KR102020339B1 - Method and apparatus for modelling random network with characteristics of water distribution system - Google Patents

Abstract

The present invention relates to a random network modeling method reflecting water supply network characteristics, and to an apparatus thereof. The random network modeling method reflecting water supply network characteristics comprises the steps of: generating an initial grid network including a node including a supply source and a demand source and an edge connecting the node; and adjusting the edge to change an initial grid network into a grid network corresponding to a given grid ratio.

Description

Random Network Modeling Method and Apparatus Reflecting Water Supply Network Characteristics METHOD AND APPARATUS FOR MODELLING RANDOM NETWORK WITH CHARACTERISTICS OF WATER DISTRIBUTION SYSTEM}

The present invention relates to a method and apparatus for randomly generating a network model by reflecting water pipe network characteristics.

Water supply network is a critical infrastructure essential for human survival. It is most important to minimize the damage from natural disasters and human disasters, and to facilitate the recovery in the event of damage, to maintain the original function as much as possible.

Existing pipe network system is designed only for efficient resource transportation based on economics, and there is no consideration of damage reduction and resilience due to external shock such as climate change in the situation that the frequency and intensity of external shock due to climate change increase.

To solve this problem, several models and indicators have been developed to analyze the network characteristics.

However, there are limitations that the models proposed to date do not fully reflect the characteristics of the water supply network and are not suitable as a control of the water supply network in statistical analysis because they do not consider the major variables of the water supply network system.

The background technology of the present application is disclosed in Korean Patent Publication No. 10-1512080.

The present invention is to solve the above-mentioned problems of the prior art, by varying and applying the main variables of the water supply network that can be easily used to identify the functionality and vulnerability of the water supply network, random network model reflecting the characteristics of the water supply network It is an object to provide a method and apparatus for generating.

The present invention is to solve the problems of the prior art described above, to generate a random network model reflecting the characteristics of the water supply network, which can analyze the results of the adjustment of the major variables of the water supply network to build a more resilient water supply network system It is an object to provide a method and apparatus.

However, the technical problem to be achieved by the embodiments of the present application is not limited to the technical problems as described above, and other technical problems may exist.

As a technical means for achieving the above technical problem, a random network modeling method reflecting the characteristics of the water supply network according to an embodiment of the present application, (a) a node including a supply source and demand source and the edge connecting the node Generating an initial grid network; And (b) adjusting the edge to change the initial grid network to a grid network corresponding to a given grid ratio.

In addition, the step (a), (a1) the source and the demand source based on the number of all nodes including the supply source and the demand source, the number of the supply source in the total node and the number of the demand source. Generating a first lattice network of a size that can include the excluded node; (a2) when the number of nodes of the first grid network is greater than the number of nodes obtained by subtracting the number of the supply sources and the number of the demand sources from the total number of nodes, it is determined that an extra node exists. Creating a second grid network by deleting as many nodes as the number of spare nodes; And (a3) randomly connecting as many nodes as the number of supply sources and the number of demand sources to the second grid network.

In addition, in the step (a1), the first grid network may be generated as a square grid network.

Further, the square lattice network of step (a1) satisfies Equations 1 and 2 below,

[Equation 1]

α × α (when β = 0)

[Equation 2]

( α +1) × ( α +1) (When 0 < β <1)

(α는 정수, β는 소수)이고, n은 상기 공급원과 상기 수요원을 포함하는 전체 노드 개수이고, s는 상기 공급원 개수이고, d는 상기 수요원의 개수일 수 있다.Where u = n- ( s + d ),

( α is an integer, β is a prime number), n is the total number of nodes including the supply source and the demand source, s is the number of the supply source, d may be the number of the demand source.

In addition, in step (a2), the second grid network may be generated by deleting at least some of the nodes corresponding to the edges in the first grid network of step (a1).

Also, the node corresponding to the edge may be a node having a connection center of 3 or less.

In addition, when there are a plurality of nodes to be deleted in the step (a2), the plurality of nodes to be deleted may be nodes arranged adjacent to each other continuously along the edge.

In addition, in the step (a3), the random connection may be a random connection in which a node randomly connected to the second grid network has a connection center degree of 1.

In addition, in step (b), the edges are randomly deleted from the initial grid network, and the total number of edges deleted is Equation 4 below.

[Equation 4]

은 상기 초기 격자 네트워크의 엣지 개수이고, p는 상기 격자비율이고, (n－1)은 완전한 수지선 네트워크의 엣지 개수이고, n은 상기 공급원과 상기 수요원을 포함하는 전체 노드 개수일 수 있다.Where m ( p ) is the total number of edges removed from the initial grid network,

Is the number of edges of the initial grid network, p is the grid ratio, ( n -1) is the number of edges of the complete resin network, n is the total number of nodes including the supply source and the demand source.

In addition, in the step (b), the lattice ratio may be calculated according to Equation 5 below.

[Equation 5]

In addition, in the step (b), if the network model is separated into two or more during the execution of the step, the separated network model is restored to its pre-separation state and an edge different from the edge causing the separation of the network model is adjusted. For example, it can be controlled to maintain one network model.

In addition, the random network modeling method reflecting the characteristics of the water supply network according to an embodiment of the present application, (c) when the number of nodes having a connection center of 1 is changed during or after performing step (b), The method may further include adjusting the connection of the nodes so that the number of nodes having a connection center degree 1 corresponds to the sum of the number of supply sources and the number of demand sources.

In addition, in the step (c), the error center except for the supply source and the demand source among the nodes having the connection center degree 1 is connected to any supply source among the supply sources or any demand source among the demand sources. The faulty node connected to any of the sources of supply or any of the sources of demand, excluding any of the sources of supply or any of the sources of demand from the sources of supply; It can be included in the supply source or the demand source.

