JP2020038460A - Apparatus and method for end-pressure control assistance and computer program - Google Patents

Abstract

To provide an apparatus and method for end-pressure control assistance and computer program capable of accurately estimating an end pressure.SOLUTION: An apparatus for end-pressure control assistance in an embodiment has an end-pressure estimating section. The end-pressure estimating section estimates a pressure at a second end based on an explanatory variable including at least one piece of information of water-distribution station information indicative of an operation state of a water-distribution station for distributing water to a water-distribution piping network, monitor information indicative of a result of monitoring a water-distribution system for distributing water from the water-distribution piping network to a user, water demand information representative of a water demand of the user, and first pressure information acquired from a first pressure-measuring apparatus permanently provided at a first end that is a place of the water-distribution piping network where a pressure is measured, and an estimation model for estimating a pressure at the second end that is a place of the water-distribution piping network where a pressure is measured. The estimation model is obtained by conducting machine learning based on the explanatory variable and second pressure information acquired from a second pressure-measuring apparatus temporarily provided at the second end.SELECTED DRAWING: Figure 2

Description

  An embodiment of the present invention relates to a terminal pressure control support device, a terminal pressure control support method, and a computer program.

  2. Description of the Related Art Terminal pressure control is known as a control method of a water distribution system that supplies water to a customer. Terminal pressure control is effective in reducing excess power consumption and water leakage of the water distribution pump. In order to perform terminal pressure control, a water supply company needs to install a terminal pressure measuring device in the distribution pipe network or construct a simulation model (hereinafter, referred to as a "pipe network model") for performing pipe network analysis. there were. However, installation of a measuring device or construction of a pipe network model requires high costs. For this reason, the water utility may estimate the terminal pressure by using an estimation model for estimating the terminal pressure. However, when the amount of information acquired to generate the estimation model is not sufficient, the estimation accuracy of the estimation model may be insufficient.

JP 2002-268703 A JP 2006-104777 A JP 2010-216089 A JP 2001-188614 A Japanese Patent No. 3851783 Japanese Patent No. 5010504

  A problem to be solved by the present invention is to provide a terminal pressure control support device, a terminal pressure control support method, and a computer program that can more accurately estimate a terminal pressure.

  The terminal pressure control support device of the embodiment has a terminal pressure estimation unit. The terminal pressure estimating unit is a distribution station information indicating an operation state of a distribution plant that distributes water to a distribution network, monitoring information indicating a result of monitoring of a distribution system that distributes water to the customer from the distribution network, and water of the customer. At least one of water demand information representing a demand amount and first pressure information obtained from a first pressure measuring device permanently installed at a first end of the distribution pipe network where pressure is measured. The pressure at the second terminal is estimated based on the explanatory variables including the pressure and an estimation model for estimating the pressure at the second terminal, which is a place where the pressure is estimated in the distribution pipe network. The estimation model is obtained by performing machine learning based on the explanatory variables and second pressure information acquired from a second pressure measurement device temporarily provided at the second end.

The figure which shows the specific example of the system configuration of the water distribution system in 1st Embodiment. FIG. 2 is a block diagram showing a specific example of a functional configuration of the terminal pressure control support device according to the first embodiment. 5 is a flowchart showing a flow of generating an estimation model of the terminal pressure control support device of the first embodiment. 5 is a flowchart illustrating a flow of generating support information of the terminal pressure control support device according to the first embodiment. FIG. 3 is a diagram illustrating a specific example of a decision tree representing an estimation model according to the first embodiment. 6 is an estimation result table summarizing the estimation results of the terminal pressure according to the first embodiment. FIG. 9 is a diagram illustrating a specific example of explanatory information in which an estimation result and an estimation model according to the first embodiment are visualized. FIG. 8 is a diagram illustrating a specific example of visualization of a decision tree after updating according to the first embodiment. FIG. 9 is a block diagram showing a specific example of a functional configuration of the terminal pressure control support device according to the second embodiment. FIG. 13 is a block diagram showing a specific example of a functional configuration of a terminal pressure control support device according to a third embodiment. The figure which shows the specific example of the system configuration of the water distribution system in 4th Embodiment. FIG. 13 is a block diagram showing a specific example of a functional configuration of a terminal pressure control support device according to a fourth embodiment. 13 is a flowchart illustrating a flow of generating an estimation model of the terminal pressure control support device according to the fourth embodiment. 13 is a flowchart illustrating a flow of generating support information of the terminal pressure control support device according to the fourth embodiment.

  Hereinafter, a terminal pressure control support device, a terminal pressure control support method, and a computer program according to an embodiment will be described with reference to the drawings.

(First embodiment)
FIG. 1 is a diagram illustrating a specific example of a system configuration of a water distribution system 100 according to the first embodiment. The water distribution system 100 includes a terminal pressure control support device 1, a monitoring control system 2, one or more water distribution stations 3, and one or more terminal pressure measuring devices 4, and supplies water to one or more customers 6 via a water distribution network 5. System for supplying FIG. 1 shows water distribution stations 3-1 and 3-2 as examples of one or more water distribution stations, and shows terminal pressure measurement apparatuses 4-1 and 4-2 as examples of one or more terminal pressure measurement apparatuses 4. The customers 6-1 to 6-3 are shown as examples of the customers 6 described above. The numbers of the water distribution plant 3, the terminal pressure measuring devices 4, and the customers 6 may be different from the example of FIG. The terminal pressure control support device 1, the monitoring control system 2, each water distribution plant 3, and each terminal pressure measuring device 4 are configured to be able to communicate with each other. The water distribution system 100 may include a water supply facility (not shown) such as a water supply station.

