JP2016130670A - Sensor arrangement position selection device, water leakage amount estimation device, water leakage diagnosis system, water leakage diagnosis method, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a sensor arrangement position selection device capable of selecting an efficient arrangement position of a hydraulic pressure sensor, and a water leakage amount estimation device, a water leakage diagnosis system, a water leakage diagnosis method and a computer program.SOLUTION: A sensor arrangement position selection device according to an embodiment comprises a connection matrix generation part, a cotree extraction part, and a selection part. The connection matrix generation part generates a connection matrix representing a graph structure of a water distribution pipe line network on the basis of information showing a connection configuration of pipe lines constituting the water distribution pipe line network. The cotree extraction part classifies pipe lines constituting the water distribution pipeline network into pipe lines forming a tree constituting an open pipe line in the water distribution pipe line network and pipe lines forming a cotree constituting a closed pipe line with the tree on the basis of the connection matrix, and extracts the pipe lines forming the cotree. The selection part selects, as arrangement positions for hydraulic pressure sensors, nodes at both ends of the extracted pipe lines forming the cotree.SELECTED DRAWING: Figure 2

Description

  Embodiments described herein relate generally to a sensor arrangement position selection device, a leakage amount estimation device, a leakage diagnosis system, a leakage diagnosis method, and a computer program.

  In general, there are two types of investigations for water leakage in the distribution pipeline network: a primary investigation that investigates the presence or absence of leakage and a secondary investigation that identifies the location of the leakage. The primary survey is conducted regularly by investigators, who investigate the presence or absence of water leaks in the water distribution network using a listening rod. The secondary survey is a survey that is conducted on locations where it is determined as a result of the primary survey that there is a high possibility that water leakage has occurred, and the location of water leakage is identified using a correlative leak detector. The primary survey is conducted evenly on the target area, and it is currently not considered which area to focus on.

  On the other hand, the introduction of water smart meters is being studied against the background of increasing awareness of environmental issues. The water smart meter is installed in each house for the purpose of efficiently distributing water by measuring the amount of water used by consumers. If water smart meters become widespread, it will be possible to construct a water leakage diagnosis system that performs water leakage diagnosis of water distribution pipeline networks by combining with water pressure sensors.

  However, at present, there is no standard for efficiently arranging the water pressure sensors necessary for the water leakage diagnosis, so there is a possibility that the water pressure sensors may be arranged excessively, which may increase the management cost. Therefore, it is desired to develop a standard for efficiently arranging water pressure sensors for water leakage diagnosis.

JP 2013-178207 A JP 2006-285389 A JP 2010-48058 A

  The problem to be solved by the present invention is to provide a sensor arrangement position selection device, a water leakage amount estimation device, a water leakage diagnosis system, a water leakage diagnosis method, and a computer program that can select an efficient arrangement position of a water pressure sensor. is there.

  The sensor arrangement position selection apparatus according to the embodiment includes a connection matrix generation unit, a complement tree extraction unit, and a selection unit. A connection matrix production | generation part produces | generates the connection matrix showing the graph structure of the said water distribution pipeline network based on the information which shows the connection structure of the pipeline which comprises a water distribution pipeline network. Based on the connection matrix, the auxiliary tree extraction unit configures a pipeline that constitutes the distribution pipeline network as a tree that constitutes an open pipeline in the distribution pipeline network, and a closed pipeline with the tree Are classified into pipelines to be complemented trees, and the pipelines to be the complementary trees are extracted. A selection part selects the node of the both ends of the pipe line used as the extracted complement tree as an arrangement position of a water pressure sensor.

The figure which shows the outline | summary of the water distribution system which concerns on 1st Embodiment, and the structure of the sensor arrangement position selection apparatus 1. FIG. 2 is a functional block diagram showing a functional configuration of the sensor arrangement position selection device 1. FIG. The figure which shows an example of the information stored in the water distribution pipe network information storage part 11 of embodiment. The figure which shows an example of the model of a distribution pipe network. The figure which shows an example of distribution pipe network information. The figure which shows an example in which the water distribution pipe network PN is regarded as one pipe line. The functional block diagram which shows the function structure of the sensor arrangement position selection apparatus 1a of a modification. Schematic which shows the outline | summary of the 1st method of aggregating a graph structure. Schematic which shows the outline | summary of the 2nd method which aggregates graph structure. The figure which shows the specific example in case a different arrangement position is selected. The functional block diagram which shows the function structure of the water leak amount estimation apparatus 2 of 2nd Embodiment. The specific example of the relationship between the effective water pressure difference in the virtual pipeline of a certain time and the differential pressure of each pipeline is shown. The block diagram which shows the outline of formulation of the nonlinear optimization problem with restrictions. The figure which shows an example of the simulation result of estimation of the amount of water leaks. The figure which shows an example of the screen by which the amount of leaks is displayed by the output part.

  Hereinafter, a sensor arrangement position selection device, a leakage amount estimation device, a leakage diagnosis system, a leakage diagnosis method, and a computer program according to embodiments will be described with reference to the drawings.

