Water distribution network monitoring method and system

Abstract

The disclosure relates to a water distribution network monitoring method and system. A water distribution network monitoring method comprises the steps of: receiving a multivariate time series of consumption measurements, the consumption measurements obtained from metering devices in a water distribution network and each consumption measurement comprising a consumption representation and a timestamp; establishing a system of linear equations on the basis of the consumption measurements; processing the system of linear equations on the basis of a solver to obtain an error estimate comprising a consumption error estimate associated with one or more of the metering devices in said water distribution network and / or a leakage estimate. A monitoring system and computer programs arranged to carry out the method are also disclosed.

Description

WATER DISTRIBUTION NETWORK MONITORING METHOD AND SYSTEMField of the invention

[0001] The present invention relates to monitoring of water distribution networks.Background of the invention

[0002] Water distribution networks, understood as pipe networks distributing waterfrom points of production or storage to points of consumption, typically comprisemetering devices at the point of production or storage to document the total amount ofwater supplied to the network, and metering devices at each point of consumption formonitoring consumption or billing the consumers according to their consumption.

[0003] A water distribution network is understood as pipe networks distributingpotable water from waterworks or water storage facilities to points of consumption,such as private houses or industrial or commercial establishments. Water distributionnetworks typically comprise metering devices at the waterworks or other supply pointsto document the total water supplied to the network, and metering devices at each pointof consumption for billing the consumers according to their consumption.

[0004] Minor leakages in the pipe network between a point of production or storageand the consumption points are typically only detected by visual inspection. Majorleakages may be indicated by the metering devices running wild, but locating theleakage requires visual inspection, sometimes throughout a huge geographical area.

[0005] Metering devices used for consumer billing are typically required byregulation to be calibrated at regular intervals to ensure correct billing. Although themetering devices are typically capable of automated remote reading for billingpurposes, the calibration may, on the other hand, be quite cumbersome and expensiveas it typically requires visiting the physical metering devices and possibly dismountingthem from the network, calibrating them, and then possibly mounting them again. Ifmetering devices are found to have an unacceptable measurement error larger than e.g.a maximum permissible error, then the metering device must either be replaced, or theerror must be eliminated such as via some form of adjustment of the metering device.Alternatively, it has been known to implement redundant metering devices or meteringdevice parts for mutual verification, also sometimes referred to as permanentperformance monitoring. Summary of the invention

[0006] The inventors have identified the above-mentioned problems and challengesrelated to water distribution networks and have developed the invention andembodiments described below in relation to detection and possible localization offaults in the water distribution network, such as leakages, and / or detection and possiblelocalization of metering devices that do not measure within the allowed tolerances.

[0007] In an aspect, the invention relates to a water distribution network monitoringmethod comprising the steps of: receiving a multivariate time series of consumptionmeasurements, the consumption measurements obtained from metering devices in a water distribution network and each consumption measurement comprising aconsumption representation and a timestamp; establishing a system of linear equationson the basis of said consumption measurements; processing said system of linearequations on the basis of a solver to obtain an error estimate comprising a consumption error estimate associated with one or more of said metering devices in said water distribution network and / or a leakage estimate.

[0008] A water distribution network monitoring method according to the inventionmay in various embodiments make it possible to directly estimate the consumption measurement error of one or more metering devices in a water distribution network and / or estimate leakages in the water distribution network by directly solving a system of linear equations on the basis of a multivariate time series of consumption measurements as measured by the metering devices in the water distribution network. This provides the advantage of being able to directly obtain a consumption error estimate for one or more of the metering devices in the water distribution network and thereby account for consumption error estimates when considering e.g. thereplacement or repair of metering devices or billing of consumers.

[0009] A water distribution network monitoring method according to the inventionmay in various embodiments make it possible to detect leakages and / or consumption measurement errors in a water distribution network by using existing sensor infrastructure. The existing sensor infrastructure may be in the form of metering devices which may already be installed in the water distribution network before the water distribution network monitoring system disclosed by the invention is implemented. Utilizing meter readings from installed metering devices offers several advantages such as reduced cost compared to other monitoring systems, which mayrequire that new or additional sensors be installed to cover the entire water distributionnetwork.

[0010] The error estimate may in some embodiments comprise information about thetype of network fault detected or localized in the water distribution network by the water distribution network monitoring system or water distribution network monitoring method. Information about the type of network fault is important when making decisions about what actions should be taken to mitigate or rectify the network fault. A leakage estimate may for example require immediate attention whereas a measurement error may be tolerable under certain circumstances or not require immediate action.

[0011] The water distribution network monitoring system or water distributionnetwork monitoring method provides an error estimate comprising a magnitude of the network fault, which is understood to be a quantifiable measure of the error caused by the network fault in the form of a consumption error estimate or a leakage estimate. The leakage estimate may be formulated as e.g. the volume of water lost to a water leakage from the point in time at which the leak was detected by the fault detector, or the volume flow rate of the leakage. The consumption error estimate may be formulated as the absolute error in volume per unit time indicated by consumption measurements provided by a metering device with a measurement error, or for example as an error percentage or factor. The error estimate therefore indicates the severity of the error and may be used to decide how quickly the network fault must be repaired or mitigated. It may further be used to select an appropriate solution such aspossibly disregarding consumption measurements from a metering device if redundant metering devices are available or applying a correction to the consumption measurements to account for or mitigate the measurement error.

[0012] A water distribution network monitoring method according to the inventionmay in various embodiments be able to detect the existence of leakages, including smaller leakages, with greater certainty than hitherto feasible by providing a leakage estimate obtained by solving a system of linear equations established on the basis of a multivariate time series of consumption measurements.

[0013] According to various embodiments of the invention, the system may furtherdetermine estimated leakage locations of detected leakages as part of the leakage estimate. Thereby more reliable indication of leakages may be achieved sooner, enabling earlier and informed dispatch of response teams or service technicians to impede and repair the leakage. Sooner detection and localization of major leakages may save huge amounts of water, protecting the environment and saving costs. Detection and localization of minor leakages that would otherwise not be detected for, sometimes, years, may also save huge amounts of water, and enable early repair to avoid developing into major leakages.

[0014] A water distribution network monitoring method according to the inventionmay in various embodiments be able to detect the existence of erroneous metering devices not measuring within allowed tolerances, i.e. having a consumption error estimate that is numerically larger than a maximum permissible error. According to various embodiments of the invention, the system may further determine estimated error locations of detected erroneous metering devices. Thereby a permanent errormonitoring may be achieved, possibly reducing the need for physical visit andcalibration to only such metering devices that have been indicated by the system as probable error causes. Furthermore, a measurement error of a metering deviceestimated by the present invention as a consumption error estimate represents meteringdevice behavior in an actual use in an actual installation, e.g. influenced by actual temperatures, pressure and consumption pattern, contrary to a calibration performed, e.g., at manufacture.

[0015] Generally, advantages may be obtained by the present invention for waterdistribution networks that can be modeled as having one or more parent node(s) with metering devices, such as a main meter at the waterworks, or a zone meter for each geographic or administrative zone that the water distribution network is divided into, as well as downstream metering devices at the leaf nodes, i.e. consumers, such as houses, commercial buildings, factories etc.

[0016] Improved or further advantages and technical effects may generally beachieved by one or more of increasing the frequency of consumption measurements, increasing the accuracy of time synchronization between meters, and increasing thenumber of metered pipe forks, i.e. joints or nodes that have a metering device mountedto meter all downstream consumption.

[0017] A water distribution network monitoring method according to the inventionmay in various alternative embodiments be able to exploit predictable water consumption patterns of e.g. consumers and commercial establishments such as factories or restaurants. Water consumption may follow a 24-hour pattern which can be used to establish a typical consumption pattern for the end consumer. A typical consumption pattern may describe average demand over a 24-hour period. Consumption patterns may be employed to identify when a significant deviation from these typical consumption patterns occurs. Consumption patterns may also be used to predict or estimate when water consumption is zero. According to various embodiments of the invention, the water distribution network monitoring system may use this information to simplify the system of linear equations established on the basis of said multivariate time series of consumption measurements and thereby confine the fault search to a smaller part of the distribution network.

[0018] A water distribution network monitoring method according to the inventionmay exploit the trend of the increasing frequency of availability of water consumption measurements from water metering devices. In the past, a water consumption measurement may only have been provided from a water metering device on e.g. a monthly or yearly basis. The trend is that water metering devices provide water consumption measurements at increasing frequency such as daily or hourlymeasurements. The increased measurement frequency of water metering devices or other types of metering devices may be exploited by the water distribution network monitoring method to provide a faster identification of consumption measurement error and / or leakages in the form of a consumption error estimate and a leakage estimate respectively.

[0019] A water distribution network is understood as a physical system that suppliesand distributes water to various points such as points of consumption or storage. A water distribution network typically comprises distinct areas such as the main network which transports large amounts of water from points of production or storage to the branching network of pipes which further distributes water to e.g. its point of consumption. The part of the water distribution network that distributes water to the end consumer may often be considered as a sub-network of the water distribution network. The sub-network may often be described as having a tree structure with branching paths constituted by pipes supplying water to e.g. its point of consumption.

[0020] The water distribution network typically comprises different interconnectedcomponents such as tanks, reservoirs, valves, pumps, and pipes. The water distribution network typically has a sensor infrastructure in the form of metering devices which measure the quantity of water flowing through e.g. the pipes, an inlet or from a storage point such as a tank. A water distribution network may have one water inlet such as e.g. from a water treatment plant, or it may have multiple water inlets from different sources. A sub-network of a water distribution network can be understood as being a water distribution network in and of itself. Thus, the sub-network of a larger water distribution network is also a water distribution network.

[0021] A metering device is understood as a physical instrument for measuring thequantity of water passing through a pipe or other outlet. A metering device is a consumption meter that provides comparable consumption measurements that comprise at least a consumption representation and a timestamp. Consumption representations are comparable because they obey an appropriate conservation principle such as e.g. conservation of mass and are therefore suitable for direct comparison such as between consumption representations provided by differentmetering devices. A consumption meter may provide a consumption representation given in physical units of e.g. volume in cubic meter m3or flow in liters per hour. A metering device may be mounted at many different points in the water distribution network such as in the main pipe, at the water inlet, in meter wells strategically positioned in the pipe network such as where the network branches, or in the pipe network of a residential or commercial building or a factory. A metering device may measure the water flow according to different measurement principles such as positive displacement or velocity.

[0022] Metering devices using different technologies to measure the water flow aretypically labeled accordingly, such as e.g. electromagnetic flow meter, multi-jet flow meter, turbine flow meter, or ultrasonic flow meter. The technology used or physical quantity measured by the metering device does not limit the functionality of the water distribution monitoring method according to the present invention. Further, a water distribution network can have a mix of metering devices of several different models and even several different metering technologies, which can also be handled by the water distribution monitoring method according to the invention.

[0023] A metering device according to the present invention has some means bywhich a consumption measurement may be provided. Communication means of the metering device may be in the form of a cable connection or wireless communicationmeans whereby the metering device may comprise a wireless communication module.

[0024] Metering devices of the water distribution network may advantageously beconsumption meters which provide consumption representations that obey a principle of conservation such as e.g. conservation of mass. Consumption representationsprovided by different consumption meters must therefore be comparable in situationswhere the appropriate principle of conservation applies. The physical quantity provided in the consumption representation may be obtained via an appropriate form of normalization such as e.g. normalizing a measured water volume to account for volume differences caused by variations in temperature and pressure.

[0025] Metering devices with a wireless communication module confer severalbenefits such as reduced installation cost and flexibility in terms of install location. Metering devices may transmit consumption measurements and other data using automated meter reading AMR systems, for example using Wireless M-BUS or proprietary metering protocols, or using standard wireless technologies such as Wi-Fi, mobile cellular network 4G or 5G, LoRaWAN, Bluetooth or ZigBee. The consumption measurements may be received directly from the metering devices, through concentrators, or from a meter reading system backend. The water distribution networkmonitoring system or water distribution network monitoring method may in turninquire or control the operation of the metering devices using the same wireless communication technology.

[0026] Consumption measurements received from a plurality of metering devicesinstalled in a water distribution network are termed a multivariate time series of consumption measurements when these consumption measurements are measured across a span of time. Each of the multiple variables considered are the consumption measurements originating from each of the metering devices respectively and as these consumption measurements comprise both a consumption representation and a timestamp, each metering device therefore provides a time series of consumption measurements which when combined with consumption measurements obtained from other metering devices together constitute a multivariate time series of consumption measurements.

[0027] The multivariate time series of consumption measurements may havecomparable timestamps and sample frequencies. That is to say the consumption measurements obtained from different metering devices are comparable both in terms of being synchronized in time and being supplied at the same sample rate.

[0028] The multivariate time series of consumption measurements may also bemixed-frequency and / or the sample rate of different metering devices may be different such that a conversion of the multivariate time series of consumption measurements may be necessary before the system of linear equations can be established. Thisconversion may for example involve interpolation, downsampling, or synchronization of timestamps.

[0029] A consumption measurement is understood to be a measurement of a physicalquantity of typically volume or flow of water through a pipe or other outlet performed by a metering device in a water distribution network, wherein the consumption measurement comprises a consumption representation and a timestamp.

[0030] The consumption measurement is represented as binary digits represented bya number of bytes suitable for storage and processing on digital computer systems. The physical quantity denoted by the consumption measurement is termed the consumption representation of said consumption measurement. A consumption measurement may comprise several consumption representations, such as volume flow rate, accumulated volume, volume difference, etc. The consumption measurement additionally comprises a timestamp, preferably indicating the time at which the measuring was performed by the metering device. The consumption measurement comprises at least one timestamp, such as measurement time, transmission time, etc.

[0031] A system of linear equations may be established by considering therelationship between consumption measurements obtained from different metering devices in the water distribution network. This relationship can for example be understood as a subtree of a tree structure which models e.g. a pipe network of the water distribution network. At the level of the subtree, a set of consumption measurements may be provided at a given time. Subsequently, an additional set of consumption measurements may be provided such that the two sets of measurements constitute a system of two linear equations. Further sets of consumption measurements each constitute an additional linear equation which may be added to the system of linear equations. The system of linear equations may thus be extended with additional equations by considering additional measurements with consecutive timestamps.

[0032] A solution to the system of linear equations may be provided by applying asuitable solution strategy or algorithm such as an analytical method for solving linearequations e.g. Gauss-Jordan elimination or any number of different numerical methods for obtaining an approximate solution such as ordinary least squares.