On the other hand, the random network modeling apparatus reflecting the characteristics of the water supply network according to an embodiment of the present application, the network generation unit for generating an initial grid network including a node including a supply source and demand source and the edge connecting the node; And a network converter for adjusting the edge to change the initial grid network into a grid network corresponding to a given grid ratio.

The network generation unit may include a node excluding the supply source and the demand source in the entire node based on the number of all nodes including the supply source and the demand source, the number of the supply sources, and the number of the demand sources. When a first grid network having a size is created, and there are redundant nodes other than the node except for the supply source and the demand source in the first grid network, the number corresponding to the number of the redundant nodes in the first grid network The second grid network may be created by deleting nodes, and as many nodes as the number of the supply sources and the number corresponding to the demand sources may be randomly connected to the second grid network.

The network generator may generate a square grid network as the first grid network.

The square grid network generated by the network generator satisfies Equations 1 and 2 below,

[Equation 1]

α × α (when β = 0)

[Equation 2]

( α +1) × ( α +1) (When 0 < β <1)

(α는 정수, β는 소수)이고, n은 상기 공급원과 상기 수요원을 포함하는 전체 노드 개수이고, s는 상기 공급원 개수이고, d는 상기 수요원의 개수일 수 있다.Where u = n- ( s + d ),

( α is an integer, β is a prime number), n is the total number of nodes including the supply source and the demand source, s is the number of the supply source, d may be the number of the demand source.

The network generator may generate a second grid network by deleting at least some of nodes corresponding to edges in the first grid network.

Also, the node corresponding to the edge may be a node having a connection center of 3 or less.

In addition, when there are a plurality of nodes deleted by the network generation unit, the plurality of deleted nodes may be nodes that are continuously arranged next to each other along an edge.

The network converter may randomly connect the number of nodes corresponding to the number of the supply sources and the number of the demand sources to the second grid network such that the connection center is one.

The network converter may randomly delete edges from the initial grid network, and the total number of edges deleted is Equation 4 below.

[Equation 4]

은 상기 초기 격자 네트워크의 엣지 개수이고, p는 상기 격자비율이고, (n－1)은 완전한 수지선 네트워크의 엣지 개수이고, n은 상기 공급원과 상기 수요원을 포함하는 전체 노드 개수일 수 있다.Where m ( p ) is the total number of edges removed from the initial grid network,

Is the number of edges of the initial grid network, p is the grid ratio, ( n -1) is the number of edges of the complete resin network, n is the total number of nodes including the supply source and the demand source.

In addition, the lattice ratio may be calculated according to Equation 5 below.

[Equation 5]

In addition, when the network model is separated into two or more during the process of changing the network, the network converter restores the separated network model to a state before separation and adjusts an edge different from the edge that caused the separation of the network model. Thus, the network model can be controlled to be kept as one.

In addition, when the number of nodes having a connection center degree of 1 is changed during or after changing the network, the network converter determines the number of nodes having the connection center degree of 1 as the number of supply sources and the demand. The connection of nodes can be adjusted to correspond to the sum of the number of circles.

The network converting unit may be configured such that an error node excluding the supply source and the demand source among the nodes having the connection center degree 1 is connected to any supply source of the supply source or any demand source of the demand source. A fault node connected to any of the sources or any of the sources of demand, wherein the source of the source or It can be included in the demand source.

The above-mentioned means for solving the problems are merely exemplary and should not be construed as limiting the present application. In addition to the above-described exemplary embodiments, additional embodiments may exist in the drawings and detailed description of the invention.

According to the above-described problem solving means of the present invention, by generating a random network model reflecting the characteristics of the water supply network by using the parameters of the water supply network, such as the source of supply, demand source as a variable, a more resilient water supply network system by utilizing such a random network model The results of adjusting key variables of the water supply network to construct can be analyzed more effectively and easily. For example, these random network models can be analyzed by statistical techniques to identify the functionality and vulnerability of the waterworks network.

According to the above-described problem solving means of the present invention, by generating a random network model reflecting the water supply network characteristics that can analyze the results of adjusting the grid ratio, the number of sources, etc., the frequency and intensity of external shocks due to climate change, etc. increases. In this situation, damages can be prevented and minimized in advance, and disaster costs can be reduced, and water necessary for humans can be stably supplied.

According to the above-described problem solving means of the present application, by modeling the system reflecting the characteristics of the water supply network, it is possible to present a more resilient water supply network design through the analysis results such as adjusting the grid ratio and the number of sources.

However, the effects obtainable herein are not limited to the effects as described above, and other effects may exist.

1 is a flowchart of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application.
2 is a conceptual diagram illustrating an example of an initial grid network generation process of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application.
FIG. 3 is a conceptual diagram illustrating an example of a process of changing a grid network corresponding to a given grid ratio of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present disclosure.
FIG. 4 illustrates an error in which the connection centrality is 1 even when the network is not a supply source or a demand source during or after changing a network of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application. It is a conceptual diagram for explaining an example of a solution process.
5 is a flowchart illustrating an entire algorithm of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application.
6 is a conceptual diagram illustrating a network model generated as a result of a random network modeling method reflecting characteristics of a water supply network according to an embodiment of the present application.
7 is a block diagram of a random network modeling apparatus reflecting water supply network characteristics according to an embodiment of the present application.

DETAILED DESCRIPTION Hereinafter, exemplary embodiments of the present disclosure will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present disclosure. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. In the drawings, parts irrelevant to the description are omitted for simplicity of explanation, and like reference numerals designate like parts throughout the specification.