(First embodiment)
Drawing 1 is a schematic diagram showing an outline of a water distribution system concerning a 1st embodiment. In this water distribution system, water (purified water) stored in the distribution reservoir 70 is supplied to a water distribution pipe network PN including homes, offices, and the like by pumps, valves, and the like. The amount of water flowing into the distribution pipe network PN is detected by the flow sensor 80.

  In the distribution pipe network PN, a plurality of nodes represented by white circles are set for convenience. In the figure, smart meters are attached to a plurality of nodes. The smart meter is attached to, for example, a home or business office where water is provided, and detects the amount of water used in the home or business office every 30 minutes to 1 hour. An arrow pointing downward from each node indicates that water is flowing out due to water use or leakage by a consumer.

  The sensor arrangement position selection device selects the arrangement position of the water pressure sensor so that the amount of water leakage at each node can be estimated from each node of such a water distribution pipe network.

FIG. 2 is a functional block diagram illustrating a functional configuration of the sensor arrangement position selection device 1 according to the first embodiment.
The sensor arrangement position selection device 1 includes a CPU (Central Processing Unit), a memory, an auxiliary storage device, and the like connected by a bus, and executes a sensor arrangement position selection program. The sensor arrangement position selection device 1 includes a distribution pipe network information storage unit 11, an input unit 12, an output unit 13, a connection matrix generation unit 14, a complement tree extraction unit 15, and an arrangement position selection unit 16 by executing a sensor arrangement position selection program. It functions as a device provided with. Note that all or a part of each function of the sensor arrangement position selection device 1 is realized by using hardware such as an application specific integrated circuit (ASIC), a programmable logic device (PLD), and a field programmable gate array (FPGA). Also good. The sensor arrangement position selection program may be recorded on a computer-readable recording medium. The computer-readable recording medium is, for example, a portable medium such as a flexible disk, a magneto-optical disk, a ROM, a CD-ROM, or a storage device such as a hard disk built in the computer system. The sensor arrangement position selection program may be transmitted via a telecommunication line.

  The water distribution network information storage unit 11 is configured using a storage device such as a magnetic hard disk device or a semiconductor storage device.

  The input unit 12 is configured using, for example, an input device such as a keyboard, a mouse, a touch panel, and a switch, and receives an input of a user operation.

  The output unit 13 (display unit) includes, for example, a display device such as an LCD (Liquid Crystal Display) and an organic EL (Electroluminescence), a display control unit, a printer, a speaker, and the like, and the arrangement position of the selected water pressure sensor Output information about.

  The connection matrix generation unit 14 generates a connection matrix for applying the graph theory to the distribution pipeline network based on the information stored in the distribution pipeline network information storage unit 11. A connection matrix is a matrix which shows the graph structure (connection structure) of a water distribution pipe network.

  Based on the connection matrix generated by the connection matrix generation unit 14, the supplementary tree extraction unit 15 extracts a pipeline serving as a complementary tree from the pipelines constituting the water distribution pipeline network. A complement tree is one of the types of branches that make up the graph structure. The branches constituting the graph structure are classified as trees or complement trees. A branch set that does not form a closed circuit is called a tree (Tree), and a branch set that is not included in the tree is called a complement tree (Cotree). Specifically, the supplementary tree extraction unit 15 classifies the pipelines constituting the water distribution pipeline network into the pipelines serving as trees and the pipelines serving as supplementary trees, and extracts the pipelines classified as supplementary trees. To do.

  The arrangement position selection unit 16 selects nodes at both ends of the pipe line that is the complement tree extracted by the complement extraction unit 15 as the arrangement position of the water pressure sensor, and outputs information indicating the selected arrangement position to the output unit 13. To do.

  Based on the pipeline network model described below, it is understood that the water pressure sensors necessary for estimating the amount of water leakage at each node may be installed at the nodes at both ends of the pipeline serving as the above-mentioned complement tree.

[Construction of pipeline network model]
The equation of motion of the incompressible fluid flowing through the water distribution pipe network is expressed by equation (1). In equation (1), i and j are node numbers. v _ij is the flow velocity of water in the pipe ij (the pipe connecting the node i and the node j). L _ij is the length [m] of the pipe line ij. ρ is the water density [kg / m ³ ]. H _i is the elevation of node i. D _ij is the diameter [m] of the pipe line ij. λ _ij is a pipe friction resistance of the pipe ij.

  In addition to the connection relationship between the nodes, the distribution pipe network information storage unit 11 stores information such as the length of the pipe, the diameter, the pipe frictional resistance, and the altitude of the node. Drawing 3 is a figure showing an example of information stored in distribution pipe network information storage part 11 of an embodiment. As shown in the figure, in the distribution pipe network information storage unit 11, in addition to the number of nodes and the number of pipes, information such as the effective head [m], type, and installation altitude [m] for each node corresponds to the node number. It is attached and described. In addition, the distribution pipe network information storage unit 11 includes information such as the start and end node numbers (that is, the connection relationship between the nodes), the pipe length (length), and the pipe friction coefficient for each pipe line. It is described in association with.

