JP6763624B1 - Pipe network analysis device, pipe network analysis method, and pipe network analysis program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a novel method for realizing a pipe network analysis by a mesh flow method in consideration of the pressure dependence of an outflow amount. SOLUTION: An analysis graph in which a conduit branch and a node known to a water head indicating a connection point between the pipeline branch and a distribution reservoir R1 and R2 are arranged at both ends of the pipeline branch, a head of the node, and a node. It is a pipeline analyzer that calculates the amount of nodal or pipeline outflow as a pressure-dependent amount, and connects all the nodes of the analysis graph with a tree and mesh group determination means of a non-looped branch set, and a fixed flow rate and mesh flow rate of the tree branch. The effective head calculation means for each node that performs non-pressure-dependent pipe network analysis processing, the means for connecting the pressure-deficient node to the reference node with a virtual connection branch, and the outflow amount of the pressure-deficient node are updated with the pressure-dependent amount of the distribution pipe network. , For the new analysis graph in which the insufficient pressure node is connected to the reference node by the virtual connection branch, each node effective head calculation means that performs pressure-dependent tube network analysis processing with the new mesh flow rate as a variable, and the effective head is less than the threshold. In the case of insufficient pressure, a new virtual connection branch is provided with a means for connecting to the reference node. [Selection diagram] Fig. 2

Description

The present invention relates to a pipe network analysis device, a pipe network analysis method, and a pipe network analysis program in consideration of the pressure dependence of the outflow amount.

Pipeline analysis is based on the pressure of each part of the pipeline when the water level of the distribution reservoir, the amount of demand at each demand point, and the characteristics of the pipeline elements (pipelines, pumps, valves) connecting the distribution reservoir and the demand point are all given. This is a steady flow analysis problem for finding the flow rate. Conventionally, for the distribution pipe network of waterworks, a technique for performing pipe network analysis has been proposed by treating each pipeline element with a line (branch) and an analysis graph showing the connection between them with a point (node).

In the initial pipe network analysis, the amount of runoff from the pipe network (demand amount, runoff water amount) was taken as a condition, and it was a constant non-pressure dependent amount regardless of the pressure. The analysis method can be roughly divided into the nodal head method and the mesh flow method depending on how the main variables are taken.

Non-Patent Document 1 discloses a technique relating to analysis of a water pipe network by a mesh flow method. The mesh here is defined in the analysis graph as "a set of loops (cycles) sequentially selected so that the number of constituent branches is as small as possible". Non-Patent Document 2 discloses a technique related to a pipeline take-out model for improving calculation accuracy when a change in flow direction or a change in opening / closing of a shutoff valve is performed.

Furthermore, in recent years, the nature of the realistic analysis that the outflow amount depends on the pressure has been clarified. Non-Patent Document 3-5 discloses a method for realizing a pipe network analysis in consideration of the pressure dependence of the outflow amount. Further, Patent Documents 1 and 2 also disclose a tube network analysis method in consideration of pressure dependence.

Non-Patent Document 6 discloses a discrete extraction model that directly deals with the reality that water is extracted at many demand points along a pipeline. This made it possible to handle pressure dependence in the pipeline take-out model.

Non-Patent Document 7 discloses a method of pipe network analysis for a pipe network including various water distribution equipment / equipment (secondary pressure fixing element) that functions to keep the secondary pressure constant.

Akihiko Uto, Yoshikazu Nishikawa, Ichiro Izumi "Analysis and Design of Water Pipe Network by Mesh Flow Method", Measurement and Control, Vol.28, No.8, pp.45-58 (August 1989) Yoshikazu Nishikawa, Akihiko Udo, "High-speed large-scale pipeline calculation and high accuracy by pipeline extraction model", Waterworks Association Magazine, Vol. 53, No. 12, pp2-16 (December 1984) Akihiko Uto, Takao Ozawa "Constant Flow Analysis of Water Pipe Network Considering Pressure Dependence of Outflow", Journal of the Society of Systems and Control Information, Vol.16, No.1, pp.54-59 (January 2003) Akihiko Uto, "Pipe network analysis considering pressure dependence of runoff water volume", Journal of Waterworks Association, Vol. 72, No. 11, pp.2-8 (November 2003) Akihiko Uto, Akira Yamashita "Refining Pipe Network Calculation Considering Pressure Dependence of Outflow Water-Introduction of Discrete Extraction Model in Node Head Method", Journal of the Society of Systems and Control Information, Vol.17, No.12, pp .561-563 (December 2004) Akihiko Uto, Koji Oguchi "Improvement of High-Precision Pipe Network Calculation by Discrete Extraction Model", Journal of the Society of Systems and Control Engineers, Vol.21, No.3, pp.69-74 (March 2008) Akihiko Uto "Data Structures and Algorithms for Pipe Network Calculations Including Secondary Pressure Fixing Elements", Journal of the Waterworks Association, Vol. 83, No. 12, pp.14-24 (December 2014)

Japanese Unexamined Patent Publication No. 2001-160043 Japanese Unexamined Patent Publication No. 2006-057407

In general, the number of variables in the mesh flow method is significantly smaller than the number of variables in the nodal head method, and the latter allows a compact formulation. In addition, in the nodal water head method, since the slope of the characteristic equation of the pipeline is infinite with respect to the variable, there may be a problem in the convergence of the solution calculation of the nonlinear simultaneous algebraic equations to be formulated. , The convergence by the mesh flow method is good.

Therefore, when comparing the calculation time for the existing pipe network, it is known that the mesh flow method is often 1/10 to 1/100 of the nodal head method. On the other hand, there has been no conventional solution method by the mesh flow rate method in consideration of pressure dependence.

The present invention has been made in view of the above circumstances, and solves the problem of providing a novel method for realizing the pipe network analysis by the mesh flow method in consideration of the pressure dependence of the outflow amount. It should be an issue.