[0033] A solver is understood in the context of the present invention as a softwarewhich is configured for providing a solution a system of linear equations. Solution is not understood as comprising only exact solutions but may also include various estimates which can be obtained using solvers that implement numerical methods for finding approximate solutions to systems of linear equations.

[0034] Error estimate in the context of the present invention is understood as anestimate of errors which is obtained by solving a system of linear equations established on the basis of a multivariate time series of consumption measurements. The error estimate is an estimation of different errors which may be observed in a water distribution network. The error estimate is obtained directly as a solution or approximate solution from the system of linear equations which is obtained by using a solver.

[0035] Consumption error estimate in the context of the present invention isunderstood to be an estimate of the measurement error of one or more metering devices installed in a water distribution network. The presence of measurement errors of one or more metering devices may cause consumers to be overbilled or underbilled for their consumption thus motivating a timely correction of such errors. Examples of overbilling or underbilling are seen in e.g. water distribution networks where water metering devices may be prone to measurement errors.

[0036] The consumption error estimate which is obtained according to the inventionmay be considered to be constant for the span of time during which the consumption measurements used to compute it were obtained. However, as the actual measurement error of metering devices may vary with respect to time, the consumption error estimate is typically provided at fixed intervals such that it can be updated and properly accounted for in the water distribution network i.e. by repairing or replacing metering devices for which a measurement error is indicated via the consumption error estimate obtained through the method.

[0037] The consumption error estimate is obtained as a digital value suitable forstoring on a computer and is typically expressed as a quantifiable measure of the measurement error e.g. in terms of a percentage of error or in absolute terms as a volume or flow.

[0038] A leakage estimate is understood in the context of the present invention to bea numerical estimate of a leakage which is understood to be a type of fault in the water distribution network which causes water to be lost to leaks in e.g. the pipe network of the water distribution network. A leakage may be caused by many different factors such as corroded, cracked, or ruptured pipes; broken or loose pipe connections; or cracks in reservoirs or tanks. Water lost through a leakage is essentially wasted since it can typically not be used for its intended purpose. A related network fault is accidental or unintended water consumption, that technically is not due to a leak, but rather due to human error or controller error of forgetting to close a valve or the like, such as a garden hose, swimming pool supply or a valve at a factory.

[0039] In an embodiment, said system of linear equations is established byconsidering the physical principle of conservation of mass and / or mass flow rate.

[0040] Applying the principle of conservation of mass and / or mass flow rate to thewater distribution network provides a method for relating the consumption measurements obtained from different metering devices in the water distributionnetwork. For substantially incompressible fluids such as water, the mass conservationprinciple may be equally true for conservation of volume and / or volumetric flow rate. Thereby the principle can be applied to determine inconsistencies related to consumption measurements based on any of mass or volume, e.g. weighing metering devices or volumetric flow rate metering devices. Due to the conservation principle, the flow into and out of a pipe must be equal in the absence of any branching of thepipe network or loss of water. For example, for an incompressible fluid, the volume offluid into and out of a pipe must be the same. Any violation of this principle may indicate a network fault. Thus, equations relating the flows or volumes into and out of pipes may be established using this principle, and further consumption measurements taken at subsequent measurement times can be used to establish additional equationstogether constituting the system of linear equations from which an error estimate comprising a consumption error estimate and / or a leakage estimate may be obtained.

[0041] In an embodiment, said consumption measurements are assigned to acomputer model comprising a plurality of nodes linked by edges in a tree structure representing a pipe network of the water distribution network.

[0042] A computer model of a physical water distribution network is understood tobe a digital representation and mapping of the structure of the pipe network of a physical water distribution network. The digital representation is comprised of a plurality of nodes linked by edges in a tree structure. The tree structure may be implemented in a computer in different ways such as some form of linked data structure. The computer model may simplify certain structural aspects of the water distribution network to emphasize the most important aspects of the network structure and to simplify the processing of consumption measurements and the determination of network faults. Mapping the structure of the pipe network and metering devices to the computer model requires that the structure of the water distribution network is known beforehand, such that the tree structure of the computer model can be established. The structure of the water distribution network may e.g. be derived from technical drawings or files or from an existing software program which provides the necessary details for building the computer model. The digital representation of the structure of the water distribution network may be established via e.g. manual input of data, or the process may be automated such as by importing the relevant data into the computer model and subsequently generating a suitable digital representation.

[0043] A tree structure is understood to be an abstract data type defining ahierarchical relationship between nodes connected via edges. The tree structure may thus define a network, and in the present invention is used to map the physical water distribution network onto a digital representation in a computer model. The tree structure contains a root node. All nodes in the tree structure, except for the root node at the root of the tree, have a parent node. Every node is connected by an edge from exactly one other node in the direction from parent node to child node. Each node can have an arbitrary number of child nodes but only one parent node. In cases where thestructure of the water distribution network motivates a mapping of child nodes with multiple parent nodes, these multiple parent nodes may be combined as a single parent node. Nodes with no child nodes are called leaves or external nodes. Nodes may be assigned a level in the tree structure according to the number of edges between the node and the root node. The root node has level zero. It is emphasized that a computer model according to the invention may represent the tree structure in any suitable way, such as a simple list, as relational database records, as linked classes, as a dedicated tree structure data type, as an array, etc. The notation of tree structure, nodes and edges are here used for explanatory purposes and may programmatically be implemented in any suitable way from which such a tree structure representation can be derived. It is noted that a physical water distribution network may have some nodes connected in a way that does not strictly resemble a tree structure. In such a system, those nodes maybe considered together as a single node in the tree structure of the computer model, orthe non-tree links between nodes may be disregarded, for example when physically closed, or be mapped into the computer model and processed by the fault detector as auxiliary data, for example associated with one of the tree structure nodes.

[0044] According to the present invention, the nodes may represent various locationsin the physical water distribution network. A node may e.g. represent the location of a metering device in the water distribution network. In such cases, the node is referred to as a metered consumption node indicating that it represents a point in the water distribution network at which consumption measurements are provided via meter readings performed by a metering device. A node in the tree structure may also represent a point at which a branch exists in the pipe network of the water distributionnetwork. A node may thus e.g. be used to map a larger pipe from which multiplesmaller pipes branch off. Sometimes a metering device will be located at such a location, for example in a meter well or meter box, thereby also making that node a metered consumption node. A node may also represent a termination of the water distribution network such as at a residential or commercial consumer or at any otherpoint of consumption. Such nodes may typically also be metered consumption nodes.Edges of the tree structure denote how the nodes are connected. In terms of the waterdistribution network, the edges may be thought of as representing the ways in whichwater may flow between different parts of the water distribution network. In some cases, edges may simply model a pipe and in other cases they may model multiple pipes. The edges need not represent the length or geographic course of the physicalpipes, but should preferably represent which nodes are connected by pipes.

[0045] The tree structure may advantageously be implemented as a hierarchical datastructure in the computer model of the water distribution network monitoring system or water distribution network monitoring method. The topmost element of the data structure represents the root node and nodes of the tree may be accessed via indexing. The data structure may represent the relationship between nodes by using e.g. pointers to represent edges and relations between parent and child nodes. The data structure may also be searched efficiently such as when certain parts of the tree structure must be analyzed due to a detected inconsistency between two or more nodes.

[0046] The tree structure may have a simple implementation whereby the structureis implicitly inferred from a table of values in e.g. a file stored on the computer hardware on which the water distribution network monitoring system runs. The values may be accessed and updated accordingly such as when consumption measurements are provided by metering devices. Data included in the table may include information that specifies node identifiers in addition to the relationship between parent nodes and child nodes. The table may also be used to record the indication of network faults or quantities associated with network faults such as measurement errors associated with specific nodes or the magnitude of a leakage.

[0047] A database may contain data entries which specify the tree structure of thecomputer model. The database may contain entries which specify the relationship between parent nodes and child nodes in addition to data entries for consumption measurements. The database may also contain data entries related to the indication of network faults such as measurement errors and magnitude of leakages.

[0048] A pipe network of the water distribution network is understood to be thenetwork of physical pipes through which water is transported and distributedthroughout the water distribution network. The pipe network may include pipes ofmany different diameters and pipes made from many different materials such as galvanized steel, stainless steel, iron, copper, and polyvinyl chloride.

[0049] In an embodiment, said consumption measurements are assigned to variables,and wherein each variable corresponds to a subset of consumption measurements.

[0050] The multivariate time series of consumption measurements can be understoodas comprising measurements of multiple variables across time wherein each variable corresponds to a subset of consumption measurements wherein the subset of consumption measurements are those consumption measurements obtained from asingle metering device. Each variable thus represents e.g. a flow or volume asmeasured by a metering device at a particular physical location in the water distribution network.

[0051] In an embodiment, a unit of measurement of said consumption representationis a volume or a volume flow rate.

[0052] A volume representation provides less precise network fault detection ascompared to flow representations. However, the requirements for time synchronization for consumption measurements from different metering devices are not as strict due to the slower dynamics of volume measurements as compared to flow measurements.

[0053] A flow representation may be used to accurately disregard instantaneousconsumption measurements that are sufficiently close to zero to simplify the networkfault analysis. However, flow representations require adequate time synchronizationbetween the timestamps of consumption measurements from different meteringdevices. If the time synchronization of meter readings performed by different metering devices is not precise enough to reflect the dynamics of changing water flows, then consumption measurements from different metering devices cannot be readily compared for analysis without applying some form of correction to account for the time difference.

[0054] In an embodiment, a unit of measurement of said consumption representationis a mass or a mass flow rate.

[0055] Consumption representations may advantageously be provided in a unit ofmeasurement which is suitable for computations such as a mass or mass flow rate.

[0056] In an embodiment, said water distribution network monitoring methodcomprises a step of converting said consumption representation from a first unit of measurement to a second unit of measurement.

[0057] It may be advantageous that, before establishing the system of linearequations on the basis of the multivariate time series of consumption measurements, the provided consumption measurements are converted from a first unit of measurement such as a volume flow to a second unit of measurement such as a volume. The conversion may for example be obtained by implementing any suitable algorithm for the conversion of units such as a numerical integrator for converting measurements of volume flow into an accumulated volume.

[0058] In an embodiment, said method further comprises a step of determining aninconsistency related to said consumption measurements.

[0059] An inconsistency related to the consumption measurements is understood asa state where the received consumption measurements do not obey the principle of conservation of mass or mass flow rate. This indicates that something is wrong, andfurther analysis may lead to the kind of error via obtaining the error estimatecomprising a consumption error estimate and / or a leakage estimate.

[0060] In an embodiment, one or more of said consumption measurements are zeroedwhen said one or more consumption measurements attain a numerical value within a predetermined interval.

[0061] A consumption measurement may indicate that no amount of or a negligibleamount of water is flowing through the part of the water distribution network which ismetered by the metering device providing the consumption measurement such that the given consumption measurement can be zeroed i.e. assumed to be zero. A negligible amount of water is understood to be an amount of water which is smaller than a predetermined flow or volume of water that is considered so close to zero as to benegligible such as a flow or volume of water that is within a predetermined interval. Zeroing may be used to simplify the system of equations obtained by relating the flows or volumes of water into and out of pipes of the water distribution network. This can be done by eliminating the term associated with the metering device with which the consumption measurement is associated. Assumptions may in some cases need to be made about the presence or absence of a measurement error associated with the metering device which provided the zeroed consumption measurement. For example, it may be possible that a measurement error is only present when a substantial water flow or volume is measured, such that the absence of a measurement error may be assumed when processing consumption measurements which have been zeroed.

[0062] The measurement error of some metering devices may advantageously beknown in advance and can therefore possibly be zeroed if the consumption measurements fall within a predetermined interval before any processing of consumption measurements takes place. This situation may e.g. be obtained when ametering device has recently been calibrated or otherwise checked to make sure that itprovides an appropriately accurate consumption measurement with a measurement error that can be estimated as a consumption error estimate with a numerical value that is within a predetermined interval. A metering device which is known to provide a consumption measurement with a measurement error that is smaller than for example a maximum permissible error can be used to simplify the processing of consumption measurements in a system of linear equations, such that a consumption error estimate or leakage estimate may be more easily obtained.

[0063] In an embodiment, the endpoints of said predetermined interval is a maximumpermissible error.

[0064] According to various embodiments, not all error estimates determined by thewater distribution network monitoring method are necessarily representative of unacceptable measurement error or leakage. In practice, metering devices cannot be adjusted to zero error, so they are typically calibrated before installation, and if necessary, adjusted to achieve a measurement error within a predetermined, acceptable range, also referred to as a maximum permissible error, for example set by relevantindustry regulation. As the metering devices and therefore the consumption measurements processed by the water distribution network monitoring method thus inherently possess a variation of acceptable errors, this may be taken into account by the water distribution network monitoring method to establish the endpoints of the predetermined interval to be the maximum permissible error within which the consumption representation of a consumption measurement may be assumed to be zero.

[0065] In an embodiment, said consumption measurements each have apredetermined measurement uncertainty.

[0066] The measurement uncertainty of a consumption representation may in analternative embodiment be continuously estimated via a statistical measure such as a standard deviation by the water distribution network monitoring method. The measurement uncertainty may also be estimated as a random variable and thus continuously be subtracted from the consumption representation.

[0067] In an embodiment, said consumption measurements are synchronized in timeacross variables of said multivariate time series.

[0068] Ensuring an adequate level of time synchronization between consumptionmeasurements from different metering devices is a prerequisite for obtaining anaccurate error estimate based on provided consumption measurements. Time synchronization accuracy is relatively more important when consumption representations are provided as flow representations than volume representations due to the difference in frequency content. Time synchronization is relevant between two or more metering devices for processing their consumption measurements together in a system of linear equations to determine an error estimate comprising a consumption error estimate and / or a leakage estimate, and / or between recent and previous consumption measurements from the same metering device i.e. when these are employed in different equations of the system of linear equations established on the basis of said consumption measurements.

[0069] In an embodiment, said consumption measurements comprise timestamps atsubstantially equal measurement times.

[0070] Metering devices may advantageously provide meter readings for example atfixed hours, or at fixed intervals. A plurality of metering devices in the water distribution network may advantageously provide consumption measurements according to the same measurement time schedule.

[0071] In an embodiment, said metering devices comprise adjustable clocks.