Throughout this specification, when a part is "connected" to another part, it is not only "directly connected" but also "electrically connected" or "indirectly connected" with another element in between. "Includes the case.

Throughout this specification, when a member is said to be located on another member "on", "upper", "top", "bottom", "bottom", "bottom", this means that any member This includes not only the contact but also the presence of another member between the two members.

Throughout this specification, when a part is said to "include" a certain component, it means that it can further include other components, without excluding the other components unless specifically stated otherwise.

Hereinafter, a random network modeling method reflecting the characteristics of the water supply network according to an embodiment of the present application (hereinafter referred to as 'the present network modeling method') and a random network modeling apparatus reflecting the characteristic of the water supply network according to an embodiment of the present application (hereinafter referred to as Network modeling device ').

1 is a flowchart of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application.

Referring to FIG. 1, the present network modeling method may include generating an initial grid network including a node including a supply source and a demand source and an edge connecting the nodes (S100). In addition, the network modeling method may include changing the initial grid network to a grid network corresponding to a given grid ratio by adjusting an edge (S200).

The network may mean a structure including a node representing an entity and an edge representing a connection relationship between the nodes. When applying network theory to a water supply network, sources, demands, and intersections can be nodes, and pipes can be edges. In this case, the intersection means a point connected by a pipe rather than a supply source or a demand source (hereinafter, a node except a supply source and a demand source is called an 'intersection point'). An intersection point in terms of connection center view may refer to a node having a connection center degree of 2 or more. In addition, the grid network may refer to a network in which nodes and edges are repeatedly arranged to form at least a portion of the grid.

The water supply network has a mixture of tree and grid networks on a two-dimensional plane, and generally transports important resources from a supply source to a demand source. The grid ratio (hereinafter referred to as 'grid ratio') in the pipe network is considered to be a major factor affecting the functionality and robustness of the entire water supply network. According to the grid ratio, the network generated by the present network modeling method can be adjusted between a network whose intersection is a grid entirely and a network composed of complete resin wires from a source to a demand source.

In step S100, an initial grid network including a node including a supply source and a demand source and an edge connecting the node is generated.

In step S100, a network may be randomly generated by designating the number and intersection ratios of grids, supply sources, and demand sources as variables. In this case, the generated network may be a primary undirected network without directivity.

In step S200, the edge is adjusted to change the initial grid network into a grid network corresponding to a given grid ratio.

In step S200, adjusting the edge may mean increasing or decreasing the number of edges.

2 is a conceptual diagram illustrating an example of an initial grid network generation process of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application.

Step S100 is a step of generating a first grid network having a size that can include nodes excluding the supply source and the demand source from all nodes based on the total number of nodes including the source and the demand source, the number of the source and the demand source. It may include (S110).

In step S110, the nodes except for the supply source and the demand source in the total node means the intersection. Referring to the network denoted by reference numeral S110 in FIG. 2, generating a first grid network having a size capable of including a node excluding a supply source and a demand source may include a horizontal node number m (eg, 8) and a vertical node number n. In generating a rectangular two-dimensional grid network (for example, 8), it may mean that m and n values are set to a size that can include both nodes (intersection points) except for a supply source and a demand source. In an exemplary embodiment, the first lattice network may be generated as a square two-dimensional lattice network having a size that may include all intersections. This will be described later in more detail through equations.

In operation S100, when the number of nodes in the first grid network is greater than the number of nodes obtained by subtracting the number of supply sources and the number of demand sources from the total number of nodes, it is determined that an extra node exists. In operation S120, a second grid network may be generated by deleting as many nodes as the number of nodes.

In operation S120, when it is determined that the spare node exists, it may mean that the first grid network is generated to have a number of nodes larger than the number of intersections. That is, creating a second grid network by deleting as many nodes as the number of spare nodes in the first grid network means that the first grid network that has been created to have a size that can include all the intersections is a point of intersection (the source of supply at all nodes). It can mean that it is generated by changing to a grid network that exactly corresponds to the number of nodes minus the demand source.

In addition, step S100 may include a step (S130) of connecting at least as many nodes corresponding to the number of sources and the number of demand sources to the second grid network (S130).

In operation S130, nodes randomly connected to the number corresponding to the number of supply sources may be modeled as supply sources, and nodes randomly connected to the number corresponding to the number of demand sources may be modeled as demand sources.

By performing the steps S110 to S130 as described above, an initial grid network of the step S100 may be generated.

Hereinafter will be described in more detail with respect to the configuration associated with the present application.

Referring to FIG. 2, in step S110, the first grid network may be generated as a square grid network. The square grid network refers to a two-dimensional network having a rectangular structure having the same length and width.

The square lattice network of step S110 satisfies Equations 1 and 2 below,

[Equation 1]

α × α (when β = 0)

[Equation 2]

( α +1) × ( α +1) (When 0 < β <1)

(α는 정수, β는 소수)이고, n은 공급원과 수요원을 포함하는 전체 노드 개수이고, s는 공급원 개수이고, d는 수요원의 개수인 것일 수 있다.Where u = n- ( s + d ),

( α is an integer, β is a prime number), n is the total number of nodes including the source and the demand source, s is the number of sources, d may be the number of demand sources.

In this case, u may mean the number of intersections. When β = 0, the number of nodes of the first lattice network is equal to the number of intersections, and when 0 < β <1, the number of nodes of the first lattice network is larger than the number of intersections, and there may be extra nodes. . Therefore, step S120 may be performed when 0 < β <1.

For example, referring to FIG. 2, when an input value of the total number of nodes n 100, the number of supply sources s 1, the number of demand sources d 40, and the grid ratio p p 0 is given, the initial grid network is the above. According to Equation 1 and 2 can be generated as follows.