In order to solve the above problems, the present invention presents a "pipeline branch" indicating a pipeline element, a "node" at one end and the other end of the pipeline branch, or a "node" which is a connection point between the pipeline branches, or the pipe. For the analysis graph in which "head known nodes" indicating the connection points between the road branch and the distribution reservoir are arranged, the "head" that treats the "effective head", which is the water pressure at the node, together with the ground height, and the outflow from the node or pipeline. A pipe network analyzer that calculates the amount as a pressure-dependent amount.
A reference node with the head set to 0 and a reference node connecting branch connecting the reference node and the known head node are added, and the head and the inflow amount of the known head node are set to the water heads at both ends of the reference node connecting branch. A means for determining a tree and a mesh group, which are a set of branches that connect all the nodes and do not form a loop in the analysis graph, which is treated as a difference "head difference" and a flow rate.
A means for calculating the effective head of each node by performing a non-pressure-dependent pipe network analysis process by iterative calculation using the fixed flow rate of the branches contained in the tree and the mesh flow rate of the mesh group.
A means for comparing the effective head obtained based on the pipe network analysis process with a threshold value and connecting a pressure-deficient node in which the effective head is less than the threshold value to the reference node by a virtual connecting branch.
The outflow amount at the underpressure node is updated as a pressure-dependent amount obtained based on the characteristic formula showing the pressure dependence of the outflow amount in the water supply distribution pipe network, and the underpressure node is connected to the reference node by a virtual connecting branch. For the new analysis graph, the pressure-dependent pipe network analysis process by iterative calculation was performed using the mesh flow rate of the mesh group including the new mesh added by the virtual connection branch as a variable, and the effective head at each node. And the means to calculate
When the effective head at the node to which the virtual connection branch is connected obtained based on the pressure-dependent tube network analysis process is equal to or more than the threshold value or 0 or less, the virtual connection branch is removed and the virtual connection branch is connected. When the effective head at no node is less than the threshold, a means for connecting to the reference node by a new virtual connection branch is provided as a pressure shortage node.
The pressure-dependent tube network analysis process is repeated until the addition and deletion of the virtual connection branch are eliminated, and the effective head at each node when the addition and deletion are eliminated is output as an effective head that gives an outflow amount as a pressure-dependent amount. ..

Further, the present invention indicates a pipeline branch indicating a pipeline element, a node which is a connection point between the pipeline branches at one end and the other end of the pipeline branch, or a connection point between the pipeline branch and a distribution reservoir. This is a pipe network analysis program that calculates the amount of outflow from the head and the node or pipeline, which treats the effective head, which is the water pressure at the node, together with the ground height, with respect to the analysis graph in which the known head nodes are arranged. Computer,
A reference node with the head set to 0 and a reference node connecting branch connecting the reference node and the known head node are added, and the head and the inflow amount of the known head node are set to the water heads at both ends of the reference node connecting branch. A means for determining a tree and a mesh group which are branch sets that connect all the nodes and do not form a loop in the analysis graph, which are treated as the difference head difference and the flow rate.
A means for calculating the effective head of each node by performing a non-pressure-dependent pipe network analysis process by iterative calculation using the fixed flow rate of the branches contained in the tree and the mesh flow rate of the mesh group.
A means for comparing the effective head obtained based on the pipe network analysis process with a threshold value and connecting a pressure-deficient node in which the effective head is less than the threshold value to the reference node by a virtual connecting branch.
The outflow amount at the underpressure node is updated as a pressure-dependent amount obtained based on the characteristic formula showing the pressure dependence of the outflow amount in the water supply distribution pipe network, and the underpressure node is connected to the reference node by a virtual connecting branch. For the new analysis graph, the pressure-dependent pipe network analysis process by iterative calculation was performed using the mesh flow rate of the mesh group including the new mesh added by the virtual connection branch as a variable, and the effective head at each node. And the means to calculate
When the effective head at the node to which the virtual connection branch is connected obtained based on the pressure-dependent tube network analysis process is equal to or more than the threshold value or 0 or less, the virtual connection branch is removed and the virtual connection branch is connected. When the effective head at no node is less than the threshold, it is made to function as a pressure shortage node as a means for connecting to the reference node by the new virtual connection branch.
The pressure-dependent tube network analysis process is repeated until the addition and deletion of the virtual connection branch are eliminated, and the effective head at each node when the addition and deletion are eliminated is output as an effective head that gives an outflow amount as a pressure-dependent amount. ..

Further, the present invention indicates a pipeline branch indicating a pipeline element, a node which is a connection point between the pipeline branches at one end and the other end of the pipeline branch, or a connection point between the pipeline branch and a distribution reservoir. This is a pipe network analysis method that calculates the amount of outflow from the head and the node or pipeline, which treats the effective head, which is the water pressure at the node, together with the ground height, with respect to the analysis graph in which the known head nodes are arranged. The computer
A reference node with the head set to 0 and a reference node connecting branch connecting the reference node and the known head node are added, and the head and the inflow amount of the known head node are set to the water heads at both ends of the reference node connecting branch. The step of determining the tree and mesh group, which is a branch set that connects all the nodes and does not form a loop, is treated as the difference head difference and flow rate.
A step of calculating the effective head of each node by performing a non-pressure dependent pipe network analysis process by iterative calculation using the fixed flow rate of the branches contained in the tree and the mesh flow rate of the mesh group.
A step of comparing the effective head obtained based on the pipe network analysis process with a threshold value and connecting a pressure-deficient node in which the effective head is less than the threshold value to the reference node by a virtual connecting branch.
The outflow amount at the underpressure node is updated as a pressure-dependent amount obtained based on the characteristic formula showing the pressure dependence of the outflow amount in the water supply distribution pipe network, and the underpressure node is connected to the reference node by a virtual connecting branch. For the new analysis graph, the pressure-dependent pipe network analysis process by iterative calculation was performed using the mesh flow rate of the mesh group including the new mesh added by the virtual connection branch as a variable, and the effective head at each node. And the steps to calculate
When the effective head at the node to which the virtual connection branch is connected obtained based on the pressure-dependent tube network analysis process is equal to or more than the threshold value or 0 or less, the virtual connection branch is removed and the virtual connection branch is connected. If the effective head at no node is less than the threshold, the pressure-deficient node is provided with a step of connecting to the reference node by the new virtual connection branch.
The pressure-dependent tube network analysis process is repeated until the addition and deletion of the virtual connection branch are eliminated, and the effective head at each node when the addition and deletion are eliminated is output as an effective head that gives an outflow amount as a pressure-dependent amount. ..