  When Expression (1) is expressed in a matrix expression, Expression (2) is obtained.

  In Expression (2), “.” Represents a vector obtained by multiplying a vector for each component. | (Vector) | represents a vector obtained by converting each component of the vector into an absolute value. Each matrix or vector component in Expression (2) is expressed by Expressions (3) to (7).

  Moreover, the mass conservation formula at each node is represented by Formula (8).

A in Equation (8) is a connection matrix. S represents the section cross section [m ² ] as a square matrix with a diagonal of zero. q is a vector whose element is the amount of water used at each node i. l is a vector having the amount of water leakage at each node i as an element. The element S _{ij of the} matrix S is derived from the diameter [m] of the pipe line ij by the equation (9).

[Generate connection matrix]
The connection matrix A is a matrix generated based on the directed graph, and is generated as a p × k matrix where p is the number of nodes and k is the number of pipes. Each element _Apk of the connection matrix A is determined by the following definition.
A _pk = −1: When node p is the starting point in pipe k A _pk = 1: When node p is the ending point in pipe k A _pk = 0: When node p is neither the starting point nor the end point in pipe k

  Hereinafter, the mass conservation formula will be described with reference to FIG. 4 as a model of the water distribution pipe network. FIG. 4 is a diagram showing an example of a water distribution pipe network PN different from FIG. Circles in FIG. 4 represent nodes, and a line connecting the circles represents a pipe line. The numbers in the circles indicate the node numbers. The numbers in parentheses attached to each pipeline indicate the pipeline number. FIG. 5 is a diagram illustrating information stored in the water distribution network information storage unit 11 corresponding to the water distribution network PN illustrated in FIG. 4.

  In the case of the water distribution pipe network PN shown in FIG. 4, the connection matrix A is represented by the following equation (10).

As described above, each row of the connection matrix A corresponds to a node, and each column corresponds to a pipe line. When the model shown in FIGS. 4 and 5 is applied to the equation (8), the following equation (11) is obtained. In equation (11), l _i is the amount of water leakage at each node and is an unknown number.

Here, dP, which is the effective water pressure difference, and the pressure value P _{i at} each node have the relationship of Expression (12), where P ₁ is zero.

  Then, equation (13) is obtained from equations (2) and (12).

  Based on equation (13), the flow rate of water flowing through each pipeline can be calculated. For example, the nonlinear simultaneous ordinary differential equation of Expression (13) can be solved by using the Newton-Raphson method or the like. Other methods may be used as a method of solving the nonlinear simultaneous ordinary differential equation of Expression (13).

Here, A * is an irreducible connection matrix obtained by removing rows corresponding to arbitrary nodes from the connection matrix A. Hereinafter, the first row of the connection matrix A is removed. An irreducible connection matrix A * obtained from the connection matrix A shown in Expression (10) is expressed by Expression (14). The matrix A * _t is a partial matrix of only the rear column when the irreducible connection matrix A * is replaced so that the complement tree comes to the front column.

Hereinafter, the matrix A * _t will be described. When the graph structure forms a closed circuit (loop), it is possible to obtain a law in which the pressure loss becomes zero once the loop is completed. That is, dP = 0 when a loop is traced from a certain starting point to return to the starting point. When this is expressed by an equation, equation (15) is obtained.

In Equation (15), B is a basic cycle matrix, each row i is a basic cycle F _i of the graph, and each column k is an i × k matrix corresponding to each branch (pipe) of the graph. Each element B _ik of the basic cycle matrix B is determined by the following definition.
B _ik = −1: When the cycle F _i includes the branch k in the negative direction B _ik = 1: When the cycle F _i includes the branch k in the positive direction B _ik = 0: The cycle F _i is When branch k is not included

  In the case of the models shown in FIGS. 3 and 4, the basic cycle matrix B is expressed by Expression (16).

  A cycle that is uniquely determined by a set of any one complementary tree and tree is called a basic cycle. The number of basic cycles in the graph is equal to the number of complement trees. The basic cycle matrix B can be obtained by the relationship of Expression (17) between the irreducible connection matrix A * and the basic cycle matrix B. In the formula, the subscript c represents a complement tree, and t represents a tree.

  The complement tree is selected, for example, by a depth-first search. Specifically, the pipeline network model construction unit 40 starts from the start node of the pipeline number 1 and searches for the end point of the pipeline number. The state variable calculation unit 42 repeats this search up to the pipeline number M, adds the start point and the end point to the stack, and calculates the pipeline number at the time when duplicate node numbers appear three or more times in the stack. And

  In the case of the models shown in FIGS. 3 and 4, the basic cycle matrix B is obtained by replacing the columns so that the columns corresponding to the pipes (3) and (5), which are complementary trees, become the previous column, and the equation (18 ). From the definition of the basic cycle, the component related to the complement tree is a unit matrix.

In response to this result, the columns A * _c and A * _t are obtained by exchanging the columns in the same manner as shown in Expression (19). Based on the theory described above, the flow rate of water flowing through each pipeline can be calculated by performing an operation according to the pipeline network model.