=7＋β (0＜β＜1)이다. 이 때, α는 7이다. 따라서, S110 단계에서는 (α＋1)×(α＋1)=(7+1)×(7+1) 즉, 8×8인 2차원의 제1 격자 네트워크를 생성할 수 있다(도 2의 S110 참조). 그런데 현재 교차점의 개수(u)는 59이므로, 8×8=64의 노드를 갖는 제1 격자 네트워크에는 5개만큼의 여분 노드가 포함된 것으로 볼 수 있다. 따라서, S120단계는 (α＋1)×(α＋1)－u=(7+1)×(7+1)－59=5만큼의 여분 노드를 삭제함으로써, 전체 노드에서 공급원과 수요원을 제외한 노드인 교차점에 정확하게 대응하도록 노드를 조절하여 제 2 격자 네트워크를 생성할 수 있다(도 2의 S120 참조). 이 때, 제 2 격자 네트워크는 노드의 개수가 u=59인 k×l 격자 네트워크를 생성할 수 있다. 이 때, k는 격자 네트워크의 가로 노드 개수일 수 있고, l은 격자 네트워크의 세로 노드 개수일 수 있다. 도 2의 S130을 참조하면, S130 단계는 (s＋d)개의 공급원과 수요원에 해당하는 노드를 생성 후 무작위로 상기 제 2 격자 네트워크의 절점에 연결할 수 있다.First, u = 100-(1 + 40) = 59,

= 7 + β (0 < β <1). ( Alpha) is 7 at this time. Therefore, in the step S110 (α +1) × (α +1) = (7 + 1) × (7 + 1) That is, it is possible to generate an 8 × 8 of the first grid network of a two-dimensional (S110, see the Fig. 2 ). However, since the number of current intersection points u is 59, it can be seen that the first grid network having nodes of 8x8 = 64 includes as many as 5 spare nodes. Thus, step S120 (α +1) × (α +1 ) - u = (7 + 1) × (7 + 1) -59 = node except the source and the demand source by deleting redundant nodes in a 5 by, in the entire node The second grid network may be generated by adjusting nodes to accurately correspond to phosphorus intersection points (see S120 of FIG. 2). In this case, the second lattice network may generate a k × l lattice network in which the number of nodes is u = 59. In this case, k may be the number of horizontal nodes of the grid network, l may be the number of vertical nodes of the grid network. Referring to S130 of FIG. 2, in step S130, nodes corresponding to ( s + d ) supply sources and demand sources may be randomly connected to nodes of the second grid network.

Referring to FIG. 2, in operation S120, a second grid network may be generated by deleting at least some of the nodes corresponding to the edges (borders) in the first grid network in step S110. In this case, unlike when randomly deleting nodes in the entire first grid network, the initial grid ratio can be maintained.

In this case, the node corresponding to the edge may be a node having a connection center of 3 or less. Also, the node corresponding to the edge may be a node having a connection center degree of 2 or more. Degree centrality means the number of edges of a node. Therefore, the nodes corresponding to the supply source and the demand source may have a connection center degree of 1, and a node corresponding to an intersection may have a connection center degree of 2 or more. However, nodes (intersections) positioned at the edge of the first grid network among the nodes corresponding to the intersection may have two or more connection centers of three or less. On the other hand, nodes (intersections) located inside the edge of the first lattice network may have a connection center degree of four. Thus, when nodes having a connection center of 2 or more and 3 or less are removed, nodes corresponding to edges in the first grid network may be removed.

For example, referring to FIG. 2, when there are a plurality of nodes to be deleted in step S120, the plurality of nodes to be deleted may be nodes that are consecutively arranged next to each other along an edge.

In addition, referring to FIG. 2, in step S130, the random connection of the nodes corresponding to the supply source and the demand source may be a random connection in which a node randomly connected to the second grid network has a connection center degree of 1. . As described above, a node having a connection center degree of 2 or more may be a supply source or a demand source in which a node corresponding to an intersection point and a node having a connection center degree of 1 are connected to a resin wire.

For reference, when modeling for comparative analysis with any actual water supply network, information on the number of nodes, sources, and demand sources is required. Based on this, nodes corresponding to the sources and demand sources are created to satisfy the connection center diagram 1. Can be.

FIG. 3 is a conceptual diagram illustrating an example of a process of changing a grid network corresponding to a given grid ratio of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present disclosure.

In step S200 of the network modeling method, edges are randomly deleted from the initial grid network, and the total number of edges deleted may be Equation 4 below.

[Equation 4]

은 초기 격자 네트워크의 엣지 개수이고, p는 격자비율이고, (n－1)은 완전한 수지선 네트워크의 엣지 개수이고, n은 공급원과 수요원을 포함하는 전체 노드 개수일 수 있다. 이 때, 초기 격자 네트워크는 S100 단계에 의해 생성된 네트워크를 의미할 수 있다.Where m ( p ) is the total number of edges removed from the initial grid network,

Is the number of edges of the initial grid network, p is the grid ratio, ( n -1) is the number of edges of the complete resin network, and n can be the total number of nodes including the source and demand source. At this time, the initial grid network may mean a network generated by the step S100.

Referring to FIG. 3, the total number of edges deleted according to the grid ratio may be adjusted. The lattice ratio may be 0 or more and 1 or less, and when the lattice ratio is 0, it may mean an initial lattice network.