With such a configuration, it is possible to perform a pipe network analysis considering the pressure dependence of the outflow amount by using the mesh flow rate method.

In a preferred embodiment of the present invention, the pressure-dependent tube network analysis process does not add the flow rate at the virtual connecting branch to the fixed flow rate at the tree branch.

In a preferred embodiment of the present invention, the characteristic formula is 0 for the outflow amount at each demand point if the pressure is 0, increases as the pressure increases, and the pressure reaches a predetermined value (threshold value). For example, the rate of increase is equal to the demand amount, the rate of increase is small near 0 and the threshold value, and is the maximum curve near the middle of the two, and the outflow when the pressure is below 0 and above the threshold value. A positive straight line with a small slope that gives the amount is extrapolated,
When the outflow amount (flow rate of the virtual connecting branch) from the pressure shortage node exceeds the negative or demand amount during the iterative calculation in the pressure-dependent tube network analysis process, the effective head given by the extrapolated straight line is given. The head difference calculated from is determined as the head difference of the virtual connecting branch during the iterative calculation.

With such a configuration, when a negative outflow amount or an outflow amount exceeding the demand amount is calculated during the iterative calculation of solving the nonlinear simultaneous equations, the outflow amount is converged while giving the outflow amount in consideration of the pressure dependence. The tube network analysis process can be performed with good properties.

In a preferred embodiment of the present invention, the pipeline analysis process is performed with the total outflow amount taken out in each pipeline branch being constant.
A point is determined so as to give the starting point flow rate and the head difference of the pipeline branch obtained based on the result of the pipeline analysis processing to a part or all of the pipeline branch corresponding to the pipeline, and the point is determined. The pressure-dependent pipe network analysis process is executed on the analysis graph including the nodes at which the total outflow is aggregated.

With such a configuration, a pipeline extraction model assuming that water is uniformly extracted along the pipeline can be applied to a pipeline analysis process in consideration of pressure dependence.

In a preferred embodiment of the present invention, in order to carry out the calculation at the time of the first specific water intake including the time of water intake of the fire hydrant by the pump car, the outflow amount at the time of water intake of the fire hydrant by the pump car is added to the intake node, and the above tree. The pressure-dependent pipe network analysis process is performed by joining the branch fixed flow rate.

With such a configuration, it is possible to perform a pipe network analysis process in consideration of pressure dependence at the time of the first specific water intake.

In a preferred embodiment of the present invention, in order to carry out the calculation at the time of water intake of the fire hydrant directly connected to the hose or at the time of the second specific water intake including water intake by the water discharge gun, the outflow amount at the intake node is measured at the time of water intake of the fire hydrant directly connected to the hose. , The pressure-dependent pipe is updated as a pressure-dependent amount determined based on a characteristic formula showing the pressure dependence of the outflow amount for water intake by the water discharge gun, and the outflow amount is not added to the fixed flow rate of the tree branch. Performs network analysis processing.

In a preferred embodiment of the present invention, the characteristic formula showing the pressure dependence of the outflow amount at the time of the second specific water intake is extrapolated by at least an equation that gives pressure when the outflow amount is negative.

With such a configuration, it is possible to perform a pipe network analysis process in consideration of pressure dependence at the time of water intake of a fire hydrant directly connected to a hose or at the time of a second specific water intake such as when a water discharge gun is used.

According to the present invention, it is possible to provide a novel method for realizing the pipe network analysis by the mesh flow method in consideration of the pressure dependence of the outflow amount.

It is a hardware block diagram of the tube network analysis apparatus which concerns on embodiment of this invention. It is a figure which shows an example of the water distribution system and the analysis graph which concerns on embodiment of this invention. It is a figure which shows an example of the analysis graph which concerns on embodiment of this invention. It is a processing flowchart of the pipe network analysis processing which considered the pressure dependence which concerns on embodiment of this invention. It is an outflow amount / pressure characteristic formula at a water supply pipe connection point when dealing with the pressure dependence of the outflow amount in the water supply distribution pipe network which concerns on embodiment of this invention. It is a figure which shows an example of the analysis graph which added the virtual connection branch which concerns on embodiment of this invention. It is the outflow amount / pressure characteristic formula of the water discharge gun which concerns on embodiment of this invention.

Hereinafter, the tube network analysis apparatus according to the embodiment of the present invention will be described with reference to the drawings. The embodiments shown below are examples of the present invention, and the present invention is not limited to the following embodiments, and various configurations can be adopted.

For example, in the present embodiment, the configuration, operation, and the like of the tube network analysis apparatus will be described, but a method of the same configuration, a computer program, a recording medium, a system, and the like can also exhibit the same effects. The program may be stored in a recording medium. Using this recording medium, for example, the program can be installed on a computer. The recording medium in which the program is stored may be a non-transient recording medium such as a CD-ROM. The system may be, for example, a form of a server-client type network analysis system in which a network analysis device is a server and a user terminal is a client.

FIG. 1 is a hardware configuration diagram of a tube network analysis device according to an embodiment of the present invention. The pipe network analysis device 1 is an information processing device that stores a pipe network analysis program. Specifically, a personal computer or the like can be used as the tube network analysis device 1.

That is, the tube network analysis device 1 includes a computing device (CPU (Central Processing Unit) 11) and a main storage device (RAM (Random Access Memory)) 12 as a working memory as hardware components. Further, the network analysis device 1 includes an auxiliary storage device 13 such as an HDD, SSD, and flash memory that rewritably stores an OS (Operating System), an application program, and various information (including data), and a communication control unit 14. A communication interface (IF) unit 15 such as a NIC (Network Interface Card), a display control unit 16, a display unit 17, and an information input / designation unit 18 are provided.

In order to logically realize the processing means described in detail later in the tube network analysis device 1, a tube network analysis program or the like is installed as an application program in the auxiliary storage device 13. Then, in the tube network analysis device 1, the arithmetic unit (CPU) 11 expands and executes the application program in the main storage device (RAM) 12 when the power is turned on or an instruction is given by the user.

Next, with reference to FIG. 1 and related diagrams (FIGS. 2 to 7), the processing in the tube network analyzer 1 will be described in more detail.