  The terminal pressure control support device 1 provides information (hereinafter, referred to as “support information”) that supports the control or monitoring to the monitoring control system 2 that monitors or controls the water distribution plant 3. Specifically, the terminal pressure control support device 1 acquires terminal pressure information indicating the measured value of the terminal pressure of the water distribution network 5 from each terminal pressure measuring device 4. The terminal pressure control support device 1 obtains water distribution station information indicating various quantities (hereinafter, referred to as “distribution water quantities”) from each of the water distribution stations 3. The distribution station information indicates the operating state of the distribution station that distributes water to the distribution network. The distribution point information includes, for example, measured values obtained at the distribution point or the transmission point, such as the distribution flow rate and the distribution pressure at the distribution point or the transmission point. The terminal pressure control support device 1 acquires information (hereinafter, referred to as “monitoring information”) in the water distribution system 100 from the monitoring control system 2. The monitoring information indicates a result of monitoring of the water distribution system 100 that distributes water from the water distribution network 5 to the customer 6. The monitoring information includes different information depending on the type of the provided sensor. The sensors provided vary depending on the business operator. For example, a sensor indicating the opening of a water stop valve for shutting off the flow of water in a part of the water distribution pipe network, a valve for changing the water pressure in the pipe and a sensor indicating the opening thereof, water pressure in the pipe or flow rate in the pipe Is installed. The sensor is not limited to these, and any sensor may be installed. The terminal pressure control support device 1 generates support information based on the obtained terminal pressure information, water distribution station information, and monitoring information. For example, the support information includes an estimated value of the terminal pressure at each terminal of the water distribution network 5. In addition, the support information may include information generated based on the estimated value of the terminal pressure, a determination result based on the estimated value of the terminal pressure, and the like.

  The monitoring control system 2 is a system that monitors or controls the water distribution plant 3 using the support information provided from the terminal pressure control support device 1. For example, the monitoring control system 2 adjusts the number of operating water distribution pumps and the output intensity in each water distribution station 3, monitors the water level of a distribution reservoir that is a water supply source, and the like.

  The distribution station 3 has various facilities (not shown) such as a distribution reservoir for storing water to be supplied to the customers 6 and a distribution pump for sending water from the distribution reservoir to the distribution network 5. It is a facility that supplies each customer 6 via the network 5. Various facilities of the water distribution plant 3 are monitored or controlled by the monitoring control system 2. Further, the water distribution station 3 transmits to the terminal pressure control support device 1 water distribution station information indicating various amounts (various amounts of water distribution stations) observable in the own facility.

  Generally, it is considered that the terminal pressure of the water distribution pipe network 5 has a high correlation with the discharge flow rate or the discharge pressure of the pump in the water distribution plant 3. For this reason, the water distribution station information includes at least information indicating the discharge flow rate or discharge pressure of the pump. In addition, since the terminal pressure of the distribution pipe network 5 is considered to be correlated with the water level of the reservoir in the distribution plant 3, the distribution station information may include information indicating the water level of the distribution reservoir.

  The terminal pressure measuring device 4 is a device that measures the terminal pressure of the water distribution pipe network 5. The terminal pressure measuring device 4 is temporarily provided at the terminal of the water distribution pipe network 5. The end is a place where the pressure is measured or estimated in the water distribution network 5. The end location is specified in advance. For example, the end may be designated in the water distribution network 5 as a place where the pressure is likely to be low or the danger is high. For example, if the pressure at the end is equal to or higher than a predetermined threshold, a place where it is considered that a pressure sufficient to convey water to the customer 6 at another point in the water distribution network 5 may be specified. . For example, a terminal may be a location that is considered to have a high contribution in increasing the accuracy of an estimation model that estimates terminal pressures of other terminals. The end may be any location as long as it is a location designated in advance. The terminal pressure measurement device 4 transmits to the terminal pressure control support device 1 terminal pressure information indicating the measured value of the measured terminal pressure. The terminal pressure is a terminal pressure. The predetermined threshold value may be, for example, a value lower than any other location in the water distribution network or a value specified in advance. The user may be, for example, a water service company or a company entrusted with a service from the water service company. The terminal pressure measuring device 4 is an embodiment of a second pressure measuring device. The location where the terminal pressure measuring device 4 is provided is one mode of the second terminal. The second end is where the pressure is estimated.

  FIG. 2 is a block diagram illustrating a specific example of a functional configuration of the terminal pressure control support device 1 according to the first embodiment. The terminal pressure control support device 1 includes a CPU (Central Processing Unit), a memory, and an auxiliary storage device connected by a bus, and executes a program. The terminal pressure control support device 1 functions as a device including the communication unit 101, the input unit 102, the display unit 103, the storage unit 104, and the control unit 105 by executing a program. Note that all or a part of each function of the terminal pressure control support device 1 is realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), and an FPGA (Field Programmable Gate Array). Is also good. The 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, and a CD-ROM, and a storage device such as a hard disk built in a computer system. The program may be transmitted via a telecommunication line.

  The communication unit 101 is a network interface. The communication unit 101 communicates with the monitoring control system 2, the water distribution plant 3, and the terminal pressure measuring device 4. The communication unit 101 may communicate using a communication method such as a wireless LAN (Local Area Network), a wired LAN, Bluetooth (registered trademark), or LTE (Long Term Evolution) (registered trademark).

  The input unit 102 is configured using input devices such as a touch panel, a mouse, and a keyboard. The input unit 102 may be an interface for connecting the input device to the terminal pressure control support device 1. In this case, the input unit 102 generates input data (for example, instruction information indicating an instruction to the terminal pressure control support device 1) from an input signal input in the input device, and inputs the data to the terminal pressure control support device 1.

  The display unit 103 is an output device such as a CRT (Cathode Ray Tube) display, a liquid crystal display, and an organic EL (Electro Luminescence) display. The display unit 103 may be an interface for connecting the output device to the terminal pressure control support device 1. In this case, the display unit 103 generates a video signal from the video data and outputs the video signal to a video output device connected thereto.

  The storage unit 104 stores various types of information used to provide support information to the monitoring control system 2. The storage unit 104 is configured using a storage device such as a magnetic hard disk device or a semiconductor storage device. The storage unit 104 includes a terminal pressure information storage unit 106 and a water distribution information storage unit 107.

  The terminal pressure information storage unit 106 stores the terminal pressure information. The water distribution information storage unit 107 stores water distribution information. Water distribution information is information including water distribution station information and monitoring information.

  The control unit 105 controls the operation of each unit of the terminal pressure control support device 1. The control unit 105 is executed by a device including a processor such as a CPU and a RAM, for example. By executing the program, the control unit 105 executes the information acquisition unit 108, the terminal pressure learning unit 109, the terminal pressure estimation unit 110, the output unit 111, the terminal pressure estimation explanation unit 112, the estimation model update unit 113, and the screen generation unit 114. Function as

  The information acquisition unit 108 acquires various information used for providing support information. Specifically, the information acquisition unit 108 acquires water distribution station information from each water distribution station 3. The information acquisition unit 108 acquires monitoring information from the monitoring control system 2. The information acquisition unit 108 acquires terminal pressure information from each terminal pressure measuring device 4. The information acquisition unit 108 records the acquired water distribution station information and monitoring information in the water distribution information storage unit 107. The information acquisition unit 108 records the acquired terminal pressure information in the terminal pressure information storage unit 106. The information obtaining unit 108 repeatedly obtains the water distribution station information, the monitoring information, and the terminal pressure information at a predetermined timing, and thereby stores the water distribution station information, the monitoring information, and the terminal pressure information in the terminal pressure information storage unit 106 and the water distribution information storage unit. Record it in 107.

