WO2014135953A2

WO2014135953A2 - Instrumenting water distribution networks

Info

Publication number: WO2014135953A2
Application number: PCT/IB2014/000241
Authority: WO
Inventors: Iyswarya NARAYANAN; Arunchandar Vasan; Venkatesh SARANGAN; Jamsheeda KADENGAL; Anand Sivasubramaniam
Original assignee: Tata Consultancy Services Limited
Priority date: 2013-03-05
Filing date: 2014-03-05
Publication date: 2014-09-12
Also published as: WO2014135953A3

Abstract

Described herein, is a method for instrumenting a water distribution network. According to an implementation, an adjacency matrix is generated for network topology of the water distribution network having pipes and nodes. The adjacency matrix is generated based on static physical properties related to the water distribution network. A centrality metric is computed for at least one of the pipes and the nodes based on the adjacency matrix. Based on the centrality metric, at least one of pipes and nodes, from amongst the pipes and the nodes, are identified for installation of at least one of meters and sensors.

Description

TECHNICAL FIELD

[0001] The present subject matter relates to instrumenting water distribution networks and, particularly but not exclusively, to instrumenting water distribution networks based on a centrality metric.

BACKGROUND

(0002) In cities, water is distributed from reservoirs to points of consumption through one or more water distribution networks. Water distribution networks have hydraulic elements, such as water pipes, and nodes. A node is a junction of two or more pipes. The water distribution networks are operated by an agency or an authority, referred to as a utility. The utility monitors the operation of water distribution networks by positioning meters and sensors at the hydraulic elements in the water distribution networks. The process of locating hydraulic elements across a water distribution network for installation of meters and/or sensors at such hydraulic elements is referred to as "Instrumenting" the water distribution network. The instrumenting of water distribution networks and, thereby, monitoring of hydraulic elements allows the utility to ensure a sustained supply and a reliable distribution of water to consumers.

SUMMARY

[00031 This summary is provided to introduce concepts related to instrumenting water distribution networks. This summary is neither intended to identify essential features of the claimed subject matter nor is it intended for use in determining or limiting the scope of the claimed subject matter.

[0004] In accordance with an implementation of the present subject matter, a method for instrumenting a water distribution network is described. An adjacency matrix is generated for network topology of the water distribution network having pipes and nodes. The adjacency matrix is generated based on static physical properties related to the water distribution network. A centrality metric is computed for at least one of the pipes and the nodes based on the adjacency matrix. Based on the centrality metric, at least one of pipes and nodes, from amongst the pipes and the nodes, are identified for installation of at least one of meters and sensors.

BRIEF DESCRIPTION OF DRAWINGS

[0005] The detailed description is described with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. The same numbers are used throughout the figures to reference like features and components. Some implementations of systems and/or methods in accordance with the present subject matter are now described, by way of example only, and with reference to the accompanying figures, in which:

[0006] Figure 1 illustrates a water distribution network instrumenting system, according to an implementation of the present subject matter.

[0007] Figure 2 illustrates a method for instrumenting a water distribution network, according to an implementation of the present subject matter.

[00081 It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative systems embodying the principles of the present subject matter. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

DETAILED DESCRIPTION

[0009] The present subject matter relates to methods and systems for instrumenting water distribution networks. Instrumenting a water distribution network means the process of identifying or locating hydraulic elements across a water distribution network for installation of meters and/or sensors at such hydraulic elements.

[0010] In view of the scale of water distribution networks and the cost involved, meters and/or sensors are not installed at all the hydraulic elements of the water distribution networks. The hydraulic elements include pipes and nodes of the water distribution network. A node is a junction of two or more pipes. Instrumenting of a water distribution network involves analysis of water distribution network through which some of the hydraulic elements are identified as important for monitoring and installation of meters and/or sensors.