FIG. 2A is a diagram showing an example of a water distribution system. The water distribution system has connection points i (i = 3 to 9) between distribution reservoirs R1 and R2 and a plurality of pipeline elements j (pipes, valves, pumps, etc.). C _i attached to an arrow extending from each connection point represents runoff water taken in consumers (the demand). The pipe network analysis process executed by the pipe network analysis device in the present embodiment will be described by taking as an example the water distribution system represented by the two distribution reservoirs and the seven connection points in the illustrated example.

FIG. 2B is an analysis graph for the water distribution system shown in FIG. 2A. In the analysis graph (in the illustrated _example, B 1 _{.about.B 11)} conduit branch _{B j} as branch _{B j} indicating the line elements j and, in their one end and the other end, connected between Kanroeda _{B j} (in the illustrated _example, N 3 to N ₉₎ node _{N i} is a point i or, in the hydraulic head known node _{N i} (example shown is a node _{N i} which indicates a connection point i of Kanroeda _{B j} and distributing reservoir, N ₁ , N ₂ ) are connected. Although arbitrarily determined orientation is set to Kanroeda B _j, or may be different from the actual flow direction.

Furthermore, the analysis graph, water head provides a reference node N ₀ is a zero at node N _i. Further, the reference node connecting branch B _j (B ₁₂ and B _{13 in the} illustrated example) is defined as the branch B _j connecting the reference node N ₀ , the known head node N ₁ and the known head node N ₂ , and the head is known. The heads of nodes N ₁ and N ₂ are given as the head difference of the reference node connecting branch. The inflow amount from N ₁ and N ₂ is obtained as the flow rate of B ₁₂ and B ₁₃ .

p _i denotes the water head of the node N _i (node hydrocephalus), a value obtained by subtracting the ground elevation from water head p _i valid hydrocephalus e _i. The head difference h _j (head loss) is expressed by Eq. (1). In Eq. (1), p _jo and p _jd indicate the heads at the start and end nodes of B _j , respectively. Further, the flow rate of the branch B _j is defined as the branch flow rate q _j .

<Pipeline characteristic formula>
Here, among the pipeline elements j represented by the pipeline branch B _j , the characteristics of the pipeline are based on the experimental formula of Hazen-Williams, and the pipeline characteristic formula represented by the equation (2) is used. Here, r _j is a resistance coefficient of the pipeline determined according to the properties of the pipeline, and is determined by the flow velocity coefficient CH _j , the pipe diameter d _j, and the pipeline length l _j as shown in equation (3). Will be done.

On the other hand, the characteristics of the valve are expressed by the equation (4). Here, r _vj is a valve resistance coefficient determined according to the valve properties, and is determined by a loss coefficient and a diameter.

Further, the variational resistance (loss partial differential coefficient) of the pipeline and the valve is defined by the equation (5).

<Flow rate continuous condition formula>
A continuous flow rate conditional expression is used in which the sum of the inflow and the sum of the outflow are equal at each node i. This condition is automatically satisfied when the mesh flow rate is used as a variable.

<Hydro head closure conditional expression>
Further, the total head difference h _j between two points is equal regardless of the route, or the total head difference h _j of the pipelines constituting the mesh (loop) is zero. Use the closure conditional expression.

Aforementioned conduit characteristic equation, by simultaneous flow continuous condition and hydrocephalus closing condition, the branch flow q _j and a water head difference h _j of each line element j (branch B _j), hydrocephalus p of each node N _{i The} problem of finding _i (effective head e _i ) is pipe network analysis. In this embodiment, the mesh flow rate is further defined, formulated as a nonlinear simultaneous algebraic equation, and the solution calculation is performed by the Newton-Raphson method (NR method).

<Fixed flow rate of tree branches>
In the analysis graph, but connecting all nodes N _i loop branches set not constituting of wood. The node that starts the search for a tree is called the root, and the tree that is searched so as to branch from the root as much as possible is called a size priority tree. In FIG. 2 (b), the branches B _j contained in the tree are indicated by solid arrows (pipeline branches B _{1 to} B ₄ , B _{7 to} B ₉ and reference node connecting branches B ₁₂ and B ₁₃ ), and are included in the tree. The unsuccessful branches B _j (supplementary tree branches: pipeline branches B ₅ , B ₆ , B ₁₀ and B ₁₁ ) are indicated by broken arrows.

Each branch B _j when a size priority tree rooted at the reference node N ₀ is laid and all the outflow from each demand node N _{3 to} N ₉ is supplied from the reference node N ₀ through the tree. The flow rate of is called a fixed flow rate a _j . Here, the fixed flow rate of the supplementary tree branch is set to zero.

In the analysis graph of FIG. 2 (b), when the breadth-first tree is stretched as shown by a solid line, fixed flow a _j of each branch B _j is as shown in (6), outflow from each node N _i represented by c _i.

<Formulation by mesh flow method>
A mesh M _k is generally _defined in a planar graph as a region surrounded by branches and containing no other branches inside, or a set of branches surrounding the region. In the present embodiment, as the number of branches B _j constituting the mesh M _k is as small as possible, as each successively selected loop to extend the mesh M _k so it becomes applicable to a stereoscopic graph. This defines a mesh group. Further, an arbitrary reference direction is defined for each mesh _Mk . The branches B _j constituting the mesh M _k are given a positive sign if the direction is the same as the reference direction of the mesh M _k in which the direction of the branch is arbitrarily defined, and a negative sign is given if the direction is opposite to the reference direction. When the mesh is searched as shown in FIG. 3, the branches B _j constituting each mesh M _k are as follows.

Mesh M ₁ : B ₁₃ , −B ₁₂ , B ₁ , B ₃ , B ₆ , −B ₄
Mesh M ₂ : B ₂ , B ₅ , -B ₃ , -B ₁
Mesh M ₃ : B ₅ , B ₈ , -B ₁₀ , -B ₇
Mesh M ₄ : B ₈ , B ₁₁ , -B ₉ , -B ₆

FIG. 3 is a diagram showing an example of the mesh searched by the analysis graph. Considering the flow rate component (circulation flow rate) common to all the branches B _j constituting each mesh M _k , it is called the mesh flow rate m _k . Branch flow q _j of the branch B _j is added all meshes flow m _k including its branches in the same direction on the fixed rate a _j of each branch, a value obtained by subtracting all the meshes flow m _k including in the opposite direction. In the example of FIG. 3, when the branch flow rate q _j is indicated by the fixed flow rate a _j and the mesh flow rate m _k , it becomes the equation (7).