[Estimation of water leakage]
As described above, by separating the components of the connection matrix A into the components of the tree and the complementary tree, it is possible to perform the calculation related to the estimation of the amount of water leakage independently between the complementary tree and the tree. When the three equations (2), (3), and (9), which are the governing equations, are written separately in the graph tree and the complement tree, the equations (20), (21), (22), and (23 )

[Selection of water pressure sensor placement position]
As described above, if the graph theory is applied, the pipes constituting the water distribution pipe network can be classified into complement trees and trees. As a result, it is possible to consider the governing equation of the water distribution pipe network by dividing it into a complementary tree and a tree part. In other words, if the pressure loss dP _c can be measured for a pipeline serving as a supplementary tree, the water distribution pipeline network can be regarded as a single pipeline constituted by the pipeline serving as a tree. If there is one pipe line, the amount of water leakage at each node directly affects the total pressure loss, so it can be handled as one system. For this reason, if water pressure sensors are arranged at both ends of a pipe line serving as a supplementary tree, it becomes possible to estimate the amount of water leakage at all nodes. For this reason, the arrangement position selection unit 16 selects the nodes at both ends of the pipeline extracted as a complementary tree as the arrangement positions of the water pressure sensors.

  FIG. 6 is a diagram illustrating an example in which the water distribution pipeline network PN is regarded as one pipeline. The left figure of FIG. 6 has shown that four pipe lines shown by a black square were extracted as a complement tree with respect to four loops of the water distribution pipe network PN. In this case, the water distribution pipeline network PN is equivalent to a single pipeline as shown in the right diagram of FIG. Then, a black circle node is selected as the arrangement position of the water pressure sensor.

  For example, in a distribution pipeline network having a graph structure with N nodes, M pipelines, and F loops, in order to calculate the amount of water leakage at each node, conventionally, water pressure sensors at all nodes are used. Was necessary. That is, N water pressure sensors are required. On the other hand, the arrangement position selection device 1 of the first embodiment selects 2 × F−α + β nodes as positions where the water pressure sensors are arranged. By selecting such an arrangement position, it is possible to reduce the number of water pressure sensors necessary for water leakage diagnosis. α represents the number of nodes that overlap in a pipeline serving as a complement tree, and β represents the number of nodes on the path constituting the loop. Specifically, in the example of FIG. 6, the node 100 is a node corresponding to α. Also, the node 101 is a node corresponding to β.

  The sensor arrangement position selection device 1 according to the first embodiment configured as described above is based on a connection matrix that represents the connection configuration of the water distribution pipeline network 2 as a graph structure, from the pipelines that configure the water distribution pipeline network 2. Then, a pipeline that is a complementary tree constituting the loop is extracted. And the sensor arrangement position selection apparatus 1 selects the both ends of the pipe line extracted as a complement tree as an installation position of a water pressure sensor. By providing such a function, the sensor arrangement position selection device 1 can select an efficient arrangement position of the water pressure sensor from the nodes of a plurality of pipelines.

  Hereinafter, a modified example of the sensor arrangement position selection device 1 according to the first embodiment will be described.

  The sensor arrangement position selection device 1 may include a graph structure aggregation unit 17 that aggregates the graph structure of the water distribution pipeline network 2 based on the configuration of the pipeline network. FIG. 7 is a functional block diagram illustrating a functional configuration of a sensor arrangement position selection device 1a according to a modification. Based on the information stored in the water distribution pipe network information storage unit 11, the graph structure aggregation unit 17 classifies each pipeline into a tree and a complementary tree in the same manner as the complementary tree extraction unit 15. The graph structure aggregating unit 17 performs the following aggregation on the graph structure of the pipe line that is a tree.

FIG. 8 is a schematic diagram showing an overview of a first method for aggregating graph structures.
FIG. 8 shows, as a first method for collecting graph structures, the pipes are classified into branches and trunks based on the graph structure of the pipes that are trees, and the pipes that become branches are trunks. Shows the method of aggregation. The left figure of FIG. 8 is a figure which shows the example of the pipe line before aggregation. The right figure of FIG. 8 is a figure which shows the example of the pipe line after aggregation. The size of each node in FIG. 8 represents the amount of water used at each node. In this case, for example, the graph structure aggregating unit 17 may consolidate the four pipelines in the left diagram into one pipeline in the right diagram. The graph structure aggregation unit 17 reflects the result of such aggregation in the information stored in the distribution pipe network information storage unit 11.

  Further, the pipes may be aggregated so that the selection result of the arrangement position selection unit 16 becomes the arrangement position of the existing water pressure sensor. By performing such aggregation, even when an existing water pressure sensor is used, the amount of water leakage for each node can be estimated (although the resolution of water leakage diagnosis becomes rough).