  The terminal pressure learning unit 109 performs a machine learning process using the water distribution information recorded in the water distribution information storage unit 107 and the terminal pressure information stored in the terminal pressure information storage unit 106 as learning data. A machine learning technique for generating or updating a classifier by supervised learning is applied to the terminal pressure learning unit 109. The terminal pressure learning unit 109 performs a machine learning process based on the learning data, and thereby learns a relationship between water distribution station information, monitoring information, and terminal pressure information of the water distribution network 5 included in the water distribution information. More specifically, the terminal pressure learning unit 109 sets the distribution model information and the monitoring information in the water distribution information as explanatory variables, and uses the terminal pressure information of the water distribution pipe network 5 as an objective variable to generate an estimation model indicating the relationship between these. Generate. The terminal pressure learning unit 109 outputs data such as the parameters representing the generated discriminator to the terminal pressure estimating unit 110 as a learning result. Hereinafter, the learning of the relationship is referred to as “learning of the terminal pressure” as necessary.

  The terminal pressure estimating unit 110 responds to the given water distribution information based on the relationship between the distribution station quantities and the monitoring information in the water distribution information learned by the terminal pressure learning unit 109 and the terminal pressure of the water distribution network 5. Estimate the end pressure to be applied. The terminal pressure estimating unit 110 outputs estimated terminal pressure information indicating the terminal pressure obtained by the estimation to the output unit 111. The terminal pressure estimating unit 110 can estimate the terminal pressure of the terminal whose terminal pressure has been learned by the terminal pressure learning unit 109.

  The output unit 111 generates support information based on the estimated terminal pressure information output from the terminal pressure estimation unit 110. The output unit 111 transmits the generated support information to the monitoring control system 2.

  The terminal pressure estimation explanation section 112 generates explanation information representing a text or a chart explaining the estimation model generated by the terminal pressure learning section 109 and the estimation result estimated by the estimation model. The terminal pressure estimation explanation unit 112 outputs the generated explanation information to the screen generation unit 114.

  The estimation model update unit 113 receives a model update instruction from a user via the input unit 102. When receiving the model update instruction, the estimated model update unit 113 updates the estimated model based on the model update instruction. The model update instruction is an instruction to generate an estimated model without using at least one of the explanatory variables used to generate the estimated model. For example, the updated estimation model is used by the terminal pressure estimating unit 110 for estimating the terminal pressure. The estimation model can be updated at any timing by receiving a model update instruction via the input unit 102.

  The screen generation unit 114 generates screen information in which the explanation information is visualized based on the explanation information. The screen generation unit 114 causes the display unit 103 to display the generated screen information.

  Next, regarding the first embodiment, an estimation model of terminal pressure at an estimation point in a distribution network for water distribution from three water distribution stations (first to third water distribution stations) and one water transmission station. An example in the case of generating is described with reference to the flowchart of FIG. The estimation point indicates a place where the terminal pressure is estimated.

  FIG. 3 is a flowchart illustrating a flow of generating an estimation model of the terminal pressure control support device 1 according to the first embodiment. The information acquisition unit 108 acquires terminal pressure information from each terminal pressure measuring device 4, distribution plant information from each distribution plant 3, and monitoring information from the monitoring control system 2 (step S101). The distribution station information includes, for example, the distribution flow rate of the first distribution station, the discharge pressure of the first pipe of the first distribution station, the discharge pressure of the second pipe of the first distribution station, the distribution flow rate of the second distribution station, and the second distribution rate. Discharge pressure of the first pipe of the distribution station, discharge pressure of the second pipe of the second distribution station, distribution flow rate of the third distribution station, discharge pressure of the first pipe of the third distribution station, second pipe of the third distribution station , The water distribution flow rate of the water supply station, the discharge pressure of the first pipe of the water supply station, and the discharge pressure of the second pipe of the water supply station. The monitoring information is, for example, the opening of the water stop valve at the first point.

  The information acquisition unit 108 records the acquired terminal pressure information in the terminal pressure information storage unit 106. The information acquisition unit 108 records the acquired water distribution station information and monitoring information in the water distribution information storage unit 107. By repeatedly executing the acquisition of such information for a certain period, the terminal pressure control support device 1 accumulates terminal pressure information, water distribution station information, and monitoring information (Step S102). In the present embodiment, a description will be given on the assumption that each information acquired every hour is accumulated for 28 days. Hereinafter, the accumulated terminal pressure information, water distribution station information, and monitoring information are referred to as learning data.

  The terminal pressure learning unit 109 uses the past water distribution information (water distribution station information and monitoring information) stored in the water distribution information storage unit 107 as an explanatory variable and the terminal pressure information stored in the past terminal pressure information storage unit 106 as an objective variable. Then, an estimation model is generated by learning these relationships (step S103). Specifically, the terminal pressure learning unit 109 generates an estimation model by machine learning using the above-described 13 items of water distribution information and the time at which the water distribution information is obtained as an explanatory variable and the terminal pressure at the estimated point as a target variable. In the present embodiment, the terminal pressure learning unit 109 generates an estimation model using a decision tree algorithm. The terminal pressure learning unit 109 is an example of a pressure learning unit.

  The terminal pressure estimation explanation section 112 generates explanation information indicating a sentence or a chart or the like explaining the generated estimation model and the estimation result estimated by the estimation model. In step S103, explanation information on the estimation result for the learning data is generated. The screen generator 114 causes the display 103 to display the screen information generated based on the explanation information (step S104).