Here, the hydraulic head closure conditional equation for each mesh M _k is as in equation (8).

p ₁ and p ₂ are known heads of nodes N ₁ and N ₂ , respectively, and are treated as head differences between reference node connecting branches B ₁₂ and B ₁₃ .

Represents the water head difference h _j of each branch in the branch flow rate q _j, further, the branch flow Expressing q _j mesh flow rate m _k, as (9), nonlinear simultaneous algebraic equations as variables mesh flow m _k is electrically Be taken.
Equation (9) is understood as equation (11), which is a four-dimensional equation with equation (10) as a variable.

T represents the transpose of the vector.

It M is obtained by solving the predetermined solving algorithm, determining that branch flow q _j and a water head difference h _j from the values each branch B _j, hydrocephalus p _{i (effective} hydrocephalus e _i) of each node N _i Can be done. In the present embodiment, this nonlinear simultaneous algebraic equation is solved by Newton's method (NR method: Newton-Raphson's method) as an example. Starting from the initial value M ^{0 of the} arbitrarily assumed M ^ν, the value of M is sequentially calculated by the modified equations consisting of equations (12) and (13), and the value of Z (M ^{ν + 1} ) is sufficient to be 0. When it is determined that it is approaching, the calculation is terminated. J ^ν is the Jacobian matrix described below, and the superscript ν is the number of repetitions.

It is assumed that the value r of the variational resistance of the pipeline element j when M = M ^ν is expressed by the equation (14). At this time, the Jacobian matrix J ^ν is given by Eq. (15). Here, the diagonal component _Cll is the sum of the variational resistances of each branch included in the mesh _Mk (the variational resistances of the reference node connecting branches are 0). In addition, the off-diagonal component C _mn is the sum of the variational resistances of the branches contained in both the mesh M _m and the mesh M _n (m corresponds to the row and n corresponds to the column number), and those branches are added to both meshes. When they are included in the same direction, they are marked with a positive sign, and when they are included in the opposite direction, they are marked with a negative sign.

<Pipe network analysis processing considering the pressure dependence of the outflow amount>
FIG. 4 is a processing flowchart of the pipe network analysis processing in consideration of the pressure dependence of the outflow amount in the present embodiment.

In step S1, the pipe network analysis device 1 is used to perform a conventional pipe network analysis process (non-pressure dependent pipe network analysis process) without considering the pressure dependence by the mesh flow method. The processor of the pipeline analysis device 1 receives the designation of the distribution reservoir, the area, and the like, and generates an analysis graph using the information about the pipeline elements and the connection points stored in the database. The information stored in the database is, for example, information on the properties of pipeline elements (length, diameter, years of use, material, etc.), and the position of connection points (latitude, longitude, ground height (elevation), etc.). Information etc. Processor tube network analyzer 1 performs a search seek mesh with tension the tree, outflow c _i of each node N _i is as equally constant demand pre-defined, the tube network by mesh flow method Perform analysis processing. Thereby, the branch flow _{q j} and a water head difference _{h j} of each branch _{B j} as a non-pressure-dependent quantity, obtains a water head _{p i} of each node _{N i.}

Here, the processor of the tube network analyzer 1 compares the effectiveness hydrocephalus e _i of each node N _i and the threshold value e ^d. In general, the node _{N i,} are said to if effective hydrocephalus _{e i} is 19 m, is equal outflow _{c i} to the value for demand _c ^{i d} is obtained. Effective hydrocephalus _{e i} that demand _c ^{i d} equal outflow _{c i} to the value for is obtained as a threshold ^{e d.} 0 <a node _{N i} which is valid hydrocephalus _{e i} <threshold ^{e d,} is determined as insufficient pressure nodes. Further, in the present embodiment, the node _{N i} is valid hydrocephalus _{e i} ≦ 0, a constant amount of runoff _c i = 0, the node _{N i} a threshold ^{e d} ≦ effective hydrocephalus _{e i,} runoff _{c i} = treated as a certain amount of demand _c ^{i d.}

Figure 5 is a characteristic showing the relationship between the effective hydrocephalus e _i and the outflow amount c _i in the water supply pipe connection point when dealing with pressure dependence of the outflow of water supply distribution network type (hereinafter, referred to as e-c characteristic expression) Is. The ec characteristic formula in the present embodiment is 0 for the outflow amount at each demand point if the pressure is 0, increases as the pressure increases, and the pressure reaches a predetermined value (threshold value ^ed ). equals demand c _i ^d if a proportion of the increase is small in the vicinity of zero pressure and the threshold is a curve which becomes maximum near both intermediate. The validity of this e-c characteristic formula is shown in Non-Patent Document 4 and the like. In the present embodiment, in order to determine the water head difference from the effective water head on the basis of the outflow c _i at iteration of the tube network analysis process to be described later, and when the pressure is below 0, the outflow amount when above the threshold A straight line with a small positive value is extrapolated. When the outflow from the pressure-deficient node (flow rate of the virtual connecting branch) exceeds the negative or demand during the iterative calculation in the pressure-dependent tube network analysis process, it is calculated from the effective head given by the extrapolated straight line. The head difference is determined as the head difference of the virtual connection branch during the iterative calculation.

<Application to pipeline take-out model>
In step S2, consider a pipeline withdrawal model assuming that water is taken out uniformly along the conduit. The processor of the pipeline analyzer 1 has the same starting flow rate q _j ^* and head difference from the total outflow amount c _j along each pipeline _j and the starting flow rate q _j ^* and the head difference h _j calculated in step S1. An aggregation point determination process for aggregating the outflow amount c _j at one point P in the pipeline j so as to give h _j is performed for each pipeline j. The flow rate from the start point to P of the pipeline j is q _j ^* , and the flow rate from P to the end point is (q _j ^* −c _j ).
When the pipeline take-out model is taken into consideration, the pipeline analysis process is executed on the analysis graph in which the node P _j in which the outflow amount c _j is aggregated is arranged in each branch B _j . The formula below, for simplification of explanation, without considering the nodes P _j, and that showing a calculation example based on the analysis graph of FIG. 3. In the case of handling conduit extraction model, nodes P _j is increased, since there is no effect on the number of meshes, it does not affect the computation time of the mesh flow method.