FIG. 9 is a schematic diagram showing an overview of a second method for aggregating graph structures.
FIG. 9 shows a method of consolidating pipelines having a small diameter as a second method of consolidating the graph structure. Similarly to FIG. 8, the left diagram in FIG. 9 shows an example of the pipeline before aggregation, and the right diagram shows an example of the pipeline after aggregation. In this case, the graph structure aggregating unit 17 may aggregate the small-diameter pipe lines indicated by the broken lines in the left figure into other pipe lines. In this case, the graph structure aggregating unit 17 may simply ignore the pipe line indicated by the broken line, instead of consolidating it to another pipe line. The graph structure aggregation unit 17 reflects the result of such aggregation in the information stored in the distribution pipe network information storage unit 11.

  In addition, the arrangement position selected by the sensor arrangement position selection device 1a differs depending on the combination of extracted complementary trees. FIG. 10 is a diagram illustrating a specific example when different arrangement positions are selected. In FIG. 10, the pipelines indicated by broken lines are pipelines extracted as complementary trees. In the left diagram and the right diagram in FIG. 10, complementary trees are extracted in different combinations. At this time, the number of water pressure sensors in the left figure is seven, and the number of water pressure sensors in the right figure is eight. Therefore, it is advantageous to select the combination in the left figure in terms of reducing the number of water pressure sensors.

  In addition, while the above-described graph structure aggregation and the selection of the combination of complementary trees enable the number of water pressure sensors to be reduced, the amount of information acquired by the water pressure sensors is reduced, and the leakage diagnosis is performed. The resolution will be reduced. Here, the resolution of the water leakage diagnosis means the fineness of the unit capable of estimating the amount of water leakage. That is, there is a trade-off relationship between reducing the number of water pressure sensors and the resolution of water leakage diagnosis. For this reason, the number of water pressure sensors may be reduced so that the two are in an appropriate balance.

  In addition, the complementary tree extracting unit 15 may be configured to extract a pipeline serving as a complementary tree so as to satisfy a preset target condition with respect to a node selected as the arrangement position of the water pressure sensor. For example, whether or not the water pressure sensor can be installed may be set as the target condition. In this case, the complementary tree extracting unit 15 extracts the pipeline when the pipeline serving as the complementary tree has a node where a water pressure sensor can be installed.

  Such a target condition may be set for the arrangement position of the selected water pressure sensor. For example, the target condition may be set so that the arrangement position of the selected water pressure sensor becomes the arrangement position of the existing water pressure sensor. In this case, the arrangement position selection unit 16 may select, as the arrangement position, the position of an existing water pressure sensor installed at a position close to the nodes at both ends of the extracted pipeline.

  The sensor arrangement position selection device may be configured to prompt the user to update the water distribution network information stored in the water distribution network information storage unit 11. For example, when there is distribution pipe network information that is newer than the currently stored distribution pipe network information, the sensor arrangement position selection device acquires information indicating the presence of the new distribution pipe network information from the outside, and An update notification unit may be provided to notify the user of an update.

(Second Embodiment)
In the second embodiment, a water pressure sensor installed at the arrangement position selected by the sensor arrangement position selection device 1 of the first embodiment, a flow meter that measures the amount of water supplied to the water distribution pipe network PN, and The water leakage amount estimation device 2 for diagnosing water leakage at each node using a smart meter arranged at the node of each pipeline will be described.

FIG. 11 is a functional block diagram illustrating a functional configuration of the water leakage amount estimation device 2 according to the second embodiment.
The water leakage amount estimation device 2 includes a CPU, a memory, an auxiliary storage device, and the like connected by a bus, and executes a water leakage diagnosis program. The leakage amount estimation device 2 includes an input unit 21, an output unit 22, a measurement data acquisition unit 23, a pipeline network model construction unit 24, a leakage coefficient optimization unit 25, and a leakage amount estimation unit 26 by executing a leakage diagnosis program. Function as. Note that all or a part of each function of the water leakage amount estimation device 2 may be realized using hardware such as an ASIC, a PLD, or an FPGA. The water leakage diagnosis program may be recorded on a computer-readable recording medium. The computer-readable recording medium is, for example, a portable medium such as a flexible disk, a magneto-optical disk, a ROM, a CD-ROM, or a storage device such as a hard disk built in the computer system. The water leakage diagnosis program may be transmitted via a telecommunication line.

  The input unit 21 is configured using, for example, an input device such as a keyboard, a mouse, a touch panel, and a switch, and receives an input of a user operation.

  The output unit 22 includes, for example, a display device such as an LCD (Liquid Crystal Display) and an organic EL (Electroluminescence), a display control unit, a printer, a speaker, and the like, and outputs information on the arrangement position of the selected water pressure sensor. To do.

  The measurement data acquisition unit 23 acquires measurement data acquired by measurement from various measurement devices installed in the distribution pipe network.

  The pipeline network model construction unit 24 acquires the distribution pipeline network information from the sensor arrangement position selection device 1 of the first embodiment. The pipeline network model construction unit 24 constructs a pipeline network model of the distribution pipeline network based on the acquired distribution pipeline network information. The construction of the pipeline network model is as described above. The pipeline network model construction unit 24 outputs information on the constructed pipeline network model to the water leakage coefficient optimization unit 22.