[0011J The important hydraulic elements of a water distribution network are generally identified or located for installation of meters and/or sensors based on understanding of operations of the water distribution network. Conventionally, the understanding of operations is established through prior experience and knowledge of personnel involved in operating the water distribution network. The utility uses such information as empirical rules of thumb to identify the important hydraulic elements. When the operating conditions of a water distribution network change, for example, due to changes in demand and supply of water, the prior knowledge and experience of the personnel do not hold well. Thus, the important hydraulic elements are not correctly identified.

[0012J Further, conventionally, the understanding of operations of a water distribution network is established based on hydraulic model simulations. For this, a hydraulic model is created that maps the physical water distribution network. The hydraulic model is also calibrated so as to replicate the actual operations of the physical water distribution network. Typically, the creation and calibration of hydraulic models is costly, complex and time consuming. Further, with the set of parameters used for the creation and the calibration of hydraulic models, the actual operations of the physical water distribution network are not substantially replicated. This affects in correct identification of important hydraulic elements for instrumenting the water distribution network.

[0013] Further, important hydraulic elements of a water distribution network can be identified by computing a centrality metric for the hydraulic element. The centrality metric of a hydraulic element is a measure of importance of that hydraulic element with respect to other hydraulic elements of the water distribution network. The values of centrality metric enable in ranking the hydraulic elements based on the level of their importance. Conventionally, only the topological connectivity information of the water distribution network is used for computing the centrality metric. Conventional methodology does not involve characteristics of hydraulic elements that influence the operational behaviour of hydraulic elements in the water distribution network. Without using the characteristics of hydraulic elements and by only using the topological connectivity information, the computation of centrality metric and the identification of hydraulic element for installation of meters and/or sensors are not substantially accurate. With conventional methodologies, the hydraulic elements that are not important may be identified during instrumentation, or the hydraulic elements that are important may be missed during instrumentation.

[0014] The present subject matter describes methods and systems for instrumenting water distribution networks. In accordance with the present subject matter, water distribution networks are analyzed to determine which pipes carry more water-flow, which nodes experience more pressure, which pipes, upon failure, have higher impact on the operation of water distribution network, or which nodes are more suitable for detection of bursts. Such determinations, individually or collectively, facilitate in establishing an understanding of operations of the water distribution network and in identifying important hydraulic elements at which meters and/or sensors can be positioned.

[0015] With the methods and the systems of the present subject matter, a centrality metric is computed for at least one of the pipes and the nodes of the water distribution network. For the purposes of the present subject matter, the centrality metric of a pipe or a node is a measure of importance of the pipe or the node with respect to other pipes and nodes of the water distribution network. The values of centrality metric enable in ranking the pipes or the nodes based on the level of their importance in the water distribution network. In an implementation, the centrality metric is augmented with static physical properties related to the water distribution network. In an example, the static physical properties may include lengths and diameters of the pipes. This facilitates in ranking the pipes in accordance with the importance for amount of water being carried by the pipes, in ranking the nodes in accordance with the importance for pressure being experienced by the nodes, in ranking the pipes in accordance with the importance for failure impacts of the nodes, or in ranking the nodes in accordance with the importance for burst detection suitability at the nodes. Based on the rankings, the important pipes and/or nodes are identified for installation of meters and/or sensors.

[0016] The methodology of instrumenting water distribution networks, in accordance with the present subject matter, is substantially simple. As the analysis to identify hydraulic elements is based on the centrahty metric for the pipes and/or the nodes, the methodology of present subject matter is cost effective in comparison to conventional methodology that uses hydraulic model simulations. With this, the water distribution network can be instrumented by the utility with a budget smaller than that required for analysis through hydraulic models and simulations. Further, with the use of easily available static physical properties of the water distribution network for computing the centrahty metric, the identification of hydraulic elements is substantially efficient and accurate.

[0017] These and other advantages of the pre'sent subject matter would be described in greater detail in conjunction with the following figures. It should be noted that the description and figures merely illustrate the principles of the present subject matter.

[0018] Figure 1 illustrates a water distribution network instrumenting system 100, according to an implementation of the present subject matter. The water distribution network instrumenting system 100, hereinafter referred to as the system 100, is configured to perform an analysis of water distribution networks for the purpose of identification of pipes and/or nodes of the water distribution networks at which meters and/or sensors can be installed. The system 100 may be implemented in a computing device, such as a desktop computer, a laptop, a tablet, a personal digital assistant, a server, and the like.