[0072] Adjustable clocks are a prerequisite for being able to synchronize the clocksof different metering devices and thereby obtain a desired precision of time synchronization across the metering devices of the water distribution network. Clock synchronization may be supplied locally to individual metering devices through for example an optical, NFC, or USB connection or via buttons. For metering devices with bidirectional communication capabilities, the clock synchronization may be performedvia a synchronization signal from a time server or a master metering device.

[0073] In an embodiment, said adjustable clocks are synchronized in time across saidmetering devices.

[0074] The water distribution network monitoring method may advantageously bethe supplier of a clock synchronization signal which is communicated to metering devices to establish the precision of time synchronization necessary for comparing consumption measurements from different metering devices.

[0075] In an embodiment, said method comprises a step of synchronizing saidconsumption measurements in time to compensate for unsynchronized clocks of said metering devices.

[0076] If the metering devices cannot be synchronized, e.g. due to having non-adjustable clocks, it may be possible to compensate if knowledge of the individual meters’ clocks can be obtained, e.g. by requesting and comparing time information from the individual meters, or by knowledge of the programmed transmission times compared to the actually experienced transmission times, or by transmissionsincluding both measurement times and transmission times, and adjusting measurement times according to the difference between transmission time and reception time. Using such knowledge at the receiver end to compensate timestamps and / or consumption values, the consumption measurement timestamps from different meters may become comparable.

[0077] In an embodiment, said metering devices provide consumption measurementswhich are synchronized in time to within an interval between 0.05 % and 2.5 % of nominal time between said consumption measurements.

[0078] The precision required by the time synchronization of different meteringdevices may advantageously be quantified by an interval such as between 0.05% and 2.5% of nominal time between meter readings.

[0079] In an embodiment, a sample frequency of said consumption measurements isvariable.

[0080] Metering devices may have an adjustable sampling frequency such that thetime interval between meter readings can be adjusted according to need. If for example the flow measured by a metering device can be assumed constant for a certain time interval, the sampling rate may be adjusted to match this assumption. Same considerations apply to situations where the flow may be assumed to be highly dynamic such that a higher sampling frequency is desirable.

[0081] In an embodiment, said method further comprises a step of indicating ageographical location in said water distribution network associated with said error estimate.

[0082] Specifying an exact or approximate geographical location of a leakage orfaulty metering devices is advantageous in terms of dispatching the relevant personneland tools, such as service technicians and excavators, to the correct site of the network fault. This avoids a time-consuming search and possibly expensive digging or measurements being performed at the wrong place instead of near or at the actual location of the network fault in the water distribution network.

[0083] Indication of a geographical location with respect to the water distributionnetwork is possible due to the layout of the water distribution network being known and furthermore to the locations of one or more metering devices being known. Ametering device exhibiting a measurement error as determined by obtaining aconsumption error estimate can thus be located due to the determined consumption error estimate being associated with one or more specific metering devices in the water distribution network.

[0084] In an embodiment, said method further comprises a step of determining aninconsistency between two or more of said metering devices in said water distribution network.

[0085] Inconsistencies between metering devices may be established by the waterdistribution network monitoring method by comparing appropriate consumption measurements obtained from different metering devices such as when two metering devices are placed at points in the water distribution network where they measure the same or similar physical quantity such as a water flow in a particular pipe.

[0086] In an embodiment, said system of linear equations is established on the basisof a statistical measure of said consumption measurements.

[0087] In some situations it may be advantageous to establish a statistical measuresuch as an average of said consumption measurements. This may for example be employed in situations where the signal to noise ratio is not favorable or where a sufficiently high sample rate can be achieved such that the physical quantity which is measured by the metering device can be considered to be constant.

[0088] In an embodiment, said system of linear equations is inhomogeneous.

[0089] The system of linear equations established on the basis of said consumptionmeasurements may advantageously be inhomogeneous. An inhomogeneous system of linear equations may for example be obtained when consumption measurements from some metering devices are assumed to have a measurement error that is numericallysmaller than a predetermined maximum permissible error. Such assumptions may simplify the system of linear equations in such a way that it becomes inhomogeneous.

[0090] In an embodiment, said system of linear equations is overdetermined.

[0091] It may be advantageous that the system of linear equations consists of moreequations than there are unknowns. This may for example happen when the number of consumption measurements provided from each metering device is larger than the total number of metering devices in the water distribution network for which an error estimate is sought. The system of linear equations being overdetermined maynecessitate the use of particular solvers such as the method of ordinary least squares.

[0092] In an embodiment, said solver is an algorithm implemented on a dataprocessor.

[0093] The solver may advantageously be an algorithm implemented on a dataprocessor such that provided consumption measurements can be automatically processed by the algorithm which provides an error estimate comprising a consumption error estimate and / or a leakage estimate.

[0094] In an embodiment, said solver implements a numerical method for solving asystem of linear equations.

[0095] The solver may advantageously implement a numerical method for solvinglinear equations such as an iterative method such as the Jacobi or Gauss Siedel method or a method using particular matrix operations such as LU decomposition. A numerical method has some advantages in that it may be used to find an approximate solution or may exploit the particular structure of the system of linear equations to arrive at a solution in fewer computational steps.

[0096] In an embodiment, said solver implements an analytical method for solvingsaid system of linear equations.

[0097] For some systems of linear equations, it may be desirable to employ analyticalmethods which provide an exact analytical solution to the system of linear equations.Analytical methods may be employed in certain cases where the structure of the system of linear equations is such that analytical methods are particularly advisable such as when the number of equations is small or when an exact solution can be found.

[0098] In an embodiment, said solver is an optimization algorithm.

[0099] The solver may implement an optimization algorithm wherein a numericalsolution to the system of linear equations is obtained by optimizing the value of a cost function with regard to some criteria.

[0100] In an embodiment, said solver is arranged to account for a predeterminedmaximum permissible error for said consumption measurements.

[0101] The solver may advantageously account for a predetermined maximumpermissible error by for example modeling the maximum permissible error as a stochastic variable with a particular distribution and propagating the associated uncertainty through to the obtained solution to the system of linear equations.

[0102] In an embodiment, the error estimate is assumed constant for at least ameasurement duration of said multivariate time series of consumption measurements.

[0103] The error estimate can advantageously be assumed to be constant for theduration of said multivariate time series of consumption measurements which is used to establish the system of linear equations. This assumption may be valid for certain shorter spans of time such as minutes or hours or when the measurement error of a particular metering device is caused by a particular issue.

[0104] In an embodiment, said consumption error estimate represents measurementerrors of one or more of said metering devices.

[0105] The consumption error estimate advantageously comprises estimates of themeasurement errors of one or more metering devices in the water distribution network.

[0106] In an embodiment, said error estimate comprises a volume estimate and / or aflow estimate.

[0107] The error estimate may advantageously be in units of measurement of volumeand / or flow i.e. the error estimate may be expressed as an absolute value of e.g. a volume of water and / or a water flow.

[0108] In an embodiment, said consumption error estimate and / or said leakageestimate comprises a percentage of volume and / or flow.

[0109] The error estimate may advantageously be computed as a percentage of thetotal volume and / or flow of water which may simplify the system of linear equations such that a solution can be obtained through fewer computational steps.

[0110] In an embodiment, said consumption error estimate is compared with ahistorical consumption error estimate by computing a difference between said consumption error estimate and said historical consumption error estimate.

[0111] The consumption error estimate may advantageously be compared to apreviously obtained historical consumption error estimate and be compared against it. This provides the advantage that changes in consumption error estimates can be tracked over time which enables the establishing of trends or forecasting which may be used to decide which metering devices need to be replaced or repaired. Furthermore, the historical consumption error estimate may be stored in a database and consequently updated to reflect the newly obtained consumption error estimate.

[0112] In an embodiment, said system of linear equations comprises one or moreleakage variables modelling one or more leakages in said water distribution network.

[0113] Leakage may advantageously be represented as variables in the system oflinear equations obtained by arranging consumption measurements as described previously. The variable may e.g. represent the magnitude of the leakage such as the amount of water lost per unit of time or the total volume of water lost in a water distribution network. The system of linear equations may then be solved such that a solution which indicates the magnitude of leakage is obtained as a leakage estimate. The variables representing leakage may be introduced into the system of linear equations which has other variables representing e.g. consumption error estimates. Insuch an embodiment, a solution to the system of linear equations may simultaneously provide a consumption error estimate and a leakage estimate.

[0114] In an embodiment, the steps of said water distribution network monitoringmethod are performed at a monitoring frequency.

[0115] The steps disclosed by the water distribution network monitoring method mayadvantageously be performed at an appropriate monitoring frequency according to different requirements. For example, a monitoring frequency may be established based on the availability of consumption measurements such that the water distribution network monitoring method is performed continuously as new consumption measurements are provided. Alternatively, it may be that the monitoring frequency is determined based on expected or actual variation of measurement errors or leakages as estimated by the consumption error estimates and / or leakage estimates such that when only small variations in the consumption error estimates and / or leakageestimates are observed, the monitoring frequency may be lower and vice versa.

[0116] In an embodiment, said monitoring frequency is on a timescale of seconds,minutes, hours, days, months, or years.

[0117] In an embodiment, one or more of said plurality of nodes are meteredconsumption nodes representing metering devices of the water distribution network.

[0118] In an embodiment, said plurality of nodes comprise at least one parent nodeand one or more child nodes, and wherein said parent node is linked to said child nodes by edges.

[0119] The system of linear equations may be established by analyzing a part of thetree structure which includes only a parent node and one or more of its children.Equations or inequalities which relate the consumption measurements of the parent node to the consumption measurements of one or more child nodes may be established using e.g. the assumption of conservation of mass and / or mass flow rate. The errorestimate obtained as the solution to said system of linear equations is confined to relateto only the parent node, the one or more child nodes, and the edges linking said nodes.Confining the location of a measurement error or a leakage to include only a parent node and one or more of its child nodes may provide advantages related to assessing consequences for other parts of the water distribution network.

[0120] Considering only a parent node and its child nodes may provide advantagesin terms of calibrating metering devices in the water distribution network. In some embodiments, it may be the case that the parent node has been calibrated such that measurement errors associated with the child nodes may be found by the water distribution network monitoring method. The measurement errors will typically beassociated with metered consumption nodes in the tree structure which represent ametering device in the water distribution network. Thus, traceability of the calibration of metering devices may be obtained for metering devices which have been installed in a water distribution network.

[0121] In an embodiment, each equation in said system of linear equations isestablished from a subset of said consumption measurements, and wherein said subset of consumption measurements are associated with a parent node and one or more child nodes.

[0122] In an embodiment, said parent node is associated with a calibrated meteringdevice, the calibrated metering device providing consumption measurements with a measurement error established to be within a range of a maximum permissible error.

[0123] Various circumstances may lead to an advantageous situation where themeasurement error or an estimate of the measurement error in the form of a consumption error estimate of certain metered consumption nodes is known before any processing of the consumption measurements by the computer model. The situation may arise when a metering device has been inspected or tested by a technician to ensure that it functions correctly with no measurement error or a measurement error that is numerically smaller than a predetermined maximum permissible error. The computer model can exploit information about known measurement errors for certain metered consumption nodes to simplify the system of linear equations which is solvedto obtain the error estimate comprising a consumption error estimate and / or a leakage estimate.

[0124] In an embodiment, said method further comprises a step of performing apressure test of said water distribution network and storing a pressure test result.

[0125] Advantageously, the water distribution network may be subjected to apressure test to ensure for example that no leakages are present in the water distribution network. The stored result of the pressure test may in turn be used to simplify thesystem of linear equations by which the error estimate is obtained because it can beassumed that there are no leakages present and thus any error estimates are likely to only comprise a consumption error estimate.

[0126] In an embodiment, said method further comprises a step of calibrating one ormore of said metering devices.

[0127] Calibration of one or more metering devices is advantageous in that it allowsfor simplification of the system of linear equations by for example reducing the number of variables or the number of equations. If consumption measurements obtained from a particular metering device can be assumed to have no measurement error or more likely a measurement error that is within a predetermined maximum permissible error, then it becomes unnecessary to compute a consumption error estimate that is associated with this metering device and consequently the number of variables required in the system of linear equations is reduced.

[0128] In an aspect, the invention relates to a water distribution network monitoringsystem comprising: a data processor implementing a computer model of a water distribution network, the computer model comprising a plurality of nodes linked by edges in a tree structure representing a pipe network of the water distribution network;and metering devices installed in said water distribution network, each metering deviceconfigured to provide a time series of consumption measurements, each consumptionmeasurement comprising a consumption representation and a timestamp; wherein saiddata processor is arranged to receive said consumption measurements, establish a system of linear equations on the basis of said computer model and said consumptionmeasurements, and process the system of linear equations on the basis of a solver to obtain an error estimate comprising a consumption error estimate and / or a leakageestimate; wherein said error estimate is associated with one or more of said meteringdevices in said water distribution network.

[0129] A water distribution network monitoring system is understood as a computer-implemented system for monitoring a water distribution network. The waterdistribution network monitoring system of the present invention involves a computer model which maps the physical structure of the water distribution network onto a data representation in a data processor such as a tree data structure. The data representation describes the physical water distribution network in terms of nodes and edges which describe the connections between nodes. The water distribution network monitoring system receives consumption measurements from metering devices located in the physical water distribution network via a data processor, and is arranged to establish a system of linear equations on the basis of a solver and the consumption measurements to obtain an error estimate. The error estimate may for example be presented via a status output which may be displayed on e.g. a screen, transferred to a backend system or stored in computer memory. The water distribution network monitoring system runs on a data processor which comprises at least a processor, memory, and communication means. The data processor on which the system or method is implemented may be directly linked with metering devices such as via cables or wireless communication means such as Wi-Fi, or may receive consumption measurements through a meter reading system or other metering backend system. Communication means facilitate the transmission of meter readings from metering devices in the water distribution network.

[0130] The water distribution network monitoring system may alternatively beimplemented on a data processor which is remote with respect to the water distribution network. Remote indicates remoteness in terms of distance such as thousands of kilometers and remoteness in terms of the communication means by which meterreadings are presented to the water distribution network monitoring system or waterdistribution network monitoring method. Remote computer hardware may for examplecomprise a cloud server on which the water distribution network monitoring system is implemented and to which consumption measurements are transferred via the internet.

[0131] In an embodiment, said error estimate comprises an indication of ageographical location with respect to said pipe network of said water distribution network, wherein said geographical location is associated with said consumption error estimate and / or said leakage estimate.

[0132] In an embodiment, one or more of said plurality of nodes are meteredconsumption nodes corresponding to said metering devices of said water distribution network.