는,

로 나타낼 수 있다. S120 단계의 제 2 격자 네트워크가 k×l일 때, 제 2 격자 네트워크의 엣지의 개수는 (k－1)·l＋(l－1)·k일 수 있다. 따라서, 제 2 격자 네트워크에 공급원의 개수와 수요원의 개수에 대응하는 개수만큼의 노드를 연결한 초기 격자 네트워크는 (k－1)·l＋(l－1)·k＋(s＋d)일 수 있다. 완전한 수지선 네트워크의 엣지의 개수인

는,

로 나타낼 수 있다. 이 때, S200 단계에서 임의의 격자비율을 갖는 네트워크 엣지 개수는

를 만족한다. 초기 격자 네트워크가 p=0인 상태로 생성되면 S200 단계는 엣지를 삭제하는 단계가 되는데, 이때 노드의 개수는 변화가 없으므로 특정 격자 비율에 대응하는 격자 네트워크의 노드의 개수인 n(p)는,

와 같이 격자비율과 무관하게 모두 동일한 것으로 나타낼 수 있다. 여기에서,

는 초기 격자 네트워크의 노드의 개수이고,

는 완전한 수지선 네트워크의 노드의 개수이다. 예를 들어, p=1인 완전한 수지선 네트워크의 엣지의 개수는 전체 노드의 개수보다 1개 적다(아래 표 1 참조).The number of edges in the initial grid network

Is,

It can be represented as. When the second lattice network in step S120 is k × l , the number of edges of the second lattice network may be ( k −1) · l + ( l −1) · k . Therefore, an initial grid network in which the number of nodes corresponding to the number of supply sources and the number of demand sources is connected to the second grid network is ( k −1) · l + ( l −1) · k + ( s + d ). Can be. The number of edges in the complete resin network

Is,

It can be represented as. At this time, the number of network edges having an arbitrary grid ratio in step S200

Satisfies. When the initial grid network is created with p = 0, the step S200 is to delete the edge. Since the number of nodes is not changed, n ( p ), which is the number of nodes of the grid network corresponding to a specific grid ratio,

It can be expressed as the same regardless of the lattice ratio. From here,

Is the number of nodes in the initial grid network,

Is the number of nodes in the complete resin network. For example, the number of edges of a complete resin network of p = 1 is one less than the total number of nodes (see Table 1 below).

In this case, the lattice ratio may be calculated according to Equation 5 below.

[Equation 5]

3 and Table 1 below show the change of the edge and the change of the network according to the change of the grid ratio p . In Table 1, p is a grid ratio, n is the number of nodes, and m is the number of edges of the grid network corresponding to a specific grid ratio. As the lattice ratio approaches 0 to 1, it can be seen that the lattice in the network decreases and the closer to the complete resin wire network.

TABLE 1

In step S200, when two or more network models are separated during the execution of the step, the separated network model is restored to its pre-separation state and the edges different from the edges causing the separation of the network models are maintained so that the network model remains one. Can be controlled. That is, in step S200, an edge may be deleted at random within a range that satisfies a condition in which one component of a network is maintained.

Restoring a detached network model to its pre-separation state may mean returning the edge that caused the detachment to the pre-separation state. For example, when a network is separated when an edge between two nodes is deleted, this may mean that the nodes are connected to the edge again.

FIG. 4 illustrates an error in which the connection centrality is 1 even when the network is not a supply source or a demand source during or after changing a network of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application. It is a conceptual diagram for explaining an example of a solution process.

In the network modeling method, when the number of nodes having a connection center degree of 1 is changed during or after performing step S200, the number of nodes having a connection center degree of 1 is equal to the sum of the number of supply sources and the number of demand sources. Adjusting the connection of the node to correspond (S300).

Before performing step S200, the number of nodes having a connection center degree of 1 may correspond to the sum of the number of supply sources and the number of demand sources. Therefore, the change in the number of nodes having a connection center degree of 1 may mean that a node having a connection center degree of 1 occurs in the process of adjusting the edge of step S200 even though it is not a supply source or a demand source. This may mean a case where the intersection point becomes 1.

In step S300, the error node excluding the supply source and the demand source among the nodes having the connection center degree 1 is connected to any supply source of the supply source or any demand source of the demand source so that the connection center degree is 1, and the supply source is any source. An error node connected to any source or any source can be included in the source or source, excluding at or any source of demand from the source.

The error node excluding the supply source and the demand source among the nodes having the connection center degree 1 may mean an intersection point at which the connection center degree is 1 in the process of deleting an edge in step S200. In step S300, such an error node is moved to be connected to any one of the sources or any one of the demand sources. In this process, the corresponding source or the demand source to which the error node is connected will no longer be 1 in the connection center. Can be. Therefore, in step S300, the corresponding supply source or the corresponding demand source whose connection center degree is not 1 as described above is excluded from the supply source or demand source, and instead, the error node newly connected to the corresponding supply source or the corresponding demand source is replaced. It can be included in the source or demand source. As the error node moves, the source or demand source of the network may be redefined in step S300. That is, the faulty node can be a new source or demand source.

For example, in the left network of FIG. 4, the source may be 7 times and the demand sources 5 and 6. In the middle network of FIG. 4, when the edge connecting the node 1 and the node 4 is deleted, the connection center diagram may be 1 even though the node 4 is not a supply source or a demand source. At this time, node 4 may be referred to as an error node. In the right network of Fig. 4, node 4, which is an error node, may be connected to the demand source 6 such that the connection center degree is 1. At this time, node 6 may be excluded from the demand source, and node 4 may be redefined as the demand source.

In the above description, steps S100 to S200 may be further divided into additional steps, or combined into fewer steps, according to embodiments herein. In addition, some steps may be omitted as necessary.

5 is a flowchart illustrating an entire algorithm of a random network modeling method reflecting water supply network characteristics according to an embodiment of the present application.