  FIG. 5 is a diagram illustrating a specific example of a decision tree representing the estimation model according to the first embodiment. In the decision tree, the terminal pressure is estimated by making a determination on the value of the explanatory variable using a threshold value. At the end node of the decision tree, the estimated value of the terminal pressure at the estimation point is indicated. The decision tree is one mode of the explanation information. Therefore, by confirming the decision tree displayed on the display unit 103, the user can grasp the basis for estimating the terminal pressure at the estimation point. In addition, the number of samples of the learning data may be displayed or the value of MSE (Mean Squared Error) may be displayed at each node or terminal node in FIG.

  FIG. 6 is an estimation result table summarizing the estimation results of the terminal pressure according to the first embodiment. The estimation result table shown in FIG. 6 is a table summarizing the result of estimating the terminal pressure at the estimated point by inputting items obtained by removing the terminal pressure at the estimated point from the learning data to the estimation model. The estimation result table is one mode of the explanation information.

  The estimation result table has columns related to the date and time of the estimation target such as date and time. The estimation result table has columns of an actual pressure that is an actual measured value pressure of the estimation point and an estimated pressure that is a pressure of the estimation point estimated based on the estimation model. The estimation result table includes columns of water distribution information used as explanatory variables such as the flow rate of the first water distribution station, the discharge pressure of the first pipe of the first water distribution station, ..., the opening of the water stop valve at the first point, and the like. Have. The terminal pressure estimation explanation unit 112 estimates the accuracy (for example, the value of RMSE (Root Mean Squared Error)) obtained by performing statistical processing on each value of the estimation result table in addition to the estimated pressure for each date and time in the estimation result table. Is generated as explanatory information. The estimation result table and the estimation accuracy are displayed on the display unit 103. The user can grasp the estimation accuracy of the terminal pressure at the estimation point by checking the estimation result table and the estimation accuracy displayed on the display unit 103. Note that the estimation result table may be a table summarizing the results estimated by leave-1out with the learning data set to 29 days and the evaluation data set to 1 day.

  FIG. 7 is a diagram illustrating a specific example of explanatory information obtained by visualizing the estimation result and the estimation model of the first embodiment. FIG. 7 illustrates a case where the screen generation unit 114 receives the generated decision tree, the estimation result table, and the explanation information indicating the estimation accuracy, generates screen information in which the received explanation information is visualized, and displays the generated screen information on the display unit. 103 is displayed. In the case of FIG. 7, the user can select one row of the estimation result table via the input unit 102. Upon receiving the selection, the terminal pressure estimation explanation unit 112 generates explanation information in which the color of the selected line has been changed. Further, the terminal pressure estimation explanation unit 112 generates explanation information for highlighting the path of the decision tree corresponding to the selected row. The screen generation unit 114 changes the color of the screen displayed on the display unit 103 based on the explanation information. In the case of FIG. 7, it can be seen that the second row of the estimation result table has been selected. In the case of FIG. 7, it can be seen that the path of the decision tree passed through False at the node of the third distribution station_flow rate, and passed through True at the node of the first distribution station_discharge pressure of the second pipe. In the case of FIG. 7, it can be seen that the value of the estimated terminal pressure is 0.3824. The highlighted display may be, for example, a thick line, a change in color or brightness, or a display in any manner. In this way, by visualizing the contents of the estimation model and displaying the contents in conjunction with the estimation result, the user's satisfaction can be increased.

  Returning to FIG. 3, the description of the flowchart will be continued. When the layer of the decision tree as shown in FIG. 5 becomes deeper, the terminal pressure estimating unit 110 estimates the terminal pressure under a combination of many conditions. For this reason, when the layer of the decision tree becomes deep, even if the estimation model is visualized, it is not easy for the user to grasp the contents of the estimation model and the basis of the estimation result in a short time. Therefore, in order to improve the efficiency for the user, it is desirable that the layer of the decision tree is not deep. When the number of explanatory variables is large, the depth of the decision tree tends to be deep. In such a case, when the user desires a simpler and easier-to-understand estimation model, the estimation model updating unit 113 may receive a model updating instruction for the generated model via the input unit 102.

  The estimated model updating unit 113 determines whether a model update instruction for the estimated model has been received from the user via the input unit 102 (Step S105). If the model update instruction has not been received (step S105: YES), the estimation model update unit 113 ends the process, and the generated estimation model is used by the terminal pressure estimation unit 110.

  If a model update instruction has been received (step S105: NO), the estimated model update unit 113 updates the estimated model based on the model update instruction (step S106). Specifically, the user instructs not to use some of the explanatory variables based on knowledge and experience regarding the water distribution system and the water distribution network targeted as the model update instruction. Note that the estimation model updating unit 113 can make a determination regarding not using some of the explanatory variables based on the result of the contribution rate or the estimation accuracy at the time of learning the estimation model by machine learning. However, it may be difficult for the estimation model updating unit 113 to make a determination based on statistical information that is a basis. In particular, if the terminal pressure learning unit 109 generates an estimation model based on data for a limited period, over-learning may occur, and as a result, generalization estimation accuracy may be deteriorated (the data may show a correlation with the objective variable). Some explanatory variables are not really relevant and may not be considered.) In the present embodiment, over-learning can be prevented and generalization performance can be improved by receiving a model update instruction from the user based on the knowledge and experience of the user.

  For example, a case will be described in which the estimation model update unit 113 receives a model update instruction indicating that the discharge pressure of the second pipe of the first water distribution station and the discharge pressure of the second pipe of the second water distribution station are not considered. For example, when estimating the terminal pressure at the estimation point from the connection status in the distribution pipe network, the user obtains information on the discharge pressure of the second pipe of the first water distribution station and the discharge pressure of the second pipe of the second water distribution station. Is considered unnecessary, a model update instruction for excluding the discharge pressure of the second pipe of the first water distribution station and the discharge pressure of the second pipe of the second water distribution station from the decision tree visualizing the estimation model is input. Input via the unit 102.

  The estimation model update unit 113 receives a model update instruction when an explanatory variable displayed on the display unit 103 is selected via the input unit 102. The estimation model updating unit 113 updates the estimation model by excluding the explanatory variables selected from the learning data and learning the estimation model again based on the model update instruction.

  FIG. 8 is a diagram illustrating a specific example of the visualization of the updated decision tree according to the first embodiment. FIG. 8 shows a case where a model update instruction indicating that the discharge pressure of the second pipe of the first water distribution station and the discharge pressure of the second pipe of the second water distribution station are not considered for the decision tree of FIG. 5 is received. Represents the generated decision tree. As shown in FIG. 8, the updated estimation model has five layers. The estimation model before updating has six layers. As described above, the estimated model updating unit 113 updates the estimated model based on the model update instruction, thereby reducing the number of layers of the estimated model. Therefore, by updating the estimation model, an estimation model that is easier for the user to understand can be generated. The user may further input a model update instruction for the changed estimated model.