  Based on the measurement data acquired by the measurement data acquisition unit 23, the water leakage coefficient optimization unit 25 determines a water leakage coefficient necessary for estimating the amount of water leakage at each node. The leakage coefficient optimization unit 25 outputs the determined leakage coefficient to the leakage amount estimation unit 26.

  The leakage amount estimation unit 26 calculates the leakage amount at each node based on the leakage coefficient determined by the leakage coefficient optimization unit 25. The leakage amount estimation unit 26 outputs the calculated leakage amount at each node to the output unit 22 as an estimated value of the leakage amount.

[Determination of water leakage coefficient]
As described in the first embodiment, if the water pressure at both ends of the pipeline extracted as a complementary tree can be measured, the water distribution pipeline network 2 having N nodes can draw water from the N-1 nodes. This is equivalent to one pipe (hereinafter referred to as “virtual pipe”). The relationship between the effective water pressure difference dP in the virtual pipe at a certain time and the differential pressure dP _{j in} each pipe is expressed as in the specific example of FIG. As shown in FIG. 12, if there is one virtual pipeline, the relationship between the water leakage at each node and the water pressure difference is uniquely determined. Therefore, the estimation of the water leakage at each node in the distribution pipeline network is limited. It can be formulated as a non-linear optimization problem. Hereinafter, two specific examples of the method for formulating such a constrained nonlinear optimization problem will be described.

[First method]
The first method is a restriction that the total amount of water leakage is expressed as the sum of the amount of water leakage at each node, and based on the measurement data measured at each time, the differential pressure from the start point to the end point of the virtual pipeline Is a method of optimizing the water leakage coefficient k _i so as to approach the measured value. The water leakage coefficient k _i is a coefficient that determines an estimated value of the water leakage amount at each node, and is expressed by Expression (24) assuming that the water pressure is proportional to the power of 1.15.

  In this case, in the first method, the estimation of the amount of water leakage at each node is formulated as shown in Equation (25).

Note that the differential pressure dP (t) from the start point to the end point of the virtual pipeline and the total amount L _{total of} water leakage are measurable and known. The total amount L _{total of} water leakage is expressed by equation (26).

The water leakage coefficient k _i is obtained by solving the above optimization problem. If the water leakage coefficient k _i is determined, V _t can be obtained by solving the nonlinear simultaneous equations of Expression (27) by convergence calculation.

[Second method]
The second method is a method of optimizing the water leakage coefficient k _i by partially relaxing the constraint conditions relating to the total water leakage amount in the first method. In this case, in the second method, the estimation of the amount of water leakage at each node is formulated as, for example, Expression (28).

Here, the objective function to be optimized was the sum of f ₁ and f _2, but may also be formulated in other formulas, such as the product of f ₁ and f _2.

  When the above-described formulation method is represented by a block diagram, it is represented as shown in FIG. Any method may be used as a method for solving the optimization problem formulated as described above. For example, the optimization problem may be solved by searching using the Newton method shown in the following equation (29). In Expression (29), F is a matrix representation of the objective function, and J is a Jacobian matrix.

  The leakage amount estimation device 2 of the second embodiment configured as described above includes the water pressure measured by the water pressure sensor arranged at the node selected by the sensor arrangement position selection device 1 of the first embodiment, The differential pressure from the start point to the end point of the open pipeline that passes through each node of the water pipeline network, the total amount of water leakage in the distribution pipeline network, the inflow rate to each node, and the amount of water used at each node And a water leakage coefficient optimization unit for determining a water leakage coefficient at each node by solving an optimization problem using the water leakage coefficient at each node as a determining variable, the determined water leakage coefficient, and the water distribution pipe It is possible to estimate the amount of water leakage at each node with fewer water pressure sensors by having a water leakage amount estimation unit that estimates the amount of water leakage at each node based on the equation of motion of the fluid reflecting the connection relationship between the nodes in the network It becomes possible.

FIG. 14 is a diagram illustrating an example of a simulation result of estimation of the amount of water leakage.
The left figure in FIG. 14 is a figure which shows a simulation result. Moreover, the right figure of FIG. 14 is a figure which shows the measured value in the environment assumed by simulation. In any figure, the horizontal axis represents each node, and the vertical axis represents the amount of water leakage at each node. As is apparent from the figure, it is understood that the amount of water leakage at each node can be accurately estimated by the above method. As described above, the leakage amount estimation device 2 of the embodiment can estimate the leakage amount of each node even when the leakage amount changes depending on the pressure.

  Hereinafter, a modified example of the water leakage amount estimation device 2 of the second embodiment will be described.

  The leak amount estimation device 2 may display the leak amount for each node estimated in this way on the output unit 22 on a screen (image) shown in FIG. 15, for example. FIG. 15 is a diagram illustrating an example of a screen displayed by the output unit 22 of the embodiment. The display control unit of the output unit 22 displays, for example, the amount of water leakage at each node on the display device in a bar graph or the like. Moreover, the display control part of the output part 22 may change the color of the symbol which shows a node by the magnitude of the amount of water leaks, and may make it display on a display apparatus.