[0019] In an implementation, the system 100 includes processor(s) 102. The processor(s) 102 may be implemented as microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) 102 fetch and execute computer-readable instructions stored in a memory. The functions of the various elements shown in Figure 1, including any functional blocks labeled as "processor(s)", may be provided through the use of dedicated hardware as well as hardware capable of executing non-transitory machine readable instructions. Moreover, the term processor may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing non-transitory machine readable instructions, random access memory (RAM), non-volatile storage. Other hardware, conventional and/or custom, may also be included.

[0020] The system 100 also includes interface(s) 104. The interface(s) 104 may include a variety of machine readable instruction-based and hardware-based interfaces that allow the system 100 to interact with other devices, including web servers, data sources and external repositories, for the purpose of instrumenting water distribution networks. Further, the interface(s) 104 may enable the system 100 to communicate with other communication devices, such as network entities, over a communication network.

[0021] Further, the system 100 includes memory 106, coupled to the processor(s) 102. The memory 106 may include any computer-readable medium including, for example, volatile memory (e.g., RAM), and/or non- volatile memory (e.g., EPROM, flash memory, etc.).

[0022] Further, the system 100 includes module(s) 108 and data 110. The modules 108 may be coupled to the processor(s) 102. The module(s) 108, amongst other things, include routines, programs, objects, components, data structures, and the like, which perform particular tasks or implement particular abstract data types. The module(s) 108 further include modules that supplement applications on the system 100, for example, modules of an operating system. The data 110 serves, amongst other things, as a repository for storing data that may be fetched, processed, received, or generated by the module(s) 108. Although the data 110 is shown internal to the system 100, it may be understood that the data 110 can reside in an external repository (not shown in the figure), which may be coupled to the system 100. The system 100 may communicate with the external repository through the interface(s) 104 to obtain information from the data 110.

[0023] In an implementation, the module(s) 108 of the system 100 includes a centrality metric computation module 112, an analysis module 114, and other module(s) 116. The centrality metric computation module 112, hereinafter, is simply referred as computation module 112. In an implementation, the data 110 of the system 100 includes water distribution network data 118, centrality metric data 120, analysis data 122, and other data 124. The other module(s) 1 16 may include programs or coded instructions that supplement applications and functions, for example, programs in the operating system of the system 100, and the other data 124 comprise data corresponding to other module(s) 116.

[0024) The following description describes the instrumenting of one water distribution network through the system 100, in accordance with the present subject matter, and it will be understood that the concepts thereto may be extended to instrument multiple water distribution networks in a similar manner.

[0025] For the purpose of instrumenting a water distribution network, the computation module 112 generates an adjacency matrix for a network topology of the water distribution network. The network topology illustrates the arrangement and the linkages of pipes and nodes in the water distribution network. The data related to the network topology is stored in the water distribution network data 1 18. The adjacency matrix of the water distribution network captures the connectivity information between the nodes and represents which nodes are adjacent to other nodes. The adjacency matrix for the network topology having multiple nodes is a two dimensional square matrix of the order equal to the number of nodes. Each element of the adjacency matrix corresponds to a pair of nodes and is indicative of connectivity information from one node to the other for that pair.

[0026] In an implementation, the adjacency matrix is generated based on static physical properties related to the water distribution network. The connectivity information in an element for a pair of nodes is based on the static physical properties for the pipe between the pair of nodes. With the static physical properties for the pipe, the characteristics of the pipe that influence the flow of water through the pipe are incorporated in the connectivity information for the pair of nodes. The static physical properties may include length of the pipe, diameter of the pipe, thickness of wall of the pipe, material property of the pipe, material property of water. The static physical properties of pipes that are utilized for generating the adjacency matrix depend on the centrality metric that is computed for the purposes of the present subject matter. The data related to static physical properties of the water distribution network is stored in the water distribution network data 118, and the data related to the generated adjacency matrix is stored in centrality metric data 120.