  FIG. 4 is a flowchart illustrating a flow of support information generation of the terminal pressure control support device 1 of the first embodiment. The information acquisition unit 108 acquires current water distribution station information from each water distribution plant 3 (Step S201). The information acquisition unit 108 acquires the current monitoring information from the monitoring control system 2 (Step S202). The terminal pressure estimating unit 110 estimates the current terminal pressure based on the estimation model generated by the terminal pressure learning unit 109, the acquired water distribution station information, and the monitoring information (Step S203). The terminal pressure estimation explanation section 112 generates explanation information indicating a sentence or a chart showing the estimated estimation result and the estimation basis. In step S204, explanation information on the estimation result of the acquired current water distribution station information and monitoring information is generated. The screen generator 114 causes the display 103 to display the screen information generated based on the explanation information (step S204). The output unit 111 generates support information based on the estimated terminal pressure information output from the terminal pressure estimation unit 110. The output unit 111 transmits the generated support information to the monitoring control system 2 (Step S205).

  According to the terminal pressure control support device 1 configured as described above, the explanation information generated by the terminal pressure estimation explanation unit 112 is displayed on the display unit 103, thereby visualizing the contents of the estimation model to the user. In addition, it is possible to make a presentation linked with the estimation result. Therefore, the user can increase the degree of satisfaction with the estimation result. Also, the user can easily introduce or use the terminal pressure control support device 1 or the monitoring control system 2 utilizing the support information. Further, the estimation model updating unit 113 updates the estimation model by receiving the model update instruction. With this configuration, the user can reduce the number of explanatory variables based on his / her own knowledge or experience. Therefore, the terminal pressure learning unit 109 can prevent over-learning of the estimation model. The terminal pressure estimating unit 110 can improve the generalization performance for unknown data that is not used for learning the estimation model, so that the terminal pressure can be more accurately estimated. As a result, the water distribution system 100 can more efficiently operate the reduction of the surplus terminal pressure, the estimation of the leak location, the terminal pressure control, and the like. In addition, since the estimation model is an estimation model in which explanatory variables are reduced based on the knowledge or experience of the user, the estimation accuracy is maintained, and humans can easily understand when the estimation model is visualized.

(Modification of First Embodiment)
The model update instruction may be specified as a constraint on a deterioration rate or a deterioration amount of the estimation accuracy, or a threshold or an allowable value of the minimum required estimation accuracy. In this case, if the updated estimated model does not satisfy the constraint, the estimated model updating unit 113 visualizes the estimated model and issues an alarm. For example, the warning may output a warning sound, or may cause the display unit 103 to display a character string indicating that the estimation accuracy is deteriorated or that the minimum required estimation accuracy is not satisfied. With this configuration, by changing the estimation model, even when the estimation performance changes, it is possible to give the user an opportunity to consider whether or not to input a model update instruction, The estimation performance can be maintained.

(Second embodiment)
Next, a terminal pressure control support device 1a according to the second embodiment will be described. FIG. 9 is a block diagram illustrating a specific example of a functional configuration of the terminal pressure control support device 1a according to the second embodiment. The terminal pressure control support device 1a according to the second embodiment differs from the first embodiment in that a storage unit 104a and a control unit 105a are provided instead of the storage unit 104 and the control unit 105, but other configurations are the same. Is the same. Hereinafter, points different from the first embodiment will be described.

  The storage unit 104a stores various types of information used to provide support information to the monitoring control system 2. The storage unit 104a is configured using a storage device such as a magnetic hard disk device or a semiconductor storage device. The storage unit 104a includes a terminal pressure information storage unit 106a and a water distribution information storage unit 107a.

  The terminal pressure information storage unit 106a stores the position information of the estimated point and the terminal pressure information. The position information is information representing a physical position such as an address or latitude / longitude. The water distribution information storage unit 107a stores water distribution information and position information indicating the location of each explanatory variable.

  The control unit 105a controls the operation of each unit of the terminal pressure control support device 1a. The control unit 105a is executed by a device including a processor such as a CPU and a RAM, for example. By executing the program, the control unit 105a executes the information acquisition unit 108, the terminal pressure learning unit 109, the terminal pressure estimation unit 110, the output unit 111, the terminal pressure estimation explanation unit 112a, the estimation model update unit 113, and the screen generation unit 114. Function as

  The terminal pressure estimation explanation unit 112a generates explanation information indicating a text model or a chart explaining the estimation model generated by the terminal pressure learning unit 109 and the estimation result estimated by the estimation model. In addition, the terminal pressure estimation explanation unit 112a is a distribution system that visualizes where the explanatory variables such as water distribution station information and monitoring information and the target variables such as terminal pressure information used in the estimation are located in the water distribution network 5. Description information including a map of the water pipe network 5 is generated. The terminal pressure estimation explanation section 112a outputs the generated explanation information to the screen generation section 114.

  Specifically, the screen generation unit 114 generates screen information for displaying a predetermined symbol at a location associated with water distribution station information, monitoring information, and terminal pressure information on a map based on the generated explanatory information, and displays the screen information. It is displayed on the unit 103. If the terminal pressure estimation explanation unit 112a records information such as the pipeline, the position of the node, and the connection information of the water distribution pipe network 5 in the terminal pressure information storage unit 106a or the water distribution information storage unit 107a, the information is also added to the map. The description information to be displayed above may be generated. The screen information of the map displayed on the display unit 103 is linked with the display of the estimation result and the estimation model shown in FIG. That is, when a certain estimation result is selected via the input unit 102, a part of the diagram in which the estimation model indicating the estimation basis is visualized as shown in FIG. 7 is highlighted. The terminal pressure estimation explanation section 112a generates explanation information for displaying the value of each explanation variable at the time of obtaining the selected estimation result on the display section 103 so as to be attached to the symbol linked on the map. Further, the terminal pressure estimation explanation section 112a generates explanation information for highlighting the symbols of the first water distribution station, the third water distribution station, and the estimated point corresponding to the estimation ground, and the value displayed in association with them.