  In addition, when there is a node where a smart meter is not attached to the water distribution pipe network, the water leak amount estimation device 2 may use meter reading data acquired by the water meter as information indicating the amount of water used at the node. Good.

  The water leak amount estimation device 2 may be configured to calculate the priority order of the pipeline update based on the water leak according to conditions such as the number of years since the pipeline was buried, material, and soil. In this case, the water leakage amount estimation device 2 includes an embedding condition information storage unit that stores embedding condition information indicating the embedding conditions including conditions such as years, materials, and soil since the conduit was embedded, and a water leakage amount estimating unit 11. And an update priority calculation unit that calculates the priority of pipeline update based on the amount of water leakage estimated by the above and the embedding condition.

  According to at least one embodiment described above, a connection matrix generation unit that generates a connection matrix representing a graph structure of a water distribution pipeline network based on information indicating a connection configuration of the pipelines constituting the water distribution pipeline network; Based on the connection matrix, the pipelines constituting the distribution pipeline network are changed to the pipelines that constitute the open pipelines in the distribution pipeline network and the pipelines that constitute the closed pipelines together with the trees. By having a complementary tree extracting unit that classifies and extracts a pipeline serving as a complementary tree, and a selection unit that selects nodes at both ends of the extracted pipeline as a hydraulic pressure sensor as the placement position of the hydraulic sensor, An efficient arrangement position of the sensor can be selected.

  Although several embodiments of the present invention have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope and gist of the invention, and are also included in the invention described in the claims and the equivalents thereof.

DESCRIPTION OF SYMBOLS 1, 1a ... Sensor arrangement position selection apparatus, 11 ... Water distribution network information storage part, 12 ... Input part, 13 ... Output part, 14 ... Connection matrix production | generation part, 15 ... Complement tree extraction part, 16 ... Arrangement position selection part , 17 ... Graph structure aggregating unit, 2 ... Water leakage amount estimation device, 21 ... Input unit, 22 ... Output unit, 23 ... Measurement data acquisition unit, 24 ... Pipe network model construction unit, 25 ... Water leakage coefficient optimization unit, 26 ... Water leakage estimation part

Claims (18)