[0133] In an embodiment, said plurality of nodes comprise at least one parent nodeand one or more child nodes, and wherein said parent node is linked to said child nodes by edges.

[0134] In an embodiment, each equation in said system of linear equations isestablished from a subset of said consumption measurements, and wherein said subset of consumption measurements are associated with a parent node and one or more child nodes.

[0135] In an embodiment, said parent node is associated with a calibrated meteringdevice, the calibrated metering device providing consumption measurements with a measurement error established to be within a range of a maximum permissible error.

[0136] In an embodiment, said error estimate comprises an indication of a logicallocation with respect to said computer model, wherein said logical location is associated with said consumption error estimate and / or said leakage estimate.

[0137] Locations in the tree structure may be specified in terms of the nodes and theedges connecting the nodes. The error estimate may thus specify a location which isconfined to e.g. a single node, a single edge, multiple nodes, or multiple edges. The error estimate may for example designate a subtree of the entire tree structure as the location of for example a leakage. Since the mapping between the computer model and the physical water distribution network may involve some simplification, confiningthe a leakage to a single node or a single edge may provide a precise physical location,or it may constitute a wider geographical area in which the network fault may be located. The type of network fault also has a bearing on how precisely a geographical area may be defined. If the network fault is a measurement error and the offending metering device can be identified, then the location of the network fault can be exactly specified, provided the location of the metering device is known. A location may for example be specified in the form of a street address. Conversely, if the network fault is a leakage, it may for example only be possible to designate a location that is accurate to within for example the length of a pipe between two metering devices.

[0138] In an embodiment, said pipe network comprises at least a main pipe and twoor more branch pipes branching off from said main pipe.

[0139] The pipe network of the water distribution network may advantageously havea structure of the pipe network wherein there is at least a main pipe and two or more branch pipes. In such a water distribution network, it is advantageous that metering devices are installed for example at the main pipe and further metering devices are installed at the two or more branch pipes that branch. Thereby it may be achieved that at least one equation relating the flow or volume of water at the main pipe with the volume or flow at the two or more branch pipes may be established.

[0140] In an embodiment, the water distribution network monitoring system isconfigured for carrying out the water distribution network monitoring method.

[0141] In an aspect, the invention relates to a data processing system comprisingmeans for carrying out the water distribution network monitoring method.

[0142] In an aspect, the invention relates to a computer program comprisinginstructions which, when the program is executed by a computer, cause the computer to carry out the water distribution network monitoring method.

[0143] In an aspect, the invention relates to a computer-readable storage mediumcomprising instructions which, when executed by a computer, cause the computer to carry out the water distribution network monitoring method.The drawings

[0144] Various embodiments of the invention will in the following be described withreference to the drawings wherefig. 1 illustrates a fluid distribution network monitoring system implemented tomonitor a fluid distribution network,figs. 2a – 2c illustrate a part of a fluid distribution network modeled by a computermodel in the form of a tree structure,fig. 3 illustrates a mapping from the computer model of the fluid distribution networkmonitoring system to a part of the fluid distribution network wherein a network faultis present,figs. 4a and 4b illustrate the tree structure of the computer model, andfig. 5 illustrates steps of the water distribution network monitoring method accordingto an embodiment of the invention.Detailed description

[0145] The figures employ reference signs to indicate different respectivecategorizations of the nodes 130 of the computer model 110 implemented by the dataprocessor 100 of the water distribution network monitoring system 90. While any nodeof the computer model 110 is a node 130, it may be the case that the same node 130can also be identified as a root node 131, parent node 132, or child node 133 whenconsidering its location in the tree structure 120. A node 130 may also be designated as a metered consumption node 140 which indicates that it models a metering device240 in the water distribution network 210. Therefore, the figures indicate certain nodes130 as being associated with several reference signs separated by commas to indicatethe appropriate categorizations of each node 130. To improve readability of thedrawings, only some nodes 130 of the computer model 110 have associated referencesigns.

[0146] Fig. 1 illustrates an embodiment of a water distribution network monitoringsystem 90 implemented to monitor a water distribution network 210.

[0147] The water distribution network 210 illustrated on fig. 1 may represent severaldifferent types of water distribution networks 210. In a preferred embodiment, thewater distribution network 210 represents a water distribution network by which e.g.potable water is distributed to various residential and commercial consumers. Thewater distribution network 210 may also illustrate other types of networks which maydistribute water to end consumers and serve other purposes. The water distributionnetwork 210 illustrated on fig. 1 may for example be a part (the forward flow or thereturn flow part) of a district heating or cooling system by which hot or cold water isdistributed to consumers for the purpose of heating or cooling.

[0148] The water distribution network 210 is shown to have one main pipe 221through which water is distributed to four main branch pipes 222 of the pipe network220. The water flow 223 through the pipe network 220 is illustrated with arrows thatindicate the direction of water flow 223 through different parts of the pipe network220.

[0149] Although only four main branch pipes 222 are shown, the main pipe 221 maydistribute water to additional branches of the pipe network 220 which are notillustrated on fig. 1. Two out of the four main branch pipes 222 are illustrated withdashed lines to indicate that the full extent of their further branching and terminationis not shown on fig. 1.

[0150] The smallest diameter pipes of the pipe network 220 are shown to terminateat consumers 280 to which the water distribution network 210 provides water. Varioustypes of consumers 280 are illustrated on fig. 1, namely residential consumers such ashouses and apartment buildings, and commercial consumers such as factories. Thetypes of consumers 280 illustrated on fig. 1 only constitute examples and do notpreclude other types of consumers 280 from being supplied by the water distributionnetwork 210.

[0151] At various points in the pipe network 220 of the water distribution network210, metering devices 240 are mounted to facilitate consumption measurements 141which are measurements of e.g. the water flow or water volume through that part ofthe pipe network 220. Metering devices 240 are shown to be mounted at various levelsof the pipe network 220 such as at the main pipe 221, at main branch pipes 222 and atpipes directly connected to consumers 280. Metering devices 240 are shown to bedistributed across the water distribution network 210 to facilitate the discovery andlocalization of network faults 261.

[0152] A network fault 261 is understood to be a physical fault in the waterdistribution network 210 which impedes the network’s ability to perform its function as related to the distribution of water to e.g. residential and commercial consumers 280. According to the present invention, several types of network faults 261 are considered. A first type of network fault 261 is leakage 262 which is understood to be a fault which causes water to be lost to leaks in e.g. the pipe network of the water distribution network 210. A leakage 262 may be caused by many different factors such as corroded, cracked, or ruptured pipes; broken or loose pipe connections; or cracks in reservoirs or tanks. Water lost through a leakage 262 is essentially wasted since it can typically not be used for its intended purpose. A related network fault 261 is accidentalor unintended water consumption, that technically is not due to a leak, but rather due to a human error or controller error of forgetting to close a valve or the like, such as a garden hose, swimming pool supply or a valve at a factory.

[0153] Another type of network fault 261 considered by the present invention ismeasurement error in the consumption measurements provided by the metering devices 240 in the water distribution network 210. Measurement error is an error in the consumption measurements 141 which causes the measured value to deviate by some amount from the actual water flow or volume in e.g. a pipe of the waterdistribution network. Measurement error of one or more metering devices 240 maycause consumers to be overbilled or underbilled for their consumption thus motivating a timely correction of such errors. Examples of overbilling or underbilling are seen in e.g. water distribution networks where water metering devices may be prone to measurement errors.

[0154] A specific instance of a network fault 261 is illustrated on fig. 1 in the formof a leakage 262 caused by a rupture in the pipe network 220 at the main pipe 221. Anarrow indicates the direction of the flow of water 223 out of the pipe network 220 atthe location of the leakage 262.

[0155] Additional network faults 261 may exist in the form of measurement errors atany of the metering devices 240 in the water distribution network 210. A measurementerror of a consumption measurement 141 provided by a metering device 240, indicatesthat the metering device 240 measures e.g. the water flow or water volume with anassociated error that is termed the measurement error.

[0156] Fig. 1 indicates the physical location of the water distribution networkmonitoring system 90 comprising a data processor 100 connected to the monitoringsystem 90. The water distribution network monitoring system 90 is implemented oncomputer hardware 100 which may be placed at a physical location within somedistance of the water distribution network 210. In other embodiments, the physicallocation of the data processor 100 of the water distribution network monitoring system90 may be a great distance from the water distribution network i.e. the data processor100 of the water distribution network monitoring system 100 may be a remote serverwhich may be located on a different continent from the water distribution network 210,or it may be run on a cloud computing system.

[0157] A view of the functional structure of the data processor 100 implementing thewater distribution network monitoring system 90 is illustrated on the bottom half offig. 1. The computer model 110 of the water distribution network monitoring system90 has been created by mapping the physical structure of the pipe network 220 and thelocations of the metering devices 240 onto a tree structure 120. The tree structure 120is comprised of nodes 130 which are linked by edges 121 to reflect the structure of thepipe network 220.

[0158] The nodes 130 represent the locations of metering devices 240 in the waterdistribution network 210. As an example, the mapping from a physical metering device240 to a node 130 of the computer model 110 is indicated with an arrow for themetering device 240 placed at the inlet of the main pipe 221. This metering device 240is mapped to the root node 131 of the tree structure 120 since it is placed at the inletof the main pipe 221, i.e. the location at which water flows into the water distributionnetwork 210. The other nodes 130 in the computer model 110 are obtained accordingto the same mapping procedure whereby metering devices 240 are mapped tocorresponding nodes 130.

[0159] The root node 131 of the computer model 110 is shown to have four edges121 which model the four main branch pipes 222 that branch off from the main pipe221. Two of the edges 121 are illustrated using dashed lines to indicate that thestructure of that part of the water distribution network 210 is, for simplicity, notconsidered in this example. In a realization of the embodiment, the computer model110 should preferably consider the entire physical network, or a part thereof relevantto a monitoring party. The edges 121 indicated with solid lines connect the root node131 with its two child nodes 133 which model the metering devices 240 placed at thetwo main branches considered in the computer model 110. The root node 131 is thusalso a parent node 132 with two child nodes 133. The remaining parts of the treestructure 120 map out the remaining metering devices 240 and the remaining pipes ofthe pipe network 220. Since all fifteen nodes 130 in the tree structure 120 of thecomputer model 110 represent a metering device 240, all fifteen nodes 130 of the treestructure 120 may also be designated as metered consumption nodes 140.

[0160] Fig. 1 further illustrates an embodiment in which consumption measurements141 provided by metering devices 240 are wirelessly transmitted to the data processor100 of the water distribution network monitoring system 90. Wireless transmissionmay be via a conventional automated meter reading AMR system using proprietary orstandardized communication protocols such as Wireless M-BUS, and optionally usingintermediate concentrators, or any other form of e.g. serial or parallel data transferusing technologies such as Wi-Fi, mobile cellular network such as 4G or 5G,LoRaWAN, Bluetooth or ZigBee. In other embodiments, the transmission may be viacables that connect each of the metering devices 240 to the data processor 100 of thewater distribution network monitoring system 90, possibly through meter readingsystems, or via proximity reading or drive-by reading, but such embodiments are notillustrated on fig.1.

[0161] A measurement input 150 is understood to be a software or hardware interfacethrough which consumption measurements may be presented to the water distribution network monitoring system or water distribution network monitoring method for processing and possibly storage.

[0162] Consumption measurements 141 are received at the measurement input 150of the data processor 100 of the water distribution network monitoring system 90. Oneor more consumption measurements 141 may be received at the measurement input150 before any processing is performed by the water distribution network monitoringsystem 90.

[0163] Each consumption measurement 141 received at the measurement input 150comprises a consumption representation 142 and a timestamp 143. The consumptionrepresentation 142 indicates e.g. a volume or flow measurement of water performedby the metering device 240 which provided the consumption measurement 141. Thevolume or flow measurement of water may e.g. be one or more of an instantaneouswater flow measurement, the accumulated total volume of water with respect to a fixedtime reference such as install date of the metering device 240, or the accumulated totalvolume of water measured since the preceding consumption measurement 141.

[0164] In an embodiment, each consumption measurement 141 may compriseseveral consumption representations 142, such as both a water flow and a watervolume, or any other combination of consumption representations 142 related to theconsumption of water. The timestamp 143 preferably indicates the time at which theconsumption measurement 141 was performed, such that each consumptionrepresentation 142 is paired with an indication of the time at which the consumptionmeasurement 141 was performed. In certain embodiments, the timestamp 143indicates the time at which the consumption measurement 141 was transmitted orestimated to be measured.

[0165] In an embodiment, each consumption measurement 141 may compriseseveral timestamps 143, such as both measurement time and transmission time, or anyother combination of timestamps 143 related to the consumption. Transmission timemay for example designate the time difference between the time at which the consumption measurement 141 was performed by a metering device 240 and the time at which the consumption measurement is supplied at the measurement input 150 of the data processor 100.

[0166] The data processor 100 of the water distribution network monitoring system90 processes the consumption measurements 141 received at the measurement input150 on the basis of the computer model 110 of the water distribution network 210.

[0167] The data processor is arranged to establish a system of linear equations 144on the basis of the computer model 110 and consumption measurements 141 receivedat the measurement input 150, and process the system of linear equations on the basisof a solver 161 to obtain an error estimate 170 comprising a consumption error estimateand / or a leakage estimate. In the present embodiment, establishing the system of linearequations is performed by the linear equation generator 160, which may beimplemented as a software program or part of a software program on the data processor 100.

[0168] The linear equation generator 160 may on the basis of received consumptionmeasurements 141 and the computer model 110 of the water distribution network 210determine a system of linear equations 144 which may represent any of the fifteendifferent metered consumption nodes 140 represented in the tree structure 120. Thesystem of linear equations 144 is provided as input to the solver 161 by which an errorestimate 170 associated with any one or more nodes 130 of the tree structure 120 isobtained, which in this embodiment is associated with one or more of the meteringdevices 240 or the leakage 262. The error estimate 170 may comprise a consumptionerror estimate which is associated with one or more of the nodes 130 which representthe metering devices 240 installed at one or more of the, in this example, elevenconsumers 280 illustrated on fig.1.