  In addition, when one of the nodes of the decision tree is selected, the terminal pressure estimation explanation unit 112a generates explanation information in which nodes and arrows existing on a path from the root node to the selected node are highlighted. The terminal pressure estimation explanation section 112a generates explanation information for highlighting the symbols related to those nodes on the map and displaying the branching conditions at the nodes linked to the symbols in association with the symbols.

  According to the terminal pressure control support device 1a configured as described above, the display information including the map generated by the terminal pressure estimation explanation unit 112a is displayed on the display unit 103. The user can further increase the degree of satisfaction with the estimation result by checking the contents of the estimation model, the estimation result, and the map in conjunction with each other.

(Third embodiment)
Next, a terminal pressure control support device 1b according to a third embodiment will be described. FIG. 10 is a block diagram illustrating a specific example of a functional configuration of the terminal pressure control support device 1b according to the third embodiment. The terminal pressure control support device 1b according to the third embodiment differs from the first embodiment in that a storage unit 104b and a control unit 105b are provided instead of the storage unit 104 and the control unit 105, but other configurations are the same. Is the same. Hereinafter, points different from the first embodiment will be described.

  The storage unit 104b stores various types of information used to provide support information to the monitoring control system 2. The storage unit 104b is configured using a storage device such as a magnetic hard disk device or a semiconductor storage device. The storage unit 104b includes a terminal pressure information storage unit 106, a water distribution information storage unit 107, and a determination condition storage unit 115.

  The determination condition storage unit 115 records an algorithm determination condition. Algorithm determination conditions are given in advance by the user. The algorithm determination condition represents a condition for determining an algorithm used by the end pressure learning unit 109b to generate the estimation model. As the algorithm determination condition, for example, items of a priority, a tie-difference difference value, and a constraint are specified. The priority determines what items are prioritized when the algorithm is determined. The priority is selected from, for example, ease of understanding of the estimation model, estimation accuracy, and calculation time. For example, when the estimation accuracy is selected as the priority, an algorithm having an excellent estimation accuracy is determined. The same-rank deemed difference value is a value that determines how much the difference in the estimation accuracy between the algorithms is regarded as the same rank, and how much the difference in the calculation time is considered as the same rate. The constraint represents a threshold such as a lower limit of the estimation accuracy and an upper limit of the calculation time. Note that the same rank deemed allowable value and constraint are optional items. That is, it is only necessary that the priority is determined as the algorithm determination condition. The item of the priority order is an example. The priority may include items for ranking the algorithms in addition to the ease of understanding the estimation model, the estimation accuracy, and the calculation time.

  The control unit 105b controls the operation of each unit of the terminal pressure control support device 1b. The control unit 105b is executed by a device including a processor such as a CPU and a RAM, for example. By executing the program, the control unit 105b executes the information acquisition unit 108, the terminal pressure learning unit 109b, the terminal pressure estimation unit 110, the output unit 111, the terminal pressure estimation explanation unit 112, the estimation model update unit 113, and the screen generation unit 114. And functions as an algorithm determining unit 116.

  The terminal pressure learning unit 109b generates an estimation model using a plurality of machine learning algorithms recorded in advance by using each algorithm. For example, when a random forest algorithm, a decision tree algorithm, and a deep learning algorithm are recorded in the terminal pressure control support device 100b, the terminal pressure learning unit 109b uses an estimation model using a random forest algorithm and a decision tree algorithm. Then, an estimated model that has been used and an estimated model that uses deep learning are generated.

  Next, the terminal pressure learning unit 109b performs a simulation for calculating the estimation accuracy and the calculation speed by using the learning data for the generated estimation model. The terminal pressure learning unit 109b weights the estimation accuracy and the calculation speed for each machine learning algorithm based on the result of the simulation. In calculating the estimation accuracy, the end pressure learning unit 109b desirably divides the learning data and the evaluation data, but may calculate without dividing. Generally, it is said that the estimation accuracy is higher in the random forest than in the decision tree algorithm. On the other hand, the decision tree algorithm is easier for humans to understand than the random forest algorithm.

  The algorithm determining unit 116 acquires an algorithm determining condition from the determining condition storage unit 115. The algorithm determination unit 116 determines one estimation model from the plurality of estimation models generated by the terminal pressure learning unit 109b based on the algorithm determination conditions.

  For example, a case where the following condition is specified in the acquired algorithm determination condition will be described. As priorities, priority is given in order of estimation accuracy, ease of understanding, and calculation time. If the difference in the estimation accuracy between the algorithms is 0.05 or less as the same-rank deemed difference value, it is regarded as the same accuracy. As a constraint, it is assumed that the estimation accuracy is RMSE 0.15 [MPa] or less. These conditions are designated as algorithm determination conditions.

  A case where the following result is obtained by the simulation performed by the terminal pressure learning unit 109b will be described. The estimation accuracy of the random forest algorithm is RMSE 0.10 [MPa]. The estimation accuracy of the decision tree algorithm is RMSE 0.14 [MPa]. In this case, it can be seen that both algorithms satisfy the constraints of the algorithm determination condition. The priority of the algorithm determination condition has the highest estimation accuracy. Therefore, the algorithm determining unit 116 selects the random forest algorithm with the highest estimation accuracy. However, since the difference in RMSE indicating the estimation accuracy between the two algorithms is 0.04, the algorithm determination unit 116 determines that the estimation accuracy is the same. Considering the second priority, "easiness of understanding", the decision tree algorithm is superior to the random forest algorithm. Therefore, the algorithm determining unit 116 selects the decision tree algorithm as the machine learning algorithm.

  If no algorithm satisfies the constraint, the algorithm determination unit 116 selects a machine learning algorithm based on the algorithm determination condition excluding the constraint that cannot be satisfied. The terminal pressure estimation explanation section 112 generates explanation information indicating that the constraint cannot be satisfied. The terminal pressure estimation explanation unit 112 outputs the generated explanation information to the screen generation unit 114. The screen generation unit 114 generates screen information based on the explanation information, and notifies the user by displaying the screen information on the display unit 103.

  According to the terminal pressure control support device 1b configured as described above, the algorithm determination condition is given in advance to the determination condition storage unit 115, so that the algorithm determination unit 116 can estimate the estimation accuracy or calculation time from among a plurality of algorithms. In consideration of such factors, it is possible to select an algorithm that is highly explanatory and easy for humans to understand. The estimation result of the terminal pressure is estimated using an estimation model generated by an algorithm determined based on the algorithm determination conditions. Therefore, the user can further increase the degree of satisfaction with the estimation result and the estimation basis.