[0027] Based on the adjacency matrix, the computation module 112 computes a centrality metric for at least one of the pipes and the nodes of the water distribution network. The centrality metric is computed for the pipes and/or the nodes to determine the importance of pipes or nodes depending on one or more of the following basis:

(a) which pipes carry more water-flow;

(b) which nodes experience more pressure;

(c) which pipes, upon failure, have higher impact on the operation of water distribution network; and

(d) which nodes are more suitable for detection of bursts.

The data related to the computed centrality metric is stored in the centrality metric data 120.

[0028] In an implementation, a current-flow centrality metric for the pipes is computed for determining importance of pipes based on the amount of water flowing through them, for determining the importance of nodes based on the pressure experienced by them, or for determining the importance of pipes based on their impact of failure on the operation of water distribution network. The current-flow centrality metric for a pipe quantifies the average amount of water that would pass through that pipe.

[0029] In an implementation, a closeness centrality metric for the nodes is computed for determining importance of nodes based on their suitability for burst detection. The closeness centrality metric for a node is a measure of degree of closeness of that node to other nodes.

[0030] Further, based on the computed centrality metric, the analysis module 114 processes the values of the centrality metric and identifies the pipes and/or the nodes that are important for positioning meters, such as flow meters, and/or sensors, such as pressure sensors or burst detection sensors. For such identification, the analysis module 114 ranks the pipes and/or the nodes for their importance either directly, based on the values of the computed centrality metric, or based on further processing of the values of the computed centrality metric as described later in the description. The data obtained from the processing of value of centrality metric for identification of pipes and/or nodes is stored in the analysis data 122.

[0031] The description below describes the details of instrumenting a water distribution network to identify pipes or nodes, individually, on the basis of which pipes carry more water- flow, or which nodes experience more pressure, or which pipes, upon failure, have higher impact on the operation of water distribution network, or which nodes are more suitable for detection of bursts. In an implementation, either one or a combination of analyses may be followed in instrumenting the water distribution network.

[0032] Consider a case where the water distribution network has E number of pipes and V number of nodes. The water distribution network is represented as a network topology illustrating the linkages of the pipes and the nodes. For the purposes of description herein, the pipes are denoted as (pi, p₂, · · · , PE) and the nodes are denoted as (ni , n₂, ... , ny). Further, the adjacency matrix is denoted as [A] and the element with the connectivity information from i^th node nj to the j^th node n_j is denoted as Aj_j. Further, the current-flow centrality metric for i^th pipe p, is denoted as MF(P_I), and the closeness centrality metric for i^th node n, is denoted as Mc(ni).

Identification of pipes that carry more water- flow [0033 J For identifying the pipes that carry more water-flow, current-flow centrality metric Mp for all the pipes is computed. For this, based on the network topology of the water distribution network, the computation module 112 generates the adjacency matrix [A] with elements A s of the adjacency matrix [A] taking the values based on equation (1) below:

Ai_j = D⁵/L : for a pair of i^th and j^th nodes (ni, n_j)

directly connected to each other; and

Aj_j = 0 : for a pair of i^th and j^th nodes (nj, n_j) (1)

not directly connected to each other, where D is the diameter and L is the length of the pipe connecting, the nodes (n,, n_j), and i and j take values from 1 to V (number of nodes). A pair of nodes (ni, n_j) is considered to be directly connected if the nodes are connected through a single pipe without any other node in between. A single pipe may be understood as one physical pipe or one pipe equivalent to multiple parallel physical pipes between the pair of nodes. If a pair of nodes (nj, nj) is connected through multiple parallel physical pipes, without any other node in between, the single pipe is an imaginary pipe that offers a resistance equivalent to that offered by the multiple pipes. A pair of nodes (nj, n_j) is considered to be not directly connected if the nodes are not connected through a single pipe.