[0169] Based on the processing of consumption measurements 141 from one or moremetered consumption nodes 140 by the linear equation generator 160, the linearequation generator 160 establishes a system of linear equations 144. The system oflinear equations 144 is processed by the solver 161 which provides an error estimate170 which may optionally comprise where the network fault 261 is located, where thenetwork fault 261 may be in the form of either measurement errors of one or moremetering devices 240 or a leakage 262. An approximate or precise geographicallocation in the tree structure 120 of the computer model 110 may optionally besupplied, and this in turn may be used to identify e.g. a specific pipe or number ofpipes in the pipe network 220 of the water distribution network 210 where the networkfault 261, such as in the form of a leakage 262 or a measurement error, may be located.

[0170] Fig. 1 illustrates an example of a network fault 261 in the form of a ruptureof the main pipe 221 of the water distribution network 210. This network fault 261may result in an error estimate 170 being generated by the water distribution networkmonitoring system 90. The error estimate 170 may in this embodiment be associatedwith consumption measurements 141 associated with the root node 131 andconsumption measurements 141 associated with the nodes 130 representing themetering devices 240 of the main branch pipes 222 of the water distribution network210. The error estimate may in this embodiment comprise one or more consumptionerror estimates and / or a leakage estimate which quantifies respectively an estimate of measurement error or a leakage at specific points in the water distribution network 210associated with one or more nodes 130 and / or edges 121 of the tree structure 120.

[0171] Fig.1 illustrates that the solver 161 provides an error estimate 170 comprisinga consumption error estimate and / or a leakage estimate which may be used for e.g.storage, logging, display, or transfer to another system such as a backend system. Theerror estimate 170 thus provides data which may be transferred to other systems,presented to stakeholders, or further be used to provide an alert such that action maybe undertaken to fix or mitigate the network fault 261.

[0172] Figs. 2a – 2c each illustrate an identical water distribution network 210subject to different conditions which may affect the corresponding computer model110 of the water distribution network monitoring system 90 and the processing ofconsumption measurements 141. Examples of these embodiments are simplified foreasier illustration and comparison between different scenarios, and the principles willalso apply to larger and more complex real-world networks. The water distributionnetwork 210 illustrated on figs. 2a – 2c is a smaller part of the larger water distributionnetwork 210 illustrated on fig. 1, namely one of the four main branches which split offfrom the main pipe 221 illustrated on fig. 1.

[0173] Fig. 2a illustrates a situation where all five consumers 280 consume watersuch that water is flowing through the parts of the pipe network that lead to the fiveconsumers 280 connected to the water distribution network 210. Fig. 2b illustrates asituation where three consumers 280 consume water and two consumers 280 do notconsume any water. Fig. 2c illustrates a situation where three consumers 280 consumewater, two consumers 280 do not consume water, and the water distribution network210 has a network fault 261 in the form of a leakage 262 caused by a rupture in the pipe network 220.

[0174] The water distribution network 210 illustrated on figs. 2a – 2c may in apreferred embodiment be a water distribution network for distributing e.g. potablewater or water for heating or cooling.

[0175] Fig. 2a illustrates a water distribution network 210 and the corresponding treestructure 120 of the computer model 110 of a water distribution network monitoringsystem 90 (not shown). The water distribution network 210 has one main branch pipe222 and five smaller pipes that supply water to five consumers 280, all of which arepresently consuming water. The directions of the water flows in the pipe network 220are indicated by arrows 223. A computer model 110 corresponding to the waterdistribution network 210 is illustrated with a tree structure 120 obtained from mappingthe pipe network 220 and metering devices 240 onto nodes 130 and edges 121 to obtainthe computer model 110. Each of the metering devices 240 are mapped onto a node130, such that all six nodes 130 of the tree structure 120 are metered consumptionnodes 140. The resulting tree structure has one node 130 which is both root node 131and parent node 132 of five child nodes 133.

[0176] Identifiers indicated on fig. 2a denote the different nodes 130, such that theroot node 131 is designated A0 and its five child nodes are designated A1, B1, C1, D1,and E1 respectively. For convenience, the node identifiers are also indicated on thecorresponding metering devices 240.

[0177] Let ^^^, ^^^, ^^^, ^^^, ^^^ and ^^^ denote consumption representations142 with approximately simultaneous timestamps 143 (not shown) denoted ^^, asmeasured by the six metering devices 240 of the water distribution network. Theconsumption representations ^^^, ^^^, ^^^, ^^^, ^^^ and ^^^ may e.g. all representwater flow or water volume difference measurements. A water volume differencemeasurement may e.g. be obtained by the metering device 240 subtracting twoaccumulated volume measurements from each and thereby obtaining the volumedifference.

[0178] If consumption representations 142 do not all represent the same physicalquantity such as water flow or water volume, then an appropriate conversion must bemade such that all consumption representations 142 represent the same physicalquantity before consumption measurements 141, provided by different meteringdevices 240 modeled as metered consumption nodes 140, are comparable and thereforesuitable for establishing a system of linear equations processable by the solver (notshown).

[0179] In an alternative embodiment of the invention, direct comparison betweenconsumption representations 142 may be performed before the consumptionrepresentations are established as a system of linear equations. This direct comparisonof may be in the form of e.g. mutual subtraction, addition before being provided as e.g.coefficients in a system of linear equations.

[0180] In some embodiments, several consumption representations 142 of differentquantity types, e.g. both an instantaneous water flow and an accumulated watervolume, may normally or upon request be provided in each consumption measurement141, so that the appropriate quantity comparable to the other metered consumption nodes 140 can be selected.

[0181] The six consumption representations 142 having approximately simultaneoustimestamps 143 denoted ^^ means that a certain amount of variation betweentimestamps 143 is deemed allowable, such as in a predetermined interval from ^^ − Δ^to ^^ + Δ^ where Δ^ represents a predetermined negligible time difference. Apredetermined negligible variation Δ^ between timestamps 143 is thus deemed to notaffect the comparison of consumption representations 142, such that all consumptionmeasurements 141 may be assigned the approximately simultaneous timestamp of ^^.An assigned timestamp 143 of ^^ therefore reflects that the actual timestamp may besomewhere in an interval between ^^ − Δ^ and ^^ + Δ^. Variation between thetimestamps 143 of consumption measurements 141 associated with nodes 130 may in other embodiments be incorporated as an additional measurement uncertainty or errorwhich can be applied to the consumption error estimate to account for the lack of timesynchronization between consumption measurements 141.

[0182] The predetermined negligible time difference Δ^ may depend e.g. on thefrequency at which consumption measurements 141 are provided and the dynamics ofthe measured water flow or water volume difference. In an example, consumptionmeasurements 141 may be provided once per hour as volume differencerepresentations, and an acceptable negligible time difference Δ^ may be given as e.g.less than one minute. For water flow representations, the required predeterminednegligible time difference Δ^ may be much smaller such as e.g. less than a few seconds.

[0183] In an alternative embodiment, assuming no measurement errors and applyingthe principle of conservation of mass or mass flow rate, the following relationshipbetween the consumption representation ^^^ of the root node A0 and the consumptionrepresentations ^^^, ^^^, ^^^, ^^^, and ^^^ of the child nodes A1, B1, C1, D1, andE1 can be described via an equation given by ^^^ = ^^^ + ^^^ + ^^^ + ^^^ +^^^, i.e. the consumption representation 142 of the metering device 240 associatedwith root node A0 must be equal to the sum of consumption representations 142 of themetering device 240 associated with child nodes A1, B1, C1, D1, and E1. Such anequation may in alternative embodiments be used together with the tree structure 120to provide an error estimate which is associated with one or more nodes 130 ormetering devices 240.

[0184] A situation in which the principle of conservation of mass or mass flow rateis violated may be indicated by an inequality e.g. ^^^ ≠ ^^^ + ^^^ + ^^^ + ^^^ +^^^ which may be caused by leakage 262 and / or measurement error of one or moremetering devices 240 in the water distribution network 210. The water distributionnetwork monitoring system 90 (not shown) may in such an alternative embodimentprovide an error estimate comprising a warning that a network fault 261 (not shown)may be present in the water distribution network 210.

[0185] In an alternative embodiment, with reference to fig.2a, it may be the case thatthe computer model 110 furthermore maintains statistical measures of consumptionmeasurements 141 associated with one or more of the nodes 130 in the tree structure120. A statistical measure may for example be established by computing the averagewater volume or flow ^^^ at specific time intervals across an entire day for node A1.The averages may e.g. be recorded at each hour over a twenty-four hour period for anumber of days, weeks or months to establish a typical consumption pattern for theconsumer 280. Deviation from the established average ^^^ by a predeterminedabsolute or relative amount of flow or volume of water as recorded by subsequentconsumption measurements 141, may indicate that the metering device 240 associatedwith node A1 is subject to a measurement error. Such statistical measures and / or consumption patterns may be used to identify network faults 261 which may beconfined to an individual metering device 240. In some cases, it may therefore not benecessary to compare consumption measurements 141 from different metered consumption nodes in order for the water distribution network monitoring system 90to make decisions about whether an error estimate needs to be computed byestablishing a system of linear equations to be solved.

[0186] Fig. 2b illustrates a water distribution network 210 equivalent to that of fig.2a. The tree structure 120 of the computer model 110 of a water distribution networkmonitoring system 90 (not shown) is also illustrated. The difference with respect tofig. 2a is that only three out of the five consumers 280 connected to the waterdistribution network 210 consume water at the time of measurement. The remainingtwo consumers 280 do not consume any water, which is indicated by the absence ofarrows 223 on the pipes leading to the two consumers 280 in question.

[0187] The resulting tree structure 120 is identical to the one depicted on fig. 2a, withthe same nodes 130 and edges 121 indicating the structure of the water distributionnetwork 210. The same identifiers for nodes 130 are used, such that A0 denotes theroot node 131 and A1, B1, C1, D1, and E1 denote the child nodes 133.

[0188] Let ^^^, ^^^, ^^^, ^^^, ^^^, and ^^^ denote six consumptionrepresentations 142 with assigned timestamps ^^ as measured by the six meteringdevices 240 of the water distribution network. The consumption representations 142may represent either water flow or water volume difference measurements.

[0189] In an embodiment, assuming no measurement errors and applying theprinciple of conservation of mass or mass flow rate, the following relationship betweenthe consumption representation ^^^ of the root node 131 and the consumptionrepresentations ^^^, ^^^, ^^^, ^^^ and ^^^ of the child nodes 133 can be describedvia an equation given by ^^^ = ^^^ + ^^^ + ^^^ + ^^^ + ^^^, i.e. theconsumption representation 142 of the metering device 240 associated with root nodeA0 must be equal to the sum of consumption representations 142 of the meteringdevices 240 associated with child nodes A1, B1, C1, D1, and E1, as with the exampleof fig. 2a above.

[0190] Because there is no water flow through two of the metering devices 240 inthis example of fig. 2b, two of the corresponding consumption representations ^^^and ^^^ are determined to be within an interval bounded by a maximum permissibleerror and are therefore zeroed i.e. assumed to be zero. Zeroed consumptionmeasurements 141 are assumed to be zero to simplify processing of consumptionrepresentations. Thus, the equation relating the consumption representation ^^^ of theroot node 131 and the consumption representations ^^^, ^^^, ^^^, ^^^ and ^^^ ofthe child nodes 133 can be simplified as ^^^ = ^^^ + ^^^ + ^^^. Zeroedconsumption measurements 141 thus allow for the elimination of terms from theequations which describe the relationship between different consumptionrepresentations 142. This in turn makes the computing e.g. the error estimate 170simpler, since the error estimate 170, due to the elimination of terms associated withcertain metering devices 240, may now be associated with fewer metering devices 240thus simplifying the corresponding system of linear equations.

[0191] The preceding optional embodiments with reference to figs. 2a and 2b modelthe consumption representations 142 as exact measurements of the water volumes orwater flows in the pipe network 220, i.e. measurement errors are not estimated. Thatis to say, the preceding examples represent alternative embodiments of the inventionwherein the water distribution network method or system comprises further initialsteps of relating and comparing consumption measurements 141 by whichmeasurement errors and / or leakage are not estimated directly.

[0192] Further processing undertaken by the water distribution network monitoringsystem when measurement errors are present, can e.g. be modeled by introducing errorfactors which are multiplied by the consumption representations 142 to establish oneor more linear equations with unknown error factors which may form part of theconsumption error estimate. The measurement error is thus assumed to bemultiplicative in such a model, i.e. the measurement error corresponds to a percentageof the water volume or water flow as represented by the consumption representation142.

[0193] With respect to fig. 2b, four non-zero consumption representations ^^^, ^^^,^^^, and ^^^ associated with nodes A0, A1, C1, and D1 respectively were previouslydefined with an assigned timestamp 143 of ^^. When the metering device 240 at themain branch pipe 222 provides an accurate consumption representation 142 with anegligible measurement error, the error factors of the remaining non-zero consumptionrepresentations 142 are given as ^^^, ^^^ and ^^^. Introducing the error factors to themodel results in a linear equation ^^^ = ^^^ ⋅ ^^^ + ^^^ ⋅ ^^^ + ^^^ ⋅ ^^^ relatingthe consumption representation 142 of the metering device 240 associated with rootnode A0 to the sum of consumption representations 142 of the metering devices 240associated with child nodes A1, C1, and D1.

[0194] A consumption error estimate can be computed from the error factor as thereciprocal of the error factor minus 1, such that e.g. an error factor ^^^ = 0.99corresponds to a consumption error estimate associated with the consumption^ representation ^^^of ^^^ − 1 ≈ 0.01, i.e. the consumption error estimate is approx.1% of the measured consumption representation 142 in this example.

[0195] Since the error factor of each consumption representation 142 is initially anunknown, a number of equations at least equal to the number of error factors shouldideally be obtained as a system of linear equations to solve for the error factors andobtain the consumption error estimate which may conveniently be represented as avector where each entry in the vector corresponds to an estimate of the measurementerror associated with a particular metering device 240.

[0196] Multiple linear equations may be obtained by observing multiple sets ofconsumption measurements 141 taken at different times, and these multiple linearequations may together be used to establish a system of linear equations according toembodiments of the invention. One set of consumption measurements 141 may forexample be defined by consumption representations ^^^, ^^^, ^^^ and ^^^ withassigned timestamp ^^; equivalently indicated using the notation ^^^(^^), ^^^(^^),^^^(^^) and ^^^(^^) with the timestamp 143 in parenthesis indicating the timestamp143 associated with the given consumption representation 142. Given two subsequentsets of consumption measurements 141 with assigned timestamps ^^ and ^^respectively, a system of three linear equations can be established as^^^(^^) = ^^^ ⋅ ^^^(^^) + ^^^ ⋅ ^^^(^^) + ^^^ ⋅ ^^^(^^)where the consumption error estimate and therefore the error factors are assumed tobe constant with respect to time. Note that with reference to fig. 2b, it is assumed inthe above example that ^^^(^^), ^^^(^^), ^^^(^^), ^^^(^^), ^^^(^^) and ^^^(^^)are all consumption representations 142 which have a numerical value within aninterval defined by a maximum permissible error and are therefore assumed to be zero.