In step S3, the addition of virtual connection branch _{A j} connecting underpressure node _{N i} and the reference node _{N 0.} At this time, the outflow quantity c _j from the node N _i which is treated as the flow rate of a virtual connection branch A _j is not added to the Kieda fixed flow a _j.

FIG. 6 is a diagram showing an example of an analysis graph to which a virtual connection branch _Aj is added. For example, from the processing result of step S1, if the nodes N ₈ and N ₉ is determined to underpressure nodes, as shown, with respect to the analysis graph, the virtual connection branch A ₁₄ and extending from the node N _8, node N adding virtual connection branch _{a 15} extending from the _9.

The processor of the network analysis device 1 searches for a mesh for a new analysis graph to which the virtual connection branch _Aj is added, and retakes the mesh. As a result, a new mesh _Mk is added. In the illustrated example, the virtual connecting branches A ₁₄ and A ₁₅ add new meshes M ₅ and M ₆ .

Mesh M ₁ : B ₁₃ , -B ₁₂ , B ₁ , B ₃ , B ₆ , -B ₄
Mesh M ₂ : B ₂ , B ₅ , -B ₃ , -B ₁
Mesh M ₃ : B ₅ , B ₈ , -B ₁₀ , -B ₇
Mesh M ₄ : B ₈ , B ₁₁ , -B ₉ , -B ₆
Mesh M ₅ : A ₁₄ , -A ₁₅ , -B ₁₁
Mesh M ₆ : A ₁₅ , -B ₁₃ , B ₄ , B ₉

In step S4, a predetermined process is performed on the pressure shortage node, and a pipe network analysis process is performed by the mesh flow method in consideration of the pressure dependence. The processor of the tube network analyzer 1 determines a new outflow amount by NR repetition based on the ec characteristic formula of FIG. 5 for the pressure shortage node. For underpressure nodes N ₈ and N _9, depending on their effectiveness hydrocephalus e _i, imparts runoff obtained from e-c characteristic equation. Further, in the present embodiment, the effective hydrocephalus _{e i} ≦ 0 and becomes the node _{N i} grant outflow _c i = 0, the threshold value ^{e d} ≦ effective hydrocephalus _{e i} become node _N in _i runoff _c i = imparting demand _c ^{i d.}

By virtual connection branch A _j is added, along with the branch flow rate q _j of the virtual connection branch A _j is defined, the branch flow rate q _j already definitions are redefined by additional mesh M _k. However, runoff _{c j} from the virtual connection branch _{A j} is not added to the Kieda fixed flow _{a j,} fixed flow _{a j} of each branch _{B j} does not change as shown in (16). In the example of FIG. 6, when the branch flow rate q _j is indicated by the fixed flow rate a _j and the mesh flow rate m _k , it becomes the equation (17). Here, the hydraulic head closure conditional equation for each mesh M _k is as in equation (18).

From the above, a nonlinear simultaneous algebraic equation with the mesh flow rate m _k as a variable is derived as equation (19). Equation (19) is understood as equation (21), which is a six-dimensional equation with equation (20) as a variable. This is solved by a predetermined solution algorithm as in step S1. The Jacobian matrix J ^{ν in} this case is given by Eq. (22).

During iteration by solving algorithm, if the flow rate of the branch A _j is the outflow from the node N _i exceeds the negative or demand, the water head difference of its branches, the effective hydrocephalus e _i ≦ 0, the threshold value e ^d ≦ It extrapolated in e-c characteristic equation when the effective hydrocephalus e _i, using a gradient was determined from a very straight small positive value value. Pipe network analysis device 1 performs the pipe network analysis processing by the mesh flow method calculates the branch flow q _j and a water head difference h _j of each branch Aj as a pressure-dependent _quantity, the water head p _i of each node N _i.

In step S5, the node _{N i} which virtual connection branch _{A j} is connected:
· If a valid hydrocephalus _{e i} obtained in step S4 exceeds the threshold value ^{e d} (threshold ^{e d} ≦ effective hydrocephalus _e i), to remove the virtual connection branch _{A j,} a constant outflow (demand _c ^{i d)} as a tree Handle by subscribing to the branch fixed flow rate _aj .
When the effective head e _i obtained in step S4 is 0 or less (effective head e _i ≤ 0), the virtual connection branch A _j is removed and the outflow amount c _i is treated as 0.
-If it is determined as a pressure shortage node (0 <effective head e _i <threshold value ^ed ), the connection of the virtual connection branch _Aj is maintained.

On the other hand, in step S5, the node _{N i} which virtual connection branch _{A j} is not connected:
- Enable hydrocephalus _{e i} obtained at step S4 is 0 or less or, if it exceeds the threshold value ^{e d} (effective hydrocephalus _{e i} ≦ 0, the threshold value ^{e d} ≦ effective hydrocephalus _e i), as is outflow constant (outflow = 0 or treated as demand _c ^{i d).}
-If it is determined as a pressure shortage node (0 <effective head e _i <threshold value ^ed ), a new virtual connection branch _Aj is connected.

In step S6, if the virtual connection branch A _j is not added or deleted in step S5 (YES in step S6), it is determined that the pipe network analysis process considering the pressure dependence is completed, and the branch flow rate q _j , water head difference _{h j,} and outputs the water head _{p i} (step S7). If the virtual connection branch _Aj is added and / or deleted in step S5 (NO in step S6), the process returns to step S4, and the pressure dependence is added to the graph to which the new virtual connection branch _Aj is connected. Perform the pipe network analysis process in consideration.

In this embodiment, first, assuming normal use in a general household or office as the demand amount, the case where the effective head and the outflow amount at the water supply pipe connection point are treated by the characteristic formula of FIG. 5 has been described. By performing the pipe network analysis process in consideration of the dependency, it is possible to calculate the outflow amount with high accuracy in various usage forms.