Referring to FIG. 5, in step S100, the number of total nodes, the number of supply sources, the number of demand sources, and the grid ratio are input, and the number of nodes obtained by subtracting the number of supply sources and the number of demand sources from the total number of nodes (hereinafter, ' Create a grid network of nodes), and if the number of intersections is less than the sum of the number of sources and demand sources, then the total number of nodes, the number of sources, and the number of sources And inputting the grid ratio again, and if the number of intersections is equal to or greater than the sum of the number of supply sources and the demand source, randomly sort all nodes, add nodes in the sorted order, connect edges, If the number of nodes corresponds to the sum of the number of sources and the number of demand sources, an initial grid network is created, and the number of nodes added is the number of sources and demand If the number of circles does not correspond to the sum of the numbers, it may include adding nodes again in the sorted order and connecting edges.

In step S200, if the total number of edges to be deleted according to the input grid ratio is 0, the result is immediately obtained. If the total number of edges to be deleted is larger than 0, all edges are sorted randomly and sorted. Delete the edges in the same order, if the network model is separated into two or more, restore the separated network model to its pre-detachment state, delete the edges in the sorted order after passing the edges, If it is maintained as one, if the total number of deleted edges does not correspond to the total number of edges to be deleted according to the input grid ratio, the edges are deleted in the sorted order again, and the total number of edges deleted. If S corresponds to the total number of edges to be deleted according to the input grid ratio, the process goes to step S300. It may include.

In the step S300, when the number of nodes having a connection center of 1 (hereinafter referred to as 'intersection and a node having a connection center of 1') of 0 is not a supply source or a demand source, the result is immediately obtained, and the intersection and connection center are obtained. If the number of nodes with a degree of 1 is greater than 0, then all the sources of demand are sorted randomly, and the set of nodes with intersections and connection centers of 1 is moved back to the demand source so that the connection centers are 1 in the sorted order. And replacing the demand source with the moved node, and repeating until the number of nodes having the intersection point and the connection center degree becomes 0.

Referring to FIG. 5, the result obtained by the network modeling method may be a two-dimensional network.

6 is a conceptual diagram illustrating a network model generated as a result of a random network modeling method reflecting characteristics of a water supply network according to an embodiment of the present application.

In FIG. 6, the left network may represent a network composed of as many nodes as the number of nodes minus the number of supply sources and the number of demand sources, which may be the second grid network in step S120 (see FIG. 2). . In addition, the middle networks may represent a process of changing to a grid network corresponding to a given grid ratio. When p = 0, the initial lattice network in step S200 can be represented, when p = 0.5, the lattice network corresponding to the lattice ratio 0.5 can be represented, and when p = 1, the complete resin wire network can be represented. .

Referring to FIG. 6, since a process of generating an initial grid network in step S100 and a process of changing to a grid network corresponding to a grid ratio in step S200 are all performed at random, the total number of nodes, the number of supply sources, and the demand source. It is possible to secure a large number of routines that combine a series of processes of transforming an initial grid network generated by inputting the number of to a complete resin network.

The present network modeling method uses a network model reflecting the characteristics of the water supply network generated by the above-described network modeling method, and inputs all the first variables to generate a random network having the corresponding input values.

In addition, the present network modeling method may include a process of generating an initial grid network by modularizing the algorithm of the network model and a process of modifying a specific grid ratio. In this case, the initial grid network may be fixed by fixing the initial value. It can be easily used for comparative evaluation. Here, the initial value is actually a specification of the water supply network of a specific region, and may include the total number of nodes, the number of supply sources, and the number of demand sources. In addition, a large number of routines can be used to evaluate the functionality and vulnerability of the network as the grid rate changes.

Furthermore, by using a network model reflecting the characteristics of the water supply network generated by the network modeling method, at least one or more of the total number of nodes, the number of supply sources, the number of demand sources, and the grid ratio may be adjusted and analyzed. Based on the analysis results, a resilient water supply network can be designed to prevent or minimize the damage from external shocks.

Meanwhile, hereinafter, a random network modeling apparatus reflecting water supply network characteristics according to an embodiment of the present application will be described. However, the random network modeling apparatus reflecting the characteristics of the water supply network according to an embodiment of the present application is the same or a corresponding technical feature only in the random network modeling method reflecting the characteristics of the water supply network according to the embodiment of the present application, but only in different categories. Since it will be referred to as an invention to share, for the convenience of description, the same reference numerals are used for the same configuration as the salping configuration, and overlapping description will be briefly or omitted.

7 is a block diagram of a random network modeling apparatus reflecting water supply network characteristics according to an embodiment of the present application.

Referring to FIG. 7, the apparatus for modeling a network may control an initial grid network by adjusting an edge and a network generator 710 for generating an initial grid network including a node including a supply source and a demand source and an edge connecting the nodes. It may include a network converter 720 for changing to a grid network corresponding to a given grid ratio.

The network generator 710 generates an initial grid network including a node including a supply source and a demand source and an edge connecting the nodes. The network converter 720 adjusts an edge to change the initial grid network into a grid network corresponding to a given grid ratio.

The network generator 710 may generate a first grid network having a size that may include nodes except for the supply source and the demand source, based on the total number of nodes including the supply source and the demand source, the number of the supply sources, and the number of the demand sources. Can be. Since this has been described above in the method category, a detailed description thereof will be omitted.

In addition, when there are redundant nodes other than the nodes excluding the supply source and the demand source in the first grid network, the network generator 710 deletes the number of nodes corresponding to the number of spare nodes in the first grid network. A two grid network can be created. Since this has been described above in the method category, a detailed description thereof will be omitted.

In addition, the network generator 710 may randomly connect as many nodes as the number of supply sources and the number of demand sources to the second grid network. Since this has been described above in the method category, a detailed description thereof will be omitted.