[0197] A set of consumption representations 142 representing for example waterflow or water volume difference according to the system of three linear equations mayin an example be given by^^^(^^) = 300, ^^^(^^) = 102, ^^^(^^) = 50, ^^^(^^) = 148.5^^^(^^) = 600,204, ^^^(^^) = 300, ^^^(^^) = 99^^^(^^) = 200, ^^^(^^) = 51, ^^^(^^) = 100, ^^^(^^) = 49.5from which the corresponding system of three linear equations can be established bythe water distribution network monitoring system or method as:300 = ^^^ ⋅ 102148.5600 = ^^^ ⋅ 204300200 = ^^^ ⋅ 51 + ^^^ ⋅ 100 + ^^^ ⋅ 49.5The above system of three linear equations may be used as input to a solver and solvedwith respect to the error factors ^^^, ^^^and ^^^using e.g. Gauss-Jordan eliminationto obtain a solution of ^^^ = 0.9804, ^^^ = 1 and ^^^ = 1.0101. The consumptionerror estimate therefore comprises the three estimates of measurement errors^ ^^^ − 1 ≈associated with the nodes A1, C1, and D1respectively.

[0198] Upon computing the consumption error estimate associated with nodes A1,C1 and D1 representing metering devices 240, the solver therefore provides an errorestimate which indicates that the metering device 240 associated with node A1 has anestimated measurement error of 2%, the metering device 240 associated with node C1has an estimated measurement error of 0%, and the metering device 240 associatedwith node D1 has an estimated measurement error of -1%. These three estimatedmeasurement errors together constitute at least a part of the consumption error estimateas provided by the water distribution network monitoring system or method.

[0199] Further, as the metering device 240 is a physical metering device, e.g. a watermeter, of a physical water distribution network 210, associated metadata or so-calledmaster data, typically has a physical geographical location, such as a street address orGPS coordinates, and / or contact information for a relevant user or manager, or suchmay be derivable due to the mapping between the computer model 110 and thephysical water distribution network 210. Thereby, the error estimate may in someembodiments further comprise geographical location information or contactinformation, or data, e.g. a meter serial number, from which such can be derived.

[0200] In the preceding example, the consumption representations 142 of the parentnode A0 were assumed to have a negligible measurement error which was assumed tobe zero. A measurement error of the parent node A0 may be considered by e.g. addinga predetermined measurement uncertainty to the consumption error estimate obtainedby solving the system of linear equations. Consumption error estimates may thus insome embodiments further be indicated in an interval which includes the measurementuncertainty attributed to the parent node.

[0201] With reference to fig. 2b, it may be the case in another example that a set ofconsumption representations 142 representing either water flow or water volumedifference may be given by a set of three linear equations as 303 = ^^^ ⋅ 50 + ^^^ ⋅ 50 + ^^^ ⋅ 200606 = ^^^ ⋅ 200300100101from which the corresponding consumption error estimate may be found to comprisea value of 1% for each of the nodes A1, C1, and D1 by the solving the system of linearequations. The consumption error estimate being equal across consumptionrepresentations 142 associated with different metered consumption nodes 140, mayindicate that a wrong assumption has been made. In this example, a reasonable conclusion would be that the parent node A0 does in fact not have a measurement errorof zero as assumed, which is indicated by the consumption error estimate comprisingestimated measurement errors being the same for all three nodes.

[0202] The measurement errors and consequently the error factors and estimatedmeasurement errors in the form of the consumption error estimate may vary as afunction of time, such that the measurement error cannot be assumed to be constantfor different sets of consumption measurements 141 with substantially differenttimestamps 143. The established system of linear equations may also beoverdetermined with more equations than unknowns, such that it may not be possibleto find a unique solution when using a solver such as Gauss-Jordan elimination to solvefor the error factors and provide a consumption error estimate. The method of ordinaryleast squares may be used as a numerical solver by the water distribution networkmethod or system in such cases, to estimate the measurement errors when these arenot constant but perturbed by e.g. a small random variation as a function of time.

[0203] In an embodiment with reference to fig. 2b, ^ sets of consumptionmeasurements 141 with consumption representations ^^^(^^), ^^^(^^), ^^^(^^),assigned timestamps ^^, …,^^ may be given forming a system of ^ linear equations of the form^^^(^^) = ^^^(^^) ⋅ ^^^(^^) + ^^^(^^) ⋅ ^^^(^^) + ^^^(^^) ⋅ ^^^(^^)⋮ ⋮ ⋮ ⋮^^^(^^) = ^^^(^^) ⋅ ^^^(^^) + ^^^(^^) ⋅ ^^^(^^) + ^^^(^^) ⋅ ^^^(^^)which may be solved for an estimate of the error factors ^^^, ^^^ and ^^^ using themethod of ordinary least squares e.g. when ^ > 3. The method of ordinary leastsquares may advantageously be implemented by defining a ^ × 3 coefficient matrixand a 3 × 1 variable vector^ = [^^̂^ ^^̂^ ^^̂^]^and a ^ × 1 constant vector^ = [^^^(^^) ⋯ ^^^(^^)]^from which the ordinary least squares solution may be obtained as ^= (^^^)^^^^^where ^^ is the transpose of coefficient matrix ^ and (^^^)^^ is the matrix inverse ofthe matrix product ^^^.

[0204] With reference to fig. 2b, it may be the case in an example that themeasurement error corresponding to ^^^ has a mean value of 2%, the measurementerror corresponding to ^^^ has a mean value of -2%, and the measurement errorcorresponding to ^^^has a mean value of 2%. Each of the measurement errors mayadditionally be assumed to be perturbed by a randomly varying error sampled from auniform distribution in the interval from -0.5% to 0.5%. Ten sets of consumptionmeasurements 141 representing either water flow or water volume difference andperturbed by measurement errors as described above may be given and represented ina 10 × 3 coefficient matrix as170 99.5 63.3é110 11ù ê0 12720.ú ê9 169 288ú ê290 60 88.5252 246 2ú ^=ê6.3ú ê169 4.74 55.8ú ê224 54.3 309ú ê118 408 50.1ú ê206 148 122ú ë173 157 38.8ûwith a 10 × 1 constant vector containing the consumption representations 142 of theparent node 330 é 344ù ê ú ê 474ú ê 432ú ^=ê 521ú ê 226ú ê 577ú ê 580ú ê 472ú ë368ûfrom which an estimate of the mean of the error factors ^ = [^^̂^ ^^̂^ ^^̂^]^maybe obtained using the method of ordinary least squares as^ = (^^^)^^^^^= [0.9787 1.019 0.9791]^from which an estimated mean of the measurement errors may be found as^ ^̂^^ − 1 =^ 2.18%, ^^̂^ − 1 = −1.87%,^ ^^̂^ − 1 = 2.14%. The consumption error estimate thuscomprises values of 2.18%, -1.87%, and 2.14% as estimated measurement errorsassociated with metering devices modeled by nodes A1, C1, and D1 respectively. Theconsumption error estimate comprising the estimated mean of the measurement errors obtained using e.g. the method of ordinary least squares is valuable since it may takevariations of the measurement error due to e.g. changes in water temperature or waterflow into account. The measurement error may also be affected by the installationconditions of the metering device 240 in the water distribution network 210, e.g. flowdisturbance due to piping changes such as bends. The consumption error estimatecomprising an estimated mean of the measurement error may thus be morerepresentative than an estimate of the measurement error obtained during e.g. production of the metering device, as a measurement error obtained by the present invention represents meter behavior in an actual use in an actual installation.

[0205] Methods for estimating a time-varying measurement error may also beemployed to track the measurement error as a consumption error estimate over timesuch that a trend or drift of the measurement error of one or more metering devices canbe identified. A solver implementing the method of ordinary least squares may e.g. beimplemented on consecutive sets of consumption measurements 141 such as e.g. tensets of consumption measurements at a time. This allows the water distributionnetwork monitoring method or system to provide updates of the estimatedmeasurement error in the form of an error estimate comprising a consumption errorestimate.

[0206] Fig. 2c illustrates a water distribution network 210 equivalent in structure tothat of figs. 2a and 2b with the difference that the water distribution network 210 hasa network fault 261 in the form of a leakage 262 caused by a rupture in the main branchpipe 222. Mapping of the water distribution network 210 onto a tree structure 120 ofthe computer model 110 may be done equivalently to figs. 2a and 2b. The same nodeidentifiers are indicated as on figs. 2a and 2b such that A0 denotes the root node 131and A1, B1, C1, D1, and E1 denote the child nodes 133. The leakage 262 has beenmodeled by adding an additional node L1 to the tree structure 120 of the computermodel 110.

[0207] As on fig. 2b, three of the consumers 280 consume water, and two consumers280 do not consume water. Let again ^^^, ^^^, ^^^, ^^^, ^^^ and ^^^ denoteconsumption representations 142 with assigned timestamps ^^ as measured by the sixmetering devices 240 of the water distribution network. Because there is no water flowthrough two of the metering devices 240, two of the corresponding consumption representations ^^^and ^^^are numerically smaller than a maximum permissible error and therefore assumed to have a value of zero.

[0208] In an alternative embodiment of the invention, given assumptions of nomeasurement error and the conservation of mass or mass flow rate, it is clear that ^^^ + ^^^ + ^^^ because of the leakage 262 seen at the main pipe of thewater distribution network 210. Rather, it is clear from fig. 2c that ^^^ > ^^^ +^^^ + ^^^ because the water lost to the leakage 262 is also included in theconsumption representation ^^^. Such an inequality may be established by the waterdistribution network monitoring system or method as a further step before establishing a system of linear equations.

[0209] The inequality ^^^ > ^^^ + ^^^ + ^^^ additionally confines the leakage262 to a location in the pipe network 220 between the metering device 240 representedby root node A0 and the metering devices 240 represented by child nodes A1, B1, C1,D1, and E1. To compensate for the loss of water, an additional variable ^^^ isintroduced to model the volume or flow of water lost through the leakage 262. Anequation describing the relation between consumption representations ^^^, ^^^, ^^^,^^^ and the leakage representation ^^^ is now given by ^^^ = ^^^ + ^^^ + ^^^ +

[0210] Solving this equation with respect to ^^^ yields ^^^ = ^^^ − (^^^ + ^^^ +^^^), i.e. the volume or flow of water lost to the leakage 262 can be obtained by thewater distribution network monitoring method or model as the difference between theconsumption representation 142 of the root node A0 and the sum of consumptionrepresentations 142 of the child nodes A1, C1, and D1. The presence of a leakage 262in the water distribution network 210 may thus in some embodiments be identified bya further step of noting inconsistencies in the expected mathematical relationshipsgoverning the water consumption measurements 141 of multiple metering devices 240.Using such a method, an approximate or precise location of a leakage 262 in additionto a leakage estimate of the water volume or water flow lost to a leakage 262 may beidentified.

[0211] With reference to fig. 2c, it may sometimes be unclear whether a leakage ispresent or not. In such an example, the presence of measurement errors of one or moremetering devices may first be assumed, and an estimate of the relevant measurementerrors as a consumption error estimate may then be computed by solving a system oflinear equations. If the estimated measurement errors are found to deviateuncharacteristically from a predetermined interval of reasonable and expected errorvalues, it may be an indication that a leakage is present. A leakage may also be presentwhen estimated measurement errors are found to be substantially identical andnegative, such as when the variation between different estimated measurement errorsis smaller than a predetermined value.

[0212] In the preceding example, the location and magnitude of the leakage 262 wasestablished by subtracting relevant consumption representations 142 from each other.A situation may arise in which the water distribution network 210 is subject to multipletypes of network faults 261 at the same time. Fig. 2c may represent a situation wherein addition to a leakage 262, the metering devices 240 represented by nodes A1 andD1 exhibit a measurement error in their respective consumption representations 142.The problem can be solved by establishing a system of linear equations from observingmultiple sets of consumption measurements 141 that together form a multivariate timeseries.

[0213] If consumption representations 142 associated with node A0 are assumed tobe without measurement error, four sets of consumption measurements 141 mayestablish a system of four linear equations from which the consumption error estimateand / or leakage estimate may be identified. The four sets of consumption measurements141 may have assigned timestamps 143 given by ^^, ^^, ^^ and ^^ such that the systemof four linear equations corresponding to the water distribution network 210 and treestructure 120 of fig. 2c is obtained as^^^(^^) = ^^^ ⋅ ^^^(^^) + ^^^ ⋅ ^^^(^^) + ^^^ ⋅ ^^^(^^) + ^^^where the error factors ^^^, ^^^, ^^^ and leakage estimate ^^ are assumed to be constantwith respect to time. Note that with reference to fig. 2c, it is implicitly assumed in thepresent example that^^^(^^) and ^^^(^^) all have a numerical value of zero i.e. that the numerical valueis for example smaller than a predetermined maximum permissible error and istherefore assumed to be equal to zero.

[0214] A set of consumption representations 142 according to the above system offour linear equations may in an example be given by^^^(^^) = 350, ^^^(^^) = 102, ^^^(^^) = 50, ^^^(^^) = 148.5^^^(^^) = 650,204, ^^^(^^) = 300, ^^^(^^) = 99^^^(^^) = 250, ^^^(^^) = 51, ^^^(^^) = 100, ^^^(^^) = 49.5^^^(^^) = 150, ^^^(^^) = 25.5, ^^^(^^) = 50, ^^^(^^) = 24.75from which the system of four linear equations can be established by the waterdistribution network monitoring method or model as350 = ^^^ ⋅ 102148.5650 = ^^^ ⋅ 204300250 = ^^^ ⋅ 51 + ^^^ ⋅ 100 + ^^^ ⋅ 49.5150 = ^^^ ⋅ 25.5 + ^^^ ⋅ 50 + ^^^ ⋅ 24.75The above system of four linear equations may be solved with respect to the errorfactors ^^^, ^^^, ^^^ and the leakage estimate ^^^ using e.g. Gauss-Jordan eliminationto obtain a solution of ^^^ = 0.9804, ^^^ = 1, ^^^ = 1.0101 and ^^^ = 50. Thecorresponding estimated measurement errors are therefore^ ^ ^^^ − 1 ≈ 2%,^^^ − 1 =0% and ^^^ − 1 ≈ −1%, and the leakage estimate has been found as ^^^ = 50. Theerror estimate provided by the water distribution network monitoring method or system therefore comprises a consumption error estimate comprising consumption error estimates of 2%, 0%, and -1% corresponding to metering devices associated with nodes A1, C1, and D1 respectively, and a leakage estimate with a numerical value of50. The present example illustrates that even if multiple types of network faults 261are present in a water distribution network 210, the water distribution networkmonitoring method or system may still localize and quantify these errors.

