networks: assessing systems vulnerabilities, failures, and risks | |
| Narayanan et al. | Little knowledge Isn’t always dangerous—Understanding water distribution networks using centrality metrics | |
| Yu et al. | A Probabilistic Approach for Modeling the Resilience of Interdependent Power and Water Infrastructure Networks |