The network generator 710 may generate a square grid network as the first grid network. At this time, the square grid network means a network having a rectangular structure having the same length and width.

The square grid network generated by the network generator 710 satisfies Equation 1 and Equation 2 below.

[Equation 1]

α × α (when β = 0)

[Equation 2]

( α +1) × ( α +1) (When 0 < β <1)

(α는 정수, β는 소수)이고, n은 상기 공급원과 상기 수요원을 포함하는 전체 노드 개수이고, s는 상기 공급원 개수이고, d는 상기 수요원의 개수인 것일 수 있다. 이 때, u는 교차점의 개수를 의미할 수 있다. β＝0일 때, 제 1 격자 네트워크의 노드의 개수는 교차점의 개수와 같고, 0＜β＜1일 때, 제 1 격자 네트워크의 노드의 개수는 교차점의 개수보다 크며, 여분 노드가 존재할 수 있다. 따라서, 네트워크 생성부(710)는, 0＜β＜1일 때 제 1 격자 네트워크에서 여분 노드의 개수에 대응하는 개수만큼의 노드를 삭제하여 제 2 격자 네트워크를 생성할 수 있다.Where u = n- ( s + d ),

( α is an integer, β is a prime number), n is the total number of nodes including the supply source and the demand source, s is the number of the supply source, d may be the number of the demand source. In this case, u may mean the number of intersections. When β = 0, the number of nodes of the first lattice network is equal to the number of intersections, and when 0 < β <1, the number of nodes of the first lattice network is larger than the number of intersections, and there may be extra nodes. . Therefore, when 0 < β <1, the network generator 710 may generate the second grid network by deleting as many nodes as the number of spare nodes in the first grid network.

In addition, the network generator 710 may generate the second grid network by deleting at least some of the nodes corresponding to the edges in the first grid network. In this case, the node corresponding to the edge may be a node having a connection center of 3 or less. Since this has been described above in the method category, a detailed description thereof will be omitted.

When there are a plurality of nodes to be deleted by the network generator 710, the plurality of nodes to be deleted may be nodes that are continuously arranged next to each other along the edge. Since this has been described above in the method category, a detailed description thereof will be omitted.

The network converter 720 may randomly connect as many nodes as the number of supply sources and the number of demand sources to the second grid network such that the connection center is one. At this time, all nodes randomly connected to the second grid network may be a supply source or a demand source.

The network converter 720 randomly deletes edges in the initial grid network, and the total number of edges deleted is Equation 4 below.

[Equation 4]

은 상기 초기 격자 네트워크의 엣지 개수이고, p는 상기 격자비율이고, (n－1)은 완전한 수지선 네트워크의 엣지 개수이고, n은 상기 공급원과 상기 수요원을 포함하는 전체 노드 개수인 것일 수 있다. 이에 대해서는 방법 카테고리에서 전술한 바 있으므로, 상세한 설명은 생략한다.Where m ( p ) is the total number of edges removed from the initial grid network,

Is the number of edges of the initial grid network, p is the grid ratio, ( n -1) is the number of edges of the complete resin network, n may be the total number of nodes including the supply source and the demand source. . Since this has been described above in the method category, a detailed description thereof will be omitted.

In this case, the lattice ratio may be calculated according to Equation 5 below.

[Equation 5]

When the network model is separated into two or more networks during the process of changing the network, the network converter 720 restores the separated network model to its pre-separation state and adjusts an edge different from the edge that caused the separation of the network model. For example, it can be controlled to maintain one network model. Since this has been described above in the method category, a detailed description thereof will be omitted.

When the number of nodes having a connection center degree of 1 is changed during or after changing the network, the network converter 720 may determine the number of nodes having a connection center degree of 1 as the number of supply sources and the demand source. The connection of nodes can be adjusted to correspond to the sum of the numbers. Since this has been described above in the method category, a detailed description thereof will be omitted.

In addition, the network converter 720 connects an error node excluding a supply source and a demand source among nodes having a connection center degree of 1 to any supply source of the supply source or any demand source of the demand source so that the connection center degree is 1. It is possible to include in the source or demand source an error node that is connected to any source or any demand source so that the concentricity is 1 for any source or any demand source, excluding any source from any source or any demand source. Since this has been described above in the method category, a detailed description thereof will be omitted.

The apparatus described above may be implemented as a hardware component, a software component, and / or a combination of hardware components and software components. For example, the devices and components described in the embodiments include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor ( d igital s ig n al p ro s ss ), a microcomputer, It may be implemented using one or more general purpose or special purpose computers, such as a field programmable array (FPA), a programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. . The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to the execution of the software. For convenience of explanation, one processing device may be described as being used, but one of ordinary skill in the art will appreciate that the processing device includes a plurality of processing elements and / or a plurality of types of processing elements. It can be seen that it may include. For example, the processing device may include a plurality of processors or one processor and one controller. In addition, other processing configurations are possible, such as parallel processors.

The software may include a computer program, code, instructions, or a combination of one or more of the above, and configure the processing device to operate as desired, or process it independently or collectively. You can command the device. Software and / or data may be any type of machine, component, physical device, virtual equipment, computer storage medium or device in order to be interpreted by or to provide instructions or data to the processing device. Or may be permanently or temporarily embodied in a signal wave to be transmitted. The software may be distributed over networked computer systems so that they may be stored or executed in a distributed manner. Software and data may be stored on one or more computer readable recording media.

Random network modeling method reflecting the characteristics of the water supply network according to an embodiment of the present application, may be implemented in the form of program instructions that can be executed by various computer means may be recorded on a computer readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination. Program instructions recorded on the media may be those specially designed and constructed for the purposes of the present invention, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, such as floppy disks. Magneto-optical media, and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

In addition, the above-described network modeling method may be implemented in the form of a computer program or an application executed by a computer stored in a recording medium.