A connection matrix generating unit that generates a connection matrix representing a graph structure of the water distribution pipe network based on information indicating a connection configuration of the pipes constituting the water distribution pipe network;
Based on the connection matrix, the pipes constituting the water distribution pipe network are the pipes that form the open pipes in the water distribution pipe network, and the pipes that are the complementary trees that form the closed pipes together with the trees. A complementary tree extraction unit that classifies the roads and extracts the pipelines that serve as the complementary trees;
A selection unit that selects the nodes at both ends of the extracted pipeline as a water pressure sensor;
A sensor arrangement position selecting device. The supplementary tree extraction unit extracts a pipe line serving as the supplementary tree so as to satisfy a target condition set in advance with respect to a node selected as an arrangement position of a water pressure sensor.
The sensor arrangement position selection device according to claim 1. The target condition is a condition indicating whether or not a water pressure sensor can be installed at each node, and the complementary tree extraction unit extracts a pipeline having a node that can be installed with a water pressure sensor as a complementary tree.
The sensor arrangement position selection device according to claim 2.   Based on the graph structure of the open pipe composed of the tree pipe, the open pipe is classified into a trunk and a branch, and when the branch pipe exists, the branch pipe is The sensor arrangement position selection device according to any one of claims 1 to 3, further comprising an aggregation unit that aggregates the main conduit. The aggregation part aggregates a small-diameter pipe line to another pipe line,
The sensor arrangement position selection device according to claim 4. The aggregation unit aggregates the pipelines so that the arrangement position selected by the arrangement position selection unit is the arrangement position of an existing water pressure sensor.
The sensor arrangement position selection device according to claim 4 or 5. The complementary tree extraction unit obtains a plurality of combinations of pipelines to be the complementary trees, and selects a combination having the smallest number of pipelines to be the complementary trees from the plurality of combinations to become the complementary trees. Extract the pipeline,
The sensor arrangement position selection device according to any one of claims 1 to 6. The selection unit selects an arrangement position close to the arrangement position of the existing water pressure sensor from the nodes at both ends of the pipe line serving as the complement tree,
The sensor arrangement position selection device according to any one of claims 1 to 7. A water pipe network information storage unit for storing water pipe network information including connection relations of nodes in the water pipe network;
When information indicating that there is newer information than the distribution pipe network information stored in the distribution pipe network information storage unit is acquired, information indicating that the distribution pipe network information should be updated is notified. An update notification section;
The sensor arrangement position selection device according to any one of claims 1 to 8, further comprising: A connection matrix generating unit that generates a connection matrix representing a graph structure of the water distribution pipe network based on information indicating a connection configuration of the pipes constituting the water distribution pipe network;
Based on the connection matrix, the pipes constituting the water distribution pipe network are the pipes that form the open pipes in the water distribution pipe network, and the pipes that are the complementary trees that form the closed pipes together with the trees. A complementary tree extraction unit that classifies the roads and extracts the pipelines that serve as the complementary trees;
A selection unit that selects the nodes at both ends of the extracted pipeline as a water pressure sensor;
As a sensor arrangement position selection device comprising:
A computer program that causes a computer to function. The water pressure of a pipeline serving as a supplementary tree in a water distribution pipeline network measured by a water pressure sensor installed at an arrangement position selected by the sensor arrangement position selection device according to any one of claims 1 to 9. Information, the differential pressure from the start point to the end point of the open pipeline that passes through each node of the distribution pipeline network, the total amount of water leakage in the distribution pipeline network, the inflow rate to each node, and at each node A water leakage coefficient optimization unit that determines a water leakage coefficient at each node by solving an optimization problem using the water leakage coefficient at each node as a determining variable based on
A leakage amount estimation unit that estimates the leakage amount of each node based on the determined leakage coefficient and the equation of motion of the fluid reflecting the connection relation between the nodes in the water distribution network;
A leakage amount estimation device comprising: A display unit that displays an image based on the water leakage amount estimated by the water leakage amount estimation unit;
The water leakage amount estimation apparatus according to claim 11. The display unit displays an image in which a symbol representing the node is drawn in a color according to the amount of water leakage estimated by the water leakage amount estimation unit;
The water leakage amount estimation apparatus according to claim 11 or 12. An embedding condition information storage unit for storing embedding condition information including embedding conditions for each pipeline;
An update priority calculation unit that calculates a priority when updating a pipeline based on the amount of water leakage for each node estimated by the water leakage amount estimation unit and the embedment condition information;
The water leak amount estimation apparatus according to any one of claims 11 to 13. Use the meter reading data acquired by the water meter for information indicating the amount of water used at some or all of the nodes.
The leakage amount estimation apparatus according to any one of claims 11 to 14. The water pressure of a pipeline serving as a supplementary tree in a water distribution pipeline network measured by a water pressure sensor installed at an arrangement position selected by the sensor arrangement position selection device according to any one of claims 1 to 9. Information, the differential pressure from the start point to the end point of the open pipeline that passes through each node of the distribution pipeline network, the total amount of water leakage in the distribution pipeline network, the inflow rate to each node, and at each node A water leakage coefficient optimization unit that determines a water leakage coefficient at each node by solving an optimization problem using the water leakage coefficient at each node as a determining variable based on
A leakage amount estimation unit that estimates the leakage amount of each node based on the determined leakage coefficient and the equation of motion of the fluid reflecting the connection relation between the nodes in the water distribution network;
As a water leak estimation device with
A computer program that causes a computer to function. A connection matrix generating unit that generates a connection matrix representing a graph structure of the water distribution pipe network based on information indicating a connection configuration of the pipes constituting the water distribution pipe network;
Based on the connection matrix, the pipes constituting the water distribution pipe network are the pipes that form the open pipes in the water distribution pipe network, and the pipes that are the complementary trees that form the closed pipes together with the trees. A complementary tree extraction unit that classifies the roads and extracts the pipelines that serve as the complementary trees;
A selection unit that selects the nodes at both ends of the extracted pipeline as a water pressure sensor;
Information indicating the water pressure of the pipeline serving as a complementary tree in the distribution pipeline network and the open pipeline passing through each node of the distribution pipeline network, measured by the water pressure sensor installed at the arrangement position selected by the selection unit The leakage coefficient at each node is calculated based on the differential pressure from the start point to the end point, the total amount of water leakage in the distribution pipeline network, the inflow flow into each node, and the amount of water used at each node. By solving the optimization problem as a decision variable, the leakage coefficient optimization unit that determines the leakage coefficient at each node,
A leakage amount estimation unit that estimates the leakage amount of each node based on the determined leakage coefficient and the equation of motion of the fluid reflecting the connection relation between the nodes in the water distribution network;
A water leakage diagnosis system comprising: A connection matrix generating step for generating a connection matrix representing a graph structure of the water distribution pipe network based on information indicating a connection configuration of the pipes constituting the water distribution pipe network;
Based on the connection matrix, the pipes constituting the water distribution pipe network are the pipes that form the open pipes in the water distribution pipe network, and the pipes that are the complementary trees that form the closed pipes together with the trees. And a complementary tree extraction step of extracting the pipelines to be the complementary trees,
A selection step of selecting nodes at both ends of the extracted pipeline as the arrangement position of the water pressure sensor;
Information indicating the water pressure of the pipeline serving as a supplementary tree in the distribution pipeline network and the open pipeline passing through each node of the distribution pipeline network measured by the water pressure sensor installed at the arrangement position selected in the selection step The leakage coefficient at each node is calculated based on the differential pressure from the start point to the end point, the total amount of water leakage in the distribution pipeline network, the inflow flow into each node, and the amount of water used at each node. A leakage coefficient optimization step for determining a leakage coefficient at each node by solving an optimization problem as a decision variable;
A leakage amount estimating step for estimating a leakage amount for each node based on the determined leakage coefficient and a fluid equation of motion reflecting a connection relation between the nodes in the water distribution network;
A method for diagnosing water leakage.

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