<Analysis of fire hydrant water intake by pump truck>
As an extension of the above, it is possible to perform a pipe network analysis process in consideration of the pressure dependence at the time of the first specific water intake such as the time of water intake of the fire hydrant by the pump truck. When water for fire extinguishing water is taken from a fire hydrant with a pump truck, the amount of water taken from one pump is usually about 1 ton per minute. Since the amount of water taken from the fire hydrant by the pump truck can be considered as a constant outflow amount regardless of the pressure, it is included in the tree branch fixed flow rate _aj as a constant outflow amount. Since the amount of water taken from the fire hydrant by the pump truck is large, the pressure in the surrounding area will drop significantly. Therefore, a certain runoff water intake from a fire hydrant by the pump wheel c _j, the extraction amount in general household by treating as a pressure-dependent quantity, immediately the real situation runoff at home or the like near to decrease The calculated result is obtained.

<Analysis of fire hydrant water intake by direct connection to hose>
Add the outflow amount / pressure characteristic formula (pressure loss formula) of the fire hydrant, the hose directly connected to the fire hydrant and the water discharge nozzle as a virtual connection branch _Aj , and add the second fire hydrant water intake by the hose direct connection or the water intake by the water discharge gun. It is possible to perform a pipe network analysis process that considers the pressure dependence at the time of specific water intake. Pressure release and discharged water c _i is calculated as a flow rate and water head difference of the virtual connection branch A _j (release water pressure + ground elevation).

<Analysis of pipe network for extinguishing fire with a water gun>
FIG. 7 shows the outflow amount / pressure characteristic formula of the water discharge gun. As shown in FIG. 7, the amount of water discharged is a function of the square root √p of the original pressure p of the water discharge gun. For water cannon used, a virtual connection branch A _j addition to nodes water cannon is connected, by giving outflow as a pressure-dependent quantity on the basis of the characteristic equation, the tube network analysis processing in consideration of pressure-dependent It can be performed.

Regarding the outflow amount / pressure characteristic formula of the fire hydrant, hose and water discharge nozzle, and the outflow amount / pressure characteristic formula of the water discharge gun, the flow rate may be a value that is practically unthinkable during repeated calculations during the analysis. When the effective head is 0 or less and the threshold value ^ed or more in the e-c characteristic formula, it is extrapolated by the predetermined formula even for an unexpected flow rate, just as it was extrapolated with a positive straight line with an extremely small slope. Keep it.

<Analysis of pipe network including constant secondary pressure element>
In order to facilitate the control of the water distribution pressure in the water distribution pipe network, a pressure reducing valve or a pressure regulating tank that keeps the secondary pressure constant is often used. Even when the pipe network including these secondary pressure fixing elements is targeted, the pipe network analysis process can be performed in consideration of the pressure dependence of the outflow amount.

1: Pipe network analysis device 13: Auxiliary storage device 14: Communication control unit 15: Communication interface (IF) unit 16: Display control unit 17: Display unit 18: Information input / designation unit A _j , B _j : Branch CH _j : flow rate coefficient J ^[nu: Jacobian _{M k:} mesh _{N i:} node R1, R2: distributing reservoir _{a j:} fixed flow _{c i:} outflow _c ^{i d:} demand _{c j:} outflow ^{e d:} effective hydrocephalus threshold e _i : Effective head h _j : Head difference i: Nodal point j: Pipeline element m _k : Mesh flow rate _pi : Nodal head q _j : Branch flow rate

Claims (9)