[0215] The preceding examples of different embodiments regarding figs. 2a – 2cwherein sets of consumption measurements 141 are used to establish a system of linearequations assumed that some consumption measurements had a numerical value smaller than a predetermined maximum permissible error and could therefore be assumed to be zero in the system of linear equations. However, such assumptions are not required for a system of linear equations to be established. With reference to fig.2a, it may be the case in an embodiment that five sets of consumption measurements141 with timestamps ^^, … , ^^ are given such that a system of five linear equations canbe established as 450102 + ^^^ ⋅ 50 + ^^^ ⋅ 148.5 + ^^^ ⋅ 51.5 + ^^^ ⋅ 98750 = ^^^ ⋅ 20430010325049.5 + ^^^ ⋅ 25.75 + ^^^ ⋅ 24.5475204 + ^^^ ⋅ 100 + ^^^ ⋅ 99 + ^^^ ⋅ 25.75 + ^^^ ⋅ 49325103 + ^^^ ⋅ 24.5from which the consumption error estimate can be found as comprising estimatedmeasurement errors of 2%, 0%, -1%, 3%, and -2% for nodes A1, B1, C1, D1, and E1respectively.

[0216] The preceding examples employ the assumption that one of the relevantmetering devices provides consumption measurements with a measurement error thatis negligible or known, such that the system of linear equations can be simplified. However, even if all metering devices are associated with an unknown measurement error, a person skilled in the art would still be able to establish a system of linearequations and solve it using an appropriate solver to obtain the error estimate.

[0217] Figs. 2a – 2c have been used to illustrate different examples of how the waterdistribution network monitoring method or system may provide an error estimatecomprising numerical estimates or values on the basis of specific consumptionmeasurements 141.

[0218] In some embodiments, it may not be possible to rely on these error estimatesalone, such as when the error estimates are considered too uncertain according to apredetermined metric. An uncertain error estimate comprising a consumption errorestimate and / or a leakage estimate may be used to take further action such as byvalidating the presence of a network fault 261 through visual inspection. Errorestimates provided by the water distribution network monitoring method or systemmay thus be used to support and guide trained personnel in their further identification and mitigation of network faults 261.

[0219] Fig. 3 illustrates an embodiment of the invention wherein a mapping is madefrom the computer model 110 of the water distribution network monitoring system 90(not shown) to the physical water distribution network 210 to indicate the geographicallocation of a network fault 261 in the form of leakage 262. The part of the tree structure120 to be mapped is indicated as a hatched area on fig. 3. The hatched area on the treestructure 120 corresponds to two edges 121, the first edge connecting node E2 withnode A3, and the second edge connecting node E2 with node B3.

[0220] The water distribution network 210 illustrated on fig. 3 comprises one mainpipe 221 and two main branch pipes 222 of the pipe network. Multiple consumers 280are connected to the water distribution network 210.

[0221] The water distribution network 210 illustrated on fig. 3 may distributedifferent types of water for different purposes such as e.g. potable water forconsumption. The water flow 223 through the pipe network is indicated with arrows.In a preferred embodiment, the water distribution network 210 of fig. 3 illustrates awater distribution network by which water is distributed to e.g. residential andcommercial consumers 280.

[0222] According to the optional embodiment illustrated on fig. 3, the leakageestimate as supplied by the water distribution network monitoring system 90 hasprovided an indication of the location of the leakage being confined to the two edges121 as indicated. The two edges connecting node E2 with nodes A3 and B3 correspondto a part of the pipe network 220 of the physical water distribution network 210. Thepart of the pipe network 220 corresponding to the two edges is indicated as a hatchedarea of the pipe network 220 confined to the pipes between the metering device 240 represented by node E2 and the two metering devices 240 represented by nodes A3and B3. The mapping from a part of the tree structure 120 to a part of the pipe network220 of the water distribution network 210 has been indicated using an arroworiginating at the hatched area of the tree structure 120 and terminating at the hatchedarea of the pipe network 220.

[0223] This illustrates that the leakage estimate may in certain embodiments furthercomprise an approximate location of the leakage which in this example is confined tothe part of the pipe network 220 indicated with hatching on fig.3.

[0224] The location of the leakage 262 with respect to the physical location of thewater distribution network 210 may be provided in various ways by the leakageestimate. It may be that the leakage estimate comprises location coordinates whichdelimit an area or identify a geographical location in which the leakage 262 maypossibly be located. Location coordinates may e.g. be defined according to a standardsuch as the Global Positioning System or be a list of possibly relevant street names oraddresses, or the coordinates may be defined according to a local reference such as a coordinate frame defined with respect to the pipe network 220.

[0225] The location of the network fault 261 may also be established with referenceto the pipe network 220 itself, such as by indicating as part of the error estimate thespecific pipes in the pipe network 220 or the parts of specific pipes which may besubject to e.g. a leakage 262. Such an error estimate comprising an indication of thelocation of a network fault 261 may rely on pipes in the pipe network 220 beingidentified in some way such as by a pipe identification number, and the error estimatemay in turn provide the relevant pipe identification numbers via the error estimate 170(not shown).

[0226] The error estimate 170 may in addition to location coordinates in somealternative embodiments provide a statistical estimate of the likelihood of the networkfault 261 being confined to the indicated location(s) such as by providing as part of theerror estimate 170 a covariance matrix indicating the uncertainties associated with theestimated location of a network fault 261.

[0227] Fig. 3 illustrates that an excavator 290 has been deployed in the vicinity ofthe part of the pipe network 220 that has been identified as being subject to a networkfault 261 in the form of leakage 262 by the supplied error estimate 170 whichcomprises a leakage estimate. The excavator 290 may constitute part of an effort tolocalize and subsequently repair the leakage 261 which has been indicated by the waterdistribution network monitoring system 90. The excavator 290 may in the embodimentillustrated on fig. 3 be used to dig into the ground to expose parts of the pipe network220 which may be located beneath the ground. The excavator 290 may, by digging inthe area designated by the error estimate 170, expose the leakage 262 such that it canbe identified by visual inspection. Trained personnel may begin the process of repairing the leakage 262 through means such as replacing the pipes of the relevantpart of the pipe network 220 or repairing the existing pipe network 220.

[0228] Fig. 3 illustrates an embodiment in which the search for a leakage 262 maybe confined to only include the location(s) as specified by the error estimate 170 whichcomprises a leakage estimate. The actual location of the leakage 262 may thus beidentified much faster than by searching e.g. randomly such as when a leakage 262 inthe water distribution network 210 is suspected, but no estimate of the location isknown. Without an approximate leakage 262 location as provided by the waterdistribution network monitoring system 90, trained personnel would at first have toperform leakage localization in a greater part of the water distribution network, suchas by using microphones for detection, which may further delay efforts to repair theleakage significantly. Depending on the physical network layout, its complexity anddistances between metering devices 240 in the water distribution network 210, theapproximate leakage location provided by the error estimate of the invention may besufficient to lead more or less directly to a suspected leakage 262, but even when onlygiving an approximate location of, for example, a certain residential area, it maysignificantly reduce the subsequent required effort, such as significantly reducing the area in which to apply microphone-based leakage localization.

[0229] Figs. 4a and 4b illustrate the tree structure 120 of the computer model 110 ofan embodiment of the water distribution network monitoring method or system whichmodels the water distribution network 210 illustrated on fig. 3. All fifteen nodes 130of the tree structure 120 are metered consumption nodes representing the meteringdevices 240 of the water distribution network 210 illustrated on fig. 3. All nodes 130of the tree structure have been designated with a unique identifier as indicated on figs.4a and 4b. The root node 131 of the tree structure has been given the identifier A0 andmodels the metering device 240 (not shown) mounted on the main pipe 221 (notshown) of pipe network 220 (not shown) illustrated on fig. 3.

[0230] Fig. 4a illustrates the hierarchical arrangement of the tree structure 120. Theroot node A0 has no parent node and forms the top-most node in the hierarchy of thetree structure 120. The root node A0 may also be said to constitute level zero of thetree structure 120. Root node A0 is the parent node 132 to child nodes A1 and B1which in turn constitute level one of the tree structure 120. Parent node A1 has childnodes A2, B2, C2, D2, E2 and parent node B1 has child nodes F2, G2, H2, I2, J2. Theten nodes A2, B2, C2, D2, E2, F2, G2, H2, I2, and J2 constitute level two in thehierarchy of the tree structure 120. Node E2 is a parent node with child nodes A3 andB3. Child nodes A3 and B3 constitute the fourth and final level of the tree structure120. The tree structure 120 illustrated on fig. 4a thus has four levels, each of which areconstituted by a subset of nodes 130. The edges 121 indicate how nodes 130 of different levels are connected.

[0231] With reference to fig. 4a, it may be the case that for each meteredconsumption node 140, a consumption measurement 141 (not shown) is given. Theconsumption measurements 141 may be synchronized in time to within an allowabletolerance which allows for consumption representations 142 (not shown) associatedwith different metered consumption nodes 140 to establish a system of linearequations. Processing of said consumption measurements 141 on the basis of thecomputer model 110 are performed to obtain the system of linear equations which issolved to obtain an error estimate comprising a consumption error estimate and / or a leakage estimate.

[0232] In an alternative embodiment of the invention, a comparison of consumptionrepresentations 142 from multiple metered consumption nodes 140 may be done usingdifferent strategies for effective traversal of the hierarchy of the tree structure 120. Thetree structure 120 traversal strategy may depend on factors such as how the computermodel 110 is implemented, the complexity of the tree structure 120, the averagenumber of child nodes 133 per parent node 132, and the type of network fault 261 (notshown) being identified.

[0233] Tree traversal may define a strategy by which each node 130 in the treestructure 120 can be accessed and the consumption measurement(s) 141 and / or otherdata associated with the specific node 130 can be written or read. Reading data refersto the process of accessing the data associated with a given node 130 such as by readingdata entries stored in memory of the data processor on which the water distributionnetwork monitoring method or system 90 (not shown) has been implemented. Writingdata may involve tree structure 120 traversal steps by which relevant data such asconsumption measurements 141 are assigned to the appropriate metered consumptionnodes 140. Tree traversal may thus in some embodiments be a part of the processingof consumption measurements 141 performed by the water distribution networkmonitoring method or system 90.

[0234] With reference to fig. 4a, a tree structure 120 traversal strategy which may beemployed by the computer model 110 of the water distribution network monitoringsystem 90 is a level-order traversal. A tree structure 120 traversal strategy by level-order may be implemented by accessing nodes 130 starting from the root node 131 andaccessing nodes 130 in the order of level from left to right. With reference to fig. 4a,the root node A0 comprises level zero of the tree structure 120, and the tree structure120 traversal strategy of level-order thus begins at node A0. The next level of the treestructure 120 to be accessed is level one, starting from the left-most node A1 andmoving on to node B1. The second level nodes A2, B2, C2, D2, E2, F2, G2, H2, I2,and J2 are subsequently accessed from left to right. Traversal of level four concludesthe level-order tree structure 120 traversal strategy by visiting nodes A3 and B3 inorder.

[0235] Upon accessing each node 130 during tree structure 120 traversal, thecomputer model 110 may perform necessary processing e.g. by assigning data such asconsumption measurement(s) 141 to the node 130 or reading data such as consumptionmeasurement(s) 141 from the node. Upon assigning to or reading data from a node130, additional processing steps may be undertaken by the computer model 110.Additional processing steps may involve optional steps of the comparison of multipleconsumption measurements 141 from one or more metered consumption nodes 140, such as by establishing a mathematical relationship between said consumptionmeasurements 141 from different metered consumption nodes 140 or multipleconsumption measurements 141 from a single metered consumption node 140.Mathematical relationships between consumption measurements 141 may e.g. beequations, inequalities, or statistical measures established in addition to the system ofequations to obtain an error estimate which estimates one or more network faults 161in the form of measurement errors and / or leakage.

[0236] With reference to fig. 4a, it may be the case that consumption representations142 assigned to nodes A0, A1 and B1 do not comply with the principle of conservationof mass or mass flow rate. This scenario may indicate a network fault 261 (not shown)confined to levels one and / or two of the tree structure 120, or possibly a network fault261 involving levels three and / or four. The level-order tree structure 120 traversalstrategy may in alternative embodiments be used by the computer model 110 toidentify such a violation of the principle of conservation of mass or mass flow rate byfirst accessing node A0 to retrieve consumption measurement(s) 141 with associatedconsumption representation(s) 142 and timestamp(s) 143. Nodes A1 and B1 of levelone are subsequently accessed in order, and the consumption measurements 141 ofeach node are retrieved.

[0237] Upon retrieval of consumption measurement(s) 141 from B1, an optionalprocessing step may entail the comparison of consumption representations 142 fromnodes A0, A1 and B1 which may identify that the consumption measurements 141 donot obey the principle of conservation of mass or mass flow rate. To establish thesystem of linear equations, it may be necessary to further traverse the tree structure120 by employing the level-order tree structure 120 traversal strategy or possiblyanother tree structure 120 traversal strategy.

[0238] With reference to fig. 4a, a different tree structure 120 traversal strategy mayaccess nodes according to a depth-first strategy in optional embodiments of theinvention. Because the root node A0 has two child nodes A1 and B1, each of these twonodes form a subtree. According to the depth-first tree structure 120 traversal strategy,the nodes 130 of each of the two subtrees are accessed in turn. The first subtree consistsof nodes A1, A2, B2, C2, D2, E2, A3, and B3. The second subtree consists of nodesB1, F2, G2, H2, I2, and J2. The depth-order tree structure 120 traversal strategy will thus access nodes 130 in an order such that all nodes of each of the two subtrees are visited in order. Completion of the first subtree thus involves accessing nodes A1, A2, B2, C2, D2, E2, A3, and B3 in order followed by accessing nodes B1, F2, G2, H2, I2,and J2. The order in which each of the two subtrees are accessed may be swapped, asmay the order in which the root node 131 is accessed.