[0034] The value of D⁵/L for a pipe is indicative of hydraulic admittance of the pipe. By incorporating hydraulic admittance of pipes in the adjacency matrix [A], connectivity information between the adjacent nodes, with respect to allowance of water to flow through the pipes, is captured in adjacency matrix [A]. This facilitates in computing the current-flow centrality metric Mp and identify important pipes and/or nodes in the water distribution network for installation of meters and/or sensors with substantial accuracy.

[0035] Based on the adjacency matrix [A], the computation module 1 12 computes the current-flow centrality metric Mp for all the pipes p of the water distribution network. For computing the current-flow centrality metric MF(P for an i^th pipe p,, all those pairs of nodes are identified for which the pipe p, lies in the path connecting the pair. For each identified pair of s^th and t^th nodes (n_s, n_t), a fraction of water-flow from the node n_s to the node n, and passing through the pipe pi is determined. This fraction of water-flow is denoted as I_Pi(n_s, n,) and is determined using the adjacency matrix [A] as generated based on equation (1 ).

[0036] In an implementation, fractions of water-flow I_Pi through the pipe pi for all the identified pairs of nodes are computed using current-flow betweenness that uses the adjacency matrix [A] of equation (1). For this computation, a Laplacian matrix, denoted as [L], of the adjacency matrix [A] is computed. The elements LyS of the Laplacian matrix [L] take the values based on equation (2) below:

Li_j = - A : for i≠j, (2)

where the summation is over j = 1 to V (number of nodes) except j = i, and i and j take values from 1 to V (number of nodes).

[0037] For computing the fraction of water-flow in the pipe p, from the s^th node n_s to the t^lh node n_t, a proxy water-supply vector, denoted as [b], is generated over all the nodes n of the water distribution network. The elements b of the proxy water-supply vector [b] take the values based on equation (3) below:

b(n_v) = 1 : if v = s;

b(n_v) = -l : if v = t; and (3)

b(n_v) = 0 : v Φ s and v≠ t,

where v = 1 to V (number of nodes). Now, considering that the total water-flow entering a node is equal to the total water-flow leaving the node, and the total potential of water across a closed loop in the water distribution network is zero, a proxy water-potential vector, denoted as [D], over all the nodes n is computed based on equation (4) below:

[D] = [!/) ]. (4)

Considering that the proxy water-supply vector [b] has only two non-zero values, i.e., the values for the nodes n_s and n_t, the proxy water-potential vector [D] computed through equations (2) and (3) is indicative of water-potentials for the pair of nodes n_s and n_t.

[0038] After computing the proxy water-potential vector [D], a water-flow vector, denoted as [I], for all the pipes p is computed based on equation (5) below: [I] = [B][D]. (5)

Here [B] is a matrix computed based on adjacency matrix [A]. The element B_kj of the matrix [B] is indicative of the admittance of k^th pipe p_k with respect to the j^th node n_j. Considering that the pipe p_k is between a node n_u at a higher water- potential and a node n_v at a lower water-potential, the elements B_kj take values based on equation (6) below:

B = A_u<v : if j = u;

B_kj = - A_u,v : if j = v; and (6)

B_kj = 0 : if j≠ u and j≠ v,

where k = 1 to E (number of pipes) and j = 1 to V (number of nodes).

[0039] Now, the value of the element in the water-flow vector [I] corresponding to the pipe pi is the fraction of water-flow I_Pi(n_s, n_t) for the nodes n_s and n_t. The fractions of water-flow I_pi through the pipe pi for all the identified pairs of nodes are computed in a similar manner.

[0040] After determining the fractions of water-flow I_p; for all the pairs of nodes identified for the pipe pi, the current-flow centrality metric MF(P is computed based on equation (7) below:

where the summation is over all the identified pair of nodes belonging to the V number of nodes. The current-flow centrality metric Mp for all the pipes p are computed in a similar manner.

[0041] After the current-flow centrality metric MF for all the pipes are computed, the analysis module 114 processes the current-flow centrality metric MF to rank the pipes in accordance with the values of current-flow centrality metric Mp. The ranking is indicative of pipes that carry more water-flow through them. Based on the ranking, the analysis module 1 14 identifies the pipes that are important for positioning meters and/or sensors.