On the other hand, the present application can provide a method for analyzing the functionality and fragility of the actual water supply network by analyzing the random network model generated by using a random network modeling method reflecting the characteristics of the water supply network according to the embodiment of the present application described above. . The method may also be provided in the form of a program, a program medium, or a device in which the method is projected.

In addition, the present application design the water supply network by analyzing the result of adjusting at least one of the grid ratio and the number of sources in the random network model generated using the random network modeling method reflecting the characteristics of the water supply network according to the embodiment of the present application described above It can provide a way to. The method may also be provided in the form of a program, a program medium, or a device in which the method is projected.

The above description of the present application is intended for illustration, and it will be understood by those skilled in the art that the present invention may be easily modified in other specific forms without changing the technical spirit or essential features of the present application. Therefore, it should be understood that the embodiments described above are exemplary in all respects and not restrictive. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined form.

The scope of the present application is indicated by the following claims rather than the above description, and it should be construed that all changes or modifications derived from the meaning and scope of the claims and their equivalents are included in the scope of the present application.

S100: step of creating an initial grid network
S200: changing to a grid network corresponding to a given grid ratio
700: Random network modeling device reflecting water supply network characteristics
710: network generator 720: network converter

Claims (15)

In the random network modeling method,
(a) creating an initial grid network comprising a node comprising a supply source and a demand source and an edge connecting the nodes; And
(b) adjusting the edge to change the initial grid network to a grid network corresponding to a given grid ratio;
In step (b),
If two or more network models are separated during the execution of the step, the separated network model is restored to its pre-separation state, and an edge different from the edge that caused the separation of the network model is controlled to maintain one network model. Random network modeling method reflecting the water supply network characteristics. The method of claim 1,
In step (a),
(a1) a first size having a size capable of including nodes except for the supply source and the demand source based on the total number of nodes including the supply source and the demand source, the number of the supply sources in the total node, and the number of the demand sources; Creating a grid network;
(a2) when the number of nodes of the first grid network is greater than the number of nodes obtained by subtracting the number of the supply sources and the number of the demand sources from the total number of nodes, it is determined that an extra node exists. Creating a second grid network by deleting as many nodes as the number of spare nodes; And
(a3) random network modeling method reflecting the water supply network characteristics comprising the step of randomly connecting the number of nodes corresponding to the number of the source and the number of the demand source to the second grid network. The method of claim 2,
In the step (a1), the first grid network is a random network modeling method that reflects the water supply network characteristics that are generated as a square grid network. The method of claim 3,
The square lattice network of step (a1) satisfies Equations 1 and 2 below,
[Equation 1]
α × α (when β = 0)
[Equation 2]
( α +1) × ( α +1) (When 0 < β <1)
Where u = n- ( s + d ),

( α is an integer, β is a prime number), n is the total number of nodes including the supply source and the demand source, s is the number of the supply source, d is the number of the demand source, reflecting the water supply network characteristics Random network modeling method. The method of claim 2,
The step (a2) is a random network modeling method that reflects the water supply network characteristics, to generate a second grid network by deleting at least some of the nodes corresponding to the edge in the first grid network of the step (a1). The method of claim 5,
The node corresponding to the edge is a node having a connection center of 3 or less, random network modeling method reflecting the water supply network characteristics. The method of claim 5,
If the plurality of nodes to be deleted in the step (a2), the plurality of deleted nodes are nodes that are arranged adjacent to each other continuously along the edge, random network modeling method reflecting the characteristics of the water supply network. The method of claim 2,
In the step (a3), the random connection is a random network modeling method that reflects the water supply network characteristics, the node that is randomly connected to the second grid network is a random connection having a connection center degree of 1. The method of claim 1,
In step (b), random edges are deleted from the initial grid network.
The total number of edges deleted is Equation 4 below,
[Equation 4]

Where m ( p ) is the total number of edges removed from the initial grid network,

Is the number of edges of the initial grid network, p is the grid ratio, ( n -1) is the number of edges of the complete resin network, n is the total number of nodes including the supply source and the demand source, Random network modeling method reflecting water supply network characteristics. The method of claim 9,
In the step (b), the grid ratio is calculated according to Equation 5, random network modeling method reflecting the characteristics of the water supply network.
[Equation 5]

delete The method of claim 1,
(c) When the number of nodes having a connection center degree of 1 is changed during or after performing step (b), the number of nodes having the connection center degree of 1 is determined by the number of supply sources and the demand source. Random network modeling method that reflects the water supply network characteristics further comprising the step of adjusting the connection of the nodes to correspond to the sum of. The method of claim 12,
In the step (c), the error center of the node except for the supply source and the demand source among the nodes having the connection center degree 1 is connected to any supply source of the supply source or any demand source of the demand source to be 1; A fault node connected to any of the sources or any of the sources of demand, wherein the source of the source or Random network modeling method that reflects the water supply network characteristics that will be included in the demand source. In the random network modeling apparatus,
A network generator for generating an initial grid network including a node including a supply source and a demand source and an edge connecting the nodes; And
A network converter for adjusting the edge to change the initial grid network into a grid network corresponding to a given grid ratio;
Including,
The network converter,
When two or more network models are separated, the separated network model is restored to its pre-separation state and controlled to maintain one network model by adjusting an edge different from the edge that caused the separation of the network model. Random Network Modeling Device Reflecting Water Supply Network Characteristics. A computer-readable recording medium having recorded thereon a program capable of executing a random network modeling method reflecting the characteristics of a water supply network of claim 1.

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