[0239] With reference to fig. 4a, it may be the case that consumption representations141 assigned to nodes E2, A3 and B3 do not comply with the principle of conservationof mass or mass flow rate as indicated by optional processing steps performed by thewater distribution network monitoring system. This scenario may indicate a networkfault 261 (not shown) confined to levels three and / or four of the tree structure 120. Thedepth-first tree structure 120 traversal strategy may be used by the computer model 110 to identify such a violation of the principle of conservation of mass or mass flow rate by first accessing the subtree consisting of nodes A1, A2, B2, C2, D2, E2, A3, andB3 in order.

[0240] Fig. 4b illustrates the tree structure 120 highlighting four subtrees 122consisting of a parent node 132 and corresponding child nodes 133. A first subtree 122includes parent and root node A0 with child nodes A1 and B1. A second subtree 122includes parent node A1 and child nodes A2, B2, C2, D2, and E2. A third subtree 122 includes parent node B1 and child nodes F2, G2, H2, I2, and J2. A fourth subtree 122includes parent node E2 and child nodes A3 and B3. Each of the four subtrees 122 aredemarcated using a dotted line.

[0241] The four subtrees 122 illustrated on fig. 4b each consist of a parent node 132and its child nodes 133 and indicate a typically useful grouping of nodes into subtrees122 which may facilitate an effective means to traverse the tree structure. A treestructure 120 traversal strategy may effectively group nodes 130 of the tree structure120 such that each parent node 132 and its child nodes 133 are considered as onesubtree 122 and such that consumption measurements 141 associated with the nodesof the subtree are compared separately from the rest of the tree structure 120. Theprinciple of conservation of mass or mass flow rate may for example in alternativeembodiments be employed to establish a mathematical relationship for comparisonbetween consumption measurements 141 associated with a parent node 132 andconsumption measurements 141 associated with all of its child nodes 133. Aprocessing step may advantageously be implemented by the computer model 110 oncethe tree structure 120 traversal strategy has accessed all the nodes of the subtree 122consisting of a parent node 132 and all of its child nodes 133.

[0242] The preceding descriptions of figs. 1 – 4b include elaborations on differenttypes of uncertainties which may affect the computation of an error estimate 170 asprovided by the water distribution network monitoring method or system 90. Theconsumption representation 142 of a consumption measurement 141 may for example be perturbed by a measurement error which constitutes a form of uncertainty. In certainsituations, the measurement error may be estimated by the water distribution networkmonitoring method or system as an error estimate 170, but in other situations it maybe necessary for the water distribution network monitoring method or system 90 toapply assumptions about the magnitude of the measurement error. The measurementerror may for example be assumed to be within an interval defined by a predeterminedmaximum permissible error. This represents an additional uncertainty and may affectthe ability of the invention to provide e.g. a numerically accurate error estimate 170.

[0243] Time synchronization may add additional uncertainties to the error estimate170. Depending on the accuracy of time synchronization achieved, consumptionrepresentations 142 from different metered consumption nodes 140 may be assumedto be perturbed by a measurement uncertainty that may be proportional to the amountof time skew between the timestamps 143 of consumption measurements 141 providedby different metering devices 240.

[0244] Other types of uncertainties may arise from assumptions which the waterdistribution network monitoring system 90 may make about the absence ofmeasurement error for certain nodes of the tree structure. For example, for a subtreeof the tree structure 120 consisting of a parent node 132 and its child nodes 133, theassumption may be made that the parent node 132 is not perturbed by any form ofmeasurement error, to simplify corresponding mathematical relationships such as thesystem of linear equations. This assumption adds additional uncertainty whenproviding an error estimate 170, since the assumption cannot always be verified ormay simply be assumed for convenience to simplify calculations as performed by e.g.the solver.

[0245] Assumptions related to the presence or absence of leakage in the waterdistribution network may also add additional uncertainty, such as when nodes whichmodel leakage are added to the tree structure 120 of the computer model 110 to accountfor possible leakages 262 in the water distribution network 210.

[0246] Different types of uncertainties may be combined to obtain a resultinguncertainty according to some form of mathematical or statistical rule. The waterdistribution network monitoring method may in certain optional embodimentsincorporate this resulting uncertainty when obtaining e.g. a consumption error estimateand / or a leakage estimate.

[0247] The invention is not limited to the herein described mathematical methodsused to solve the system of linear equations. A person skilled in the art will, afterhaving been presented with the central concepts of the invention, be able to adaptalternative numerical or analytical methods to obtain the error estimate from the system of linear equations.

[0248] Fig. 5 illustrates the steps S1-3 of the water distribution network monitoringmethod of the invention. A first step S1 comprises receiving a multivariate time series of consumption measurements, the consumption measurements obtained from metering devices in a water distribution network and each consumption measurement comprising a consumption representation and a timestamp.

[0249] A second step S2 comprises establishing a system of linear equations on thebasis of said consumption measurements.

[0250] A third step S3 comprises processing said system of linear equations on thebasis of a solver to obtain an error estimate comprising a consumption error estimate associated with one or more of said metering devices in said water distribution networkand / or a leakage estimate.

[0251] List of reference signs:90 water distribution network monitoring system100 data processor110 computer model of a physical water distribution network120 tree structure121 edges of the tree structure122 subtree130 node131 root node132 parent node133 child node140 metered consumption node141 consumption measurement142 consumption representation143 timestamp144 system of linear equations150 measurement input160 linear equation generator161 solver170 error estimate210 water distribution network220 pipe network221 main pipe of the pipe network222 main branch pipe of the pipe network223 water flow through the pipe network240 metering device261 network fault262 leakage280 consumer290 excavatorS1-3 steps of the water distribution network monitoring method

Claims

Claims 1. A water distribution network monitoring method comprising the steps of: receiving a multivariate time series of consumption measurements (141), theconsumption measurements (141) obtained from metering devices (240) in a waterdistribution network (210) and each consumption measurement (141) comprising aconsumption representation (142) and a timestamp (143);establishing a system of linear equations (144) on the basis of said consumptionmeasurements (141);processing said system of linear equations (144) on the basis of a solver (161) toobtain an error estimate (170) comprising a consumption error estimate associated withone or more of said metering devices (240) in said water distribution network (210)and / or a leakage estimate.

2. The method of claim 1, wherein said system of linear equations (144) is establishedby considering the physical principle of conservation of mass and / or mass flow rate.

3. The method of any of the preceding claims, wherein said consumptionmeasurements (141) are assigned to a computer model (110) comprising a plurality ofnodes (130) linked by edges (121) in a tree structure (120) representing a pipe network(220) of the water distribution network (210).

4. The method of claim 3, wherein one or more of said plurality of nodes (130) are metered consumption nodes (140) representing metering devices (240) of the water distribution network (210).

5. The method of any of the claims 3-4, wherein said plurality of nodes (130) comprise at least one parent node (132) and one or more child nodes (133), and wherein said parent node (132) is linked to said child nodes (133) by edges (121).

6. The method of any of the claim 3-5, wherein each equation in said system of linearequations (144) is established from a subset of said consumption measurements (141),and wherein said subset of consumption measurements are associated with a parent node (132) and one or more child nodes (133).

7. The method of any of the claims 5-6, wherein said parent node (132) is associatedwith a calibrated metering device (240), the calibrated metering device (240) providing consumption measurements (141) with a measurement error established to be within a range of a maximum permissible error.

8. The method of any of the preceding claims, wherein said consumptionmeasurements (141) are assigned to variables, and wherein each variable correspondsto a subset of consumption measurements (141).

9. The method of any of the preceding claims, wherein a unit of measurement of saidconsumption representation (142) is a volume or a volume flow rate.

10. The method of any of the preceding claims, wherein a unit of measurement of saidconsumption representation (142) is a mass or a mass flow rate.

11. The method of any of the preceding claims, wherein said method further comprisesa step of converting said consumption representation (142) from a first unit ofmeasurement to a second unit of measurement.

12. The method of any of the preceding claims, wherein said method further comprises a step of determining an inconsistency related to said consumption measurements (141).

13. The method of any of the preceding claims, wherein one or more of saidconsumption measurements (141) are zeroed when said one or more consumptionmeasurements (141) attain a numerical value within a predetermined interval.

14. The method of claim 10, wherein the endpoints of said predetermined interval is amaximum permissible error.

15. The method of any of the preceding claims, wherein said consumptionmeasurements (141) each have a predetermined measurement uncertainty.

16. The method of any of the preceding claims, wherein said consumptionmeasurements (141) are synchronized in time across variables of said multivariate timeseries.

17. The method of any of the preceding claims, wherein said consumptionmeasurements (141) comprise timestamps (143) at substantially equal measurementtimes.

18. The method of any of the preceding claims, wherein said metering devices (240)comprise adjustable clocks.

19. The method according to claim 18, wherein said adjustable clocks are synchronizedin time across said metering devices (240).

20. The method of any of the preceding claims, wherein said method comprises a stepof synchronizing said consumption measurements (141) in time to compensate forunsynchronized clocks of said metering devices (240).

21. The method of any of the preceding claims, wherein said metering devices (240)provide consumption measurements (141) which are synchronized in time to withinan interval between 0.05 % and 2.5 % of nominal time between said consumptionmeasurements (141).

22. The method of any of the preceding claims, wherein a sample frequency of saidconsumption measurements (141) is variable.

23. The method of any of the preceding claims, wherein said method further comprisesa step of indicating a geographical location in said water distribution network (210)associated with said error estimate (170).

24. The method of any of the preceding claims, wherein said method further comprises a step of determining an inconsistency between two or more of said metering devices(240) in said water distribution network (210).

25. The method of any of the preceding claims, wherein said system of linear equations(144) is established on the basis of a statistical measure of said consumptionmeasurements (141).

26. The method of any of the preceding claims, wherein said system of linear equations(144) is inhomogeneous.

27. The method of any of the preceding claims, wherein said system of linear equations(144) is overdetermined.

28. The method of any of the preceding claims, wherein said solver (161) is analgorithm implemented on a data processor (100).

29. The method of any of the preceding claims, wherein said solver (161) implementsa numerical method for solving a system of linear equations (144).

30. The method of any of the preceding claims, wherein said solver (161) implementsan analytical method for solving said system of linear equations (144).

31. The method of any of the preceding claims, wherein said solver (161) is anoptimization algorithm.

32. The method of any of the preceding claims, wherein said solver (161) is arrangedto account for a predetermined maximum permissible error for said consumptionmeasurements (141).

33. The method of any of the preceding claims, wherein the error estimate (170) isassumed constant for at least a measurement duration of said multivariate time seriesof consumption measurements (141).

34. The method of any of the preceding claims, wherein said consumption errorestimate represents measurement errors of one or more of said metering devices (240).

35. The method of any of the preceding claims, wherein said error estimate (170)comprises a volume estimate and / or a flow estimate.

36. The method of any of the preceding claims, wherein said consumption error estimate and / or said leakage estimate comprises a percentage of volume and / or flow.

37. The method of any of the preceding claims, wherein said consumption error estimate is compared with a historical consumption error estimate by computing a difference between said consumption error estimate and said historical consumption error estimate.

38. The method of any of the preceding claims, wherein said system of linear equations(144) comprises one or more leakage variables modelling one or more leakages in saidwater distribution network (210).

39. The method of any of the preceding claims, wherein the steps of said water distribution network monitoring method are performed at a monitoring frequency.

40. The method of claim 39, wherein said monitoring frequency is on a timescale of seconds, minutes, hours, days, months, or years.

41. The method of any of the preceding claims, wherein said method further comprisesa step of performing a pressure test of said water distribution network (210) and storinga pressure test result.

42. The method of any of the preceding claims, wherein said method further comprisesa step of calibrating one or more of said metering devices (240).

43. A water distribution network monitoring system (90) comprising:a data processor (100) implementing a computer model (110) of a waterdistribution network (210), the computer model (110) comprising a plurality of nodes(130) linked by edges (121) in a tree structure (120) representing a pipe network (220)of the water distribution network (210); andmetering devices (240) installed in said water distribution network (210), eachmetering device (240) configured to provide a time series of consumptionmeasurements (141), each consumption measurement (141) comprising a consumptionrepresentation and a timestamp; wherein said data processor (100) is arranged to receive said consumptionmeasurements (141), establish a system of linear equations (144) on the basis of saidcomputer model (110) and said consumption measurements (141), and process thesystem of linear equations (144) on the basis of a solver (161) to obtain an errorestimate (170) comprising a consumption error estimate and / or a leakage estimate;wherein said error estimate (170) is associated with one or more of said meteringdevices (240) in said water distribution network (210).

44. The system according to claim 43, wherein said error estimate (170) comprises anindication of a geographical location with respect to said pipe network (220) of saidwater distribution network (210), wherein said geographical location is associated withsaid consumption error estimate and / or said leakage estimate.

45. The system according to any of the claims 43-44, wherein one or more of saidplurality of nodes (130) are metered consumption nodes (140) corresponding to saidmetering devices (240) of said water distribution network (210).

46. The system according to any of the claims 43-45, wherein said plurality of nodes(130) comprise at least one parent node (132) and one or more child nodes (133), andwherein said parent node (132) is linked to said child nodes (133) by edges (121).

47. The system according to claim 46, wherein each equation in said system of linearequations (144) is established from a subset of said consumption measurements (141),and wherein said subset of consumption measurements (141) are associated with aparent node (132) and one or more child nodes (133).

48. The system according to any of the claims 46-47, wherein said parent node (132)is associated with a calibrated metering device (240), the calibrated metering device(240) providing consumption measurements (141) with a measurement errorestablished to be within a range of a maximum permissible error.

49. The system according to any of the claims 43-48, wherein said error estimate (170)comprises an indication of a logical location with respect to said computer model (110), wherein said logical location is associated with said consumption error estimate and / or said leakage estimate.

50. The system according to any of the claims 43-49, wherein said pipe network (220)comprises at least a main pipe (221) and two or more branch pipes (222) branching offfrom said main pipe (221).

51. The system according to any of the claims 43-50, wherein the water distributionnetwork monitoring system (90) is configured for carrying out the method of any ofthe claims 1-42.

52. A data processing system comprising means for carrying out the method of any of the claims 1-42.

53. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the water distribution networkmonitoring method of any of the claims 1-42.

54. A computer-readable storage medium comprising instructions which, whenexecuted by a computer, cause the computer to carry out the method of any of theclaims 1-42.

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