(Fourth embodiment)
Next, a water distribution system 100c according to a fourth embodiment will be described. FIG. 11 is a diagram illustrating a specific example of a system configuration of a water distribution system 100c according to the fourth embodiment. The water distribution system 100c differs from the first embodiment in that the water demand information of the customer 6 and the terminal pressure information from the permanent terminal pressure measuring device 7 are transmitted to the terminal pressure control support device 1c. The water demand information is information on the water demand of each customer 6. The water demand information is transmitted from a measuring instrument such as a smart meter installed in a customer house or the like. A plurality of permanent terminal pressure measuring devices 7 may be provided in the water distribution network 5. The first terminal is a place where the permanent terminal pressure measuring device 7 is provided. The first end is where the pressure is measured. The permanent terminal pressure measuring device 7 is an embodiment of a first pressure measuring device. Hereinafter, points different from the first embodiment will be described.

  Next, a terminal pressure control support device 1c according to a fourth embodiment will be described. FIG. 12 is a block diagram illustrating a specific example of a functional configuration of the terminal pressure control support device 1c according to the fourth embodiment. The terminal pressure control support device 1c in the fourth embodiment is different from the first embodiment in that a storage unit 104c and a control unit 105c are provided instead of the storage unit 104 and the control unit 105, but other configurations are the same. Is the same. Hereinafter, points different from the first embodiment will be described.

  The storage unit 104c stores various types of information used to provide support information to the monitoring control system 2. The storage unit 104c is configured using a storage device such as a magnetic hard disk device or a semiconductor storage device. The storage unit 104c includes a terminal pressure information storage unit 106c and a water distribution information storage unit 107c.

  The terminal pressure information storage unit 106c stores the terminal pressure information. The terminal pressure information in the fourth embodiment includes terminal pressure information obtained from the terminal pressure measuring device 4 and terminal pressure information obtained from the permanent terminal pressure measuring device 7. The water distribution information storage unit 107c stores water distribution information. The water distribution information in the fourth embodiment is information including water distribution station information, monitoring information, and water demand information.

  The control unit 105c controls the operation of each unit of the terminal pressure control support device 1c. The control unit 105c is executed by a device including a processor such as a CPU and a RAM, for example. By executing the program, the control unit 105c executes the information acquisition unit 108c, the terminal pressure learning unit 109c, the terminal pressure estimation unit 110c, the output unit 111, the terminal pressure estimation explanation unit 112, the estimation model update unit 113, and the screen generation unit 114. Function as

  The information acquisition unit 108c acquires various information used for providing support information. Specifically, the information acquisition unit 108c acquires water distribution station information from each water distribution station 3. The information acquisition unit 108c acquires monitoring information from the monitoring control system 2. The information acquisition unit 108c acquires terminal pressure information from each terminal pressure measuring device 4 and the permanent terminal pressure measuring device 7. The information acquisition unit 108c acquires water demand information from the customer 6. The information acquisition unit 108c records the acquired water distribution station information, monitoring information, and water demand information in the water distribution information storage unit 107c. The information acquisition unit 108c records the acquired terminal pressure information in the terminal pressure information storage unit 106c. The information obtaining unit 108c repeatedly obtains the water distribution station information, the monitoring information, the water demand information, and the terminal pressure information at a predetermined timing, thereby distributing the water distribution station information, the monitoring information, the water demand information, and the terminal pressure information to the terminal pressure information. The information is recorded in the storage unit 106c and the water distribution information storage unit 107c.

  The terminal pressure learning unit 109c converts the acquired water distribution information including the past water distribution station information, monitoring information, and water demand information and the past terminal pressure information obtained from the permanent terminal pressure measuring device 7 into explanatory variables, the terminal pressure measuring device. A terminal pressure estimation model is generated using the past terminal pressure information obtained from Step 4 as an objective variable.

  The terminal pressure estimating unit 110c is based on the obtained current water distribution station information, the distribution information including the monitoring information and the water demand information, the terminal pressure information obtained from the permanent terminal pressure measuring device 7, and the generated estimation model. , Estimate the current end pressure. The estimation target of the terminal pressure estimation unit 110c is a terminal pressure at a point where the permanent terminal pressure measurement device 7 is not provided (for example, a point where the terminal pressure measurement device 4 is provided). The terminal pressure estimating unit 110c records the estimated terminal pressure in the terminal pressure information storage unit 106c.

  FIG. 13 is a flowchart illustrating a flow of generating an estimation model of the terminal pressure control support device 1c according to the fourth embodiment. Steps S104 to S106 in FIG. 13 are the same as steps S104 to S106 in FIG.

  The information acquisition unit 108c receives the terminal pressure information from each terminal pressure measuring device 4, the terminal pressure information from the permanent terminal pressure measuring device 7, the water distribution plant information from each water distribution plant 3, the monitoring information from the monitoring control system 2, and the demand. Water demand information is acquired from the house 6 (step S301). The information acquisition unit 108c records the acquired terminal pressure information in the terminal pressure information storage unit 106c. The information acquisition unit 108c records the acquired water distribution station information, monitoring information, and water demand information in the water distribution information storage unit 107c. By repeatedly acquiring such information for a certain period, the terminal pressure control support device 1 accumulates terminal pressure information, water distribution station information, monitoring information, and water demand information (step S302).

  The terminal pressure learning unit 109c uses the past water distribution information stored in the water distribution information storage unit 107c and the past terminal pressure information of the permanent terminal pressure measurement device 7 stored in the terminal pressure information storage unit 106c as explanatory variables, Using the past terminal pressure information of the terminal pressure measuring device 4 stored in the information storage unit 106c as the target variable, an estimation model is generated by learning these relationships (step S303).

  FIG. 14 is a flowchart illustrating a flow of support information generation of the terminal pressure control support device 1 according to the fourth embodiment. Steps S204 and S205 in FIG. 12 are the same as steps S204 and S205 in FIG. The information acquisition unit 108c acquires current water distribution station information from each water distribution station 3 (step S401). The information acquisition unit 108c acquires the current monitoring information from the monitoring control system 2 (Step S402). The information acquisition unit 108c acquires the current terminal pressure information from the permanent terminal pressure measuring device 7 (Step S403). The information acquisition unit 108c acquires current water demand information from the customer 6 (Step S404). The terminal pressure estimating unit 110c estimates the current terminal pressure based on the estimation model generated by the terminal pressure learning unit 109c and the obtained water distribution station information, monitoring information, terminal pressure information, and water demand information (Step S405). .