A pipeline branch indicating a pipeline element and a node indicating a connection point between the pipeline branches or a head known node indicating a connection point between the pipeline branch and a distribution reservoir are arranged at one end and the other end of the pipeline branch. It is a pipe network analysis device that calculates the amount of outflow from the head and the node or the pipeline that treats the effective head, which is the water pressure at the node, together with the ground height, as the pressure-dependent amount with respect to the analysis graph.
A reference node with the head set to 0 and a reference node connecting branch connecting the reference node and the known head node are added, and the head and the inflow amount of the known head node are set to the water heads at both ends of the reference node connecting branch. A means for determining a tree and a mesh group which are branch sets that connect all the nodes and do not form a loop in the analysis graph, which are treated as the head difference and the flow rate, which are the differences.
A means for calculating the effective head of each node by performing a non-pressure-dependent pipe network analysis process by iterative calculation using the fixed flow rate of the branches contained in the tree and the mesh flow rate of the mesh group.
A means for comparing the effective head obtained based on the pipe network analysis process with a threshold value and connecting a pressure-deficient node in which the effective head is less than the threshold value to the reference node by a virtual connecting branch.
The outflow amount at the underpressure node is updated as a pressure-dependent amount obtained based on the characteristic formula showing the pressure dependence of the outflow amount in the water supply distribution pipe network, and the underpressure node is connected to the reference node by a virtual connecting branch. For the new analysis graph, the pressure-dependent pipe network analysis process by iterative calculation was performed using the mesh flow rate of the mesh group including the new mesh added by the virtual connection branch as a variable, and the effective head at each node. And the means to calculate
When the effective head at the node to which the virtual connection branch is connected obtained based on the pressure-dependent tube network analysis process is equal to or more than the threshold value or 0 or less, the virtual connection branch is removed and the virtual connection branch is connected. When the effective head at no node is less than the threshold, a means for connecting to the reference node by a new virtual connection branch is provided as a pressure shortage node.
The pressure-dependent pipe network analysis process is repeated until the addition and deletion of the virtual connection branch are eliminated, and the effective head at each node when the addition and deletion are eliminated is output as an effective head that gives an outflow amount as a pressure-dependent amount. Pipe network analyzer. The pipe network analysis apparatus according to claim 1, wherein the pressure-dependent pipe network analysis process does not add the flow rate in the virtual connection branch to the tree branch fixed flow rate. The characteristic formula is 0 for the outflow amount at each demand point when the pressure is 0, increases as the pressure increases, becomes equal to the demand amount when the pressure reaches the threshold value, and the rate of increase is equal to the demand amount. Extrapolation is a positive straight line with a small slope near 0 and the threshold, and a maximum curve near the middle of the two, with a small slope giving the outflow when the pressure is below 0 and above the threshold. Has been
When the outflow from the pressure shortage node exceeds the negative or demand during the iterative calculation in the pressure-dependent tube network analysis process, the head difference calculated from the effective head given by the extrapolated straight line is calculated. The tube network analyzer according to claim 1 or 2, which is determined as the head difference of the virtual connection branch during the iterative calculation. The pipe network analysis process is executed with the total outflow amount taken out in each pipe branch as a constant.
A point is determined so as to give the starting point flow rate and the head difference of the pipeline branch obtained based on the result of the pipeline analysis processing to a part or all of the pipeline branch corresponding to the pipeline, and the point is determined. The pipe network analysis apparatus according to any one of claims 1 to 3, wherein the pressure-dependent pipe network analysis process is executed on an analysis graph including nodes in which the total outflow amount is aggregated. In order to carry out the calculation at the time of the first specific water intake including the time of water intake of the fire hydrant by the pump car, the outflow amount at the time of water intake of the fire hydrant by the pump car is added to the intake node, and the tree branch fixed flow rate is added. The pipe network analysis apparatus according to any one of claims 1 to 4, wherein the pressure-dependent pipe network analysis process is performed. In order to carry out the calculation at the time of water intake of the fire hydrant directly connected to the hose or at the time of the second specific water intake including the water intake by the water discharge gun, the amount of the outflow at the intake node is calculated for the time of water intake of the fire hydrant directly connected to the hose or the water intake by the water discharge gun. A claim that updates the outflow amount as a pressure-dependent amount determined based on a characteristic formula indicating the pressure dependence of the outflow amount, and performs the pressure-dependent tube network analysis process without adding the outflow amount to the tree branch fixed flow rate. The tube network analyzer according to any one of 1 to 5. The tube network analyzer according to claim 6, wherein the characteristic formula showing the pressure dependence of the outflow amount at the time of the second specific water intake is at least an extrapolated formula for giving pressure when the outflow amount is negative. A pipeline branch indicating a pipeline element and a node indicating a connection point between the pipeline branches or a head known node indicating a connection point between the pipeline branch and a distribution reservoir are arranged at one end and the other end of the pipeline branch. This is a pipe network analysis program that calculates the amount of outflow from the head and the node or pipeline, which treats the effective head, which is the water pressure at the node, together with the ground height, as the pressure-dependent amount.
A reference node with the head set to 0 and a reference node connecting branch connecting the reference node and the known head node are added, and the head and the inflow amount of the known head node are set to the water heads at both ends of the reference node connecting branch. A means for determining a tree and a mesh group which are branch sets that connect all the nodes and do not form a loop in the analysis graph, which are treated as the head difference and the flow rate, which are the differences.
A means for calculating the effective head of each node by performing a non-pressure dependent pipe network analysis process by iterative calculation using the fixed flow rate of the branches contained in the tree and the mesh flow rate of the mesh group.
A means for comparing the effective head obtained based on the pipe network analysis process with a threshold value and connecting a pressure-deficient node in which the effective head is less than the threshold value to the reference node by a virtual connecting branch.
The outflow amount at the underpressure node is updated as a pressure-dependent amount obtained based on the characteristic formula showing the pressure dependence of the outflow amount in the water supply distribution pipe network, and the underpressure node is connected to the reference node by a virtual connecting branch. For the new analysis graph, the pressure-dependent pipe network analysis process by iterative calculation was performed using the mesh flow rate of the mesh group including the new mesh added by the virtual connection branch as a variable, and the effective head at each node. And the means to calculate
When the effective head at the node to which the virtual connection branch is connected obtained based on the pressure-dependent tube network analysis process is equal to or more than the threshold value or 0 or less, the virtual connection branch is removed and the virtual connection branch is connected. When the effective head at no node is less than the threshold, it is made to function as a pressure shortage node as a means for connecting to the reference node by the new virtual connection branch.
The pressure-dependent pipe network analysis process is repeated until the addition and deletion of the virtual connection branch are eliminated, and the effective head at each node when the addition and deletion are eliminated is output as an effective head that gives an outflow amount as a pressure-dependent amount. Pipe network analysis program. A pipeline branch indicating a pipeline element and a node indicating a connection point between the pipeline branches or a head known node indicating a connection point between the pipeline branch and a distribution reservoir are arranged at one end and the other end of the pipeline branch. This is a pipe network analysis method in which the effective head, which is the water pressure at the node, is treated together with the ground height, and the outflow amount from the head and the node or the pipeline is calculated as a pressure-dependent amount with respect to the analysis graph.
A reference node with the head set to 0 and a reference node connecting branch connecting the reference node and the known head node are added, and the head and the inflow amount of the known head node are set to the water heads at both ends of the reference node connecting branch. The step of determining the tree and mesh group, which is a branch set that connects all the nodes and does not form a loop, is treated as the difference head difference and flow rate.
A step of calculating the effective head of each node by performing a non-pressure dependent pipe network analysis process by iterative calculation using the fixed flow rate of the branches contained in the tree and the mesh flow rate of the mesh group.
A step of comparing the effective head obtained based on the pipe network analysis process with a threshold value and connecting a pressure-deficient node in which the effective head is less than the threshold value to the reference node by a virtual connecting branch.
The outflow amount at the underpressure node is updated as a pressure-dependent amount obtained based on the characteristic formula showing the pressure dependence of the outflow amount in the water supply distribution pipe network, and the underpressure node is connected to the reference node by a virtual connecting branch. For the new analysis graph, the pressure-dependent pipe network analysis process by iterative calculation was performed using the mesh flow rate of the mesh group including the new mesh added by the virtual connection branch as a variable, and the effective head at each node. And the steps to calculate
When the effective head at the node to which the virtual connection branch is connected obtained based on the pressure-dependent tube network analysis process is equal to or more than the threshold value or 0 or less, the virtual connection branch is removed and the virtual connection branch is connected. If the effective head at no node is less than the threshold, the pressure-deficient node is provided with a step of connecting to the reference node by the new virtual connection branch.
The pressure-dependent pipe network analysis process is repeated until the addition and deletion of the virtual connection branch are eliminated, and the effective head at each node when the addition and deletion are eliminated is output as an effective head that gives an outflow amount as a pressure-dependent amount. Pipe network analysis method.