  According to the terminal pressure control support device 1c configured as described above, the terminal pressure learning unit 109c includes the water demand information and the permanent terminal pressure measuring device 7 in addition to the water distribution station information, the monitoring information, and the terminal pressure information of the estimated point. An estimation model is generated based on the terminal pressure information obtained from Therefore, since the estimation model is generated based on more information, the terminal pressure estimating unit 110c can estimate the terminal pressure with higher accuracy.

Note that any machine learning technique may be used for learning the end pressure in the present embodiment. For example, a technique such as SVM (Support Vector Machine) or DL (Deep Learning) may be used.
In the above embodiments, the information acquisition unit, the terminal pressure learning unit, the terminal pressure estimation unit, the output unit, the terminal pressure estimation explanation unit, the estimation model update unit, the screen generation unit, and the algorithm determination unit are assumed to be software function units. May be a hardware function unit such as an LSI.

  In the present embodiment, the terminal pressure control support device 1 has been described as a single device, but may be configured as a plurality of devices. The terminal pressure control support device 1 may be configured by a cloud computing system.

  According to at least one embodiment described above, the terminal pressure can be estimated more accurately by having the terminal pressure learning unit 109, the terminal pressure estimation unit 110, and the terminal pressure estimation explanation unit 112.

  Although several embodiments of the present invention have been described, these embodiments are provided by way of example and are not intended to limit the scope of the invention. These embodiments can be implemented in other various 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 equivalents thereof.

1, 1a, 1b, 1c: Terminal pressure control support device, 2: Monitoring and control system, 3,3-1, 3-2: Water distribution station, 4,4-1, 4-2: Terminal pressure measuring device, 5: Distribution network, 6,6-1 to 6-3 ... Consumer, 7 ... Permanent terminal pressure measurement device, 100, 100c ... Distribution system, 101 ... Communication unit, 102 ... Input unit, 103 ... Display unit, 104 ... Storage Unit, 105: Control unit, 106: Terminal pressure information storage unit, 107: Water distribution information storage unit, 108, 108c: Information acquisition unit, 109109b, 109c: Terminal pressure learning unit, 110, 110c: Terminal pressure estimation unit, 111 ... output unit, 112, 112a ... terminal pressure estimation explanation unit, 113 ... estimation model update unit, 114 ... screen generation unit, 115 ... determination condition storage unit, 116 ... algorithm determination unit

Claims (12)

Water distribution information indicating an operation state of a distribution plant that distributes water to a distribution network, water monitoring information indicating a result of monitoring a distribution system that distributes water from the distribution network to a customer, and water demand indicating a water demand of the customer. An explanatory variable including at least one of information and first pressure information obtained from a first pressure measuring device permanently installed at a first end which is a place where pressure is measured in the distribution pipe network,
An estimation model for estimating the pressure at the second end where the pressure is estimated in the distribution network,
Comprising a terminal pressure estimating unit that estimates the pressure of the second terminal based on
The estimation model is obtained by performing machine learning based on the explanatory variable and second pressure information acquired from a second pressure measurement device temporarily provided at the second end,
Terminal pressure control support device. An estimation result indicating the pressure of the second terminal estimated based on the estimation model, and an estimation basis indicating the basis on which the estimation result was obtained, and an end pressure estimation explanation unit that generates explanation information including:
A display unit that displays the explanatory information on a display device,
The terminal pressure control support device according to claim 1. A model update unit that updates the estimation model based on a model update instruction that gives update information for updating the estimation model,
The terminal pressure control support device according to claim 2. The model update instruction is an instruction to update the estimation model without using at least one of the explanatory variables used to generate the estimation model.
The terminal pressure control support device according to claim 3. An algorithm determination unit that determines an algorithm of machine learning that generates the estimation model based on an algorithm determination condition that represents a condition for determining machine learning used to generate the estimation model,
The terminal pressure control support device according to any one of claims 1 to 4. The terminal pressure estimation explanation section, when receiving a predetermined input for the estimation result included in the explanation information displayed on the display device, highlights and displays a screen corresponding to the estimation basis from which the previous estimation result was obtained. Generate descriptive information,
The terminal pressure control support device according to any one of claims 2 to 4. The explanatory information further includes a map of the water distribution network,
The terminal pressure estimation explanation unit, the water distribution station information, the monitoring information, the first pressure information and a symbol associated with the estimation result of the pressure of the second terminal, based on the position information of the symbol, the Generating explanatory information to be displayed on a map and receiving a predetermined input for the estimation result, the value of the explanatory variable when the estimation result is obtained is displayed so as to accompany the symbol on the map. And further generating explanatory information that highlights and displays the value of the symbol and the explanatory variable corresponding to the estimated basis.
The terminal pressure control support device according to any one of claims 2 to 4. The terminal pressure estimation explanation unit generates explanation information to be displayed on the map together with a connection state between a node of the water distribution network and a pipeline on the map,
The terminal pressure control support device according to claim 7. The water distribution station information is information indicating a value of a discharge flow rate and a discharge pressure of a water supply station or a water distribution station,
The terminal pressure control support device according to any one of claims 1 to 8. The monitoring information is information indicating at least one value of the valve opening, the flow rate or the pressure,
The terminal pressure control support device according to any one of claims 1 to 9. Terminal pressure control device, distribution plant information indicating the operation state of the distribution plant that distributes water to the distribution network, monitoring information indicating the result of monitoring the distribution system that distributes water to the customer from the distribution network, and water of the customer At least one of water demand information representing a demand amount and first pressure information obtained from a first pressure measuring device permanently installed at a first end which is a place where pressure is measured in the distribution pipe network. An explanatory variable that includes a terminal pressure estimating step of estimating the pressure of the second terminal based on an estimation model for estimating the pressure of the second terminal that is a place where the pressure is estimated in the distribution pipe network,
The estimation model is obtained by performing machine learning based on the explanatory variable and second pressure information acquired from a second pressure measurement device temporarily provided at the second end,
Terminal pressure control support method.   A computer program for causing a computer to function as the terminal pressure control support device according to any one of claims 1 to 10.

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