[0042] In an example, the pipes are ranked according to the descending order of values of current-flow centrality metric Mp, and a predefined percentage of pipes in top of the order are identified as the pipes for positioning meters and/or sensors. The predefined percentage may be in a range from about 10 % to about 50 %.

Identification of nodes that experience more pressure

[0043] The pressure experienced by the nodes is related to the pressure head at the nodes. The pressure head is indicative of active component of energy of the water. The stress on the wall of a pipe and the rate of leakage of water from the pipe or the nodes depends on the total pressure head at the associated nodes. Thus, for identifying the nodes that experience more pressure, the total pressure head for all the nodes is computed. For the purpose of the description herein, the total pressure head for an i^th node nj is denoted as H(n;).

[0044] For this, based on the network topology of the water distribution network, the computation module 112 generates the adjacency matrix [A] with elements Ays of the adjacency matrix [A] taking the values as per equation (1). Based on the adjacency matrix [A], the computation module 112 computes the current-flow centrality metric Mp for all the pipes p of the water distribution network as described above through equation (7).

[0045] Further, based on the computed current-flow centrality metric MF for all the pipes p, the analysis module 1 14 computes the total pressure head H for all the nodes n. The description for computing the total pressure head H for the nodes n is described below.

[0046] Consider a case where the water distribution network has s number of reservoirs. The r^th reservoir is denoted as R_r. For computing the total pressure head H(n for the node n„ the pressure head at the node nj due to r^th reservoir R_r is computed. For this, the shortest path from the reservoir R_r to the node n_f is identified. The shortest path is denoted as QR_r,ni. The reservoir R_r is understood to be as a node in the network topology of the water distribution network. The shortest path Q_R^ is identified as a path from the node representing the reservoir R_r to the node n, for which the sum of the elements of the adjacency matrix [A] governing the path is minimum. The length of the path may be understood as the hydraulic distance between the reservoir R_r and the node nj.

[0047] After the shortest path QR_r>ni is identified, the pressure head at the node ni due to r^th reservoir Rr, denoted as Z_ni_;R_r, is computed based on equation (8) below:

where liRr is the pressure head of the reservoir R_r, Mp(p_j) is the current-flow centrality metric for j^th pipe pj in the shortest path (¾._Γ,_ηί, Lp_j is the length of the pipe pj, R_Pj is the radius of the pipe pj, and K is a constant that normalizes the unit of the summation term to the unit of liR_r. The term pj e (¾_Γ,_ηί means all the pipes that are in the shortest path <¾_Γ,_η,.

[0048J The pressure heads Z^R at the node nj due to all the reservoirs R are computed in a similar manner. After such computation, the total pressure head H(ni) for the node n; is computed based on equation (9) below:

Σ Z ni.Rr

H(n, j h_ni , (9)

s

where h_ni is the pressure head due to elevation or depression of the node j, and the summation is over all the reservoirs R. The total pressure heads H for all the nodes n are computed in a similar manner.

[0049] In an implementation, the constant K of equation (8) is determined by computing the total pressure head H(n_z) for a node n_z having the highest elevation in the water distribution network and equating the value of the total pressure head H(n_z) to the minimum pressure that is to be maintained in the water distribution network.

[0050] After the total pressure heads H for all the nodes are computed, the analysis module 1 14 processes the total pressure heads H to rank the nodes in accordance with the values of total pressure heads H for the nodes. The ranking is indicative of which nodes experience more pressure. Based on the ranking, the analysis module 1 14 identifies the nodes that are important for positioning meters and/or sensors.

[0051] In an example, the nodes are ranked according to the descending order of values of total pressure heads H, and a predefined percentage of nodes in top of the order are identified as the nodes for positioning meters and/or sensors. The predefined percentage may be in a range from about 10 % to about 50 %.

Identification of pipes that, upon failure, have higher impact on the operation of water distribution network

[0052] The failure of pipe refers to the bursting of pipe. When a pipe fails, the failed pipe is blocked and the water-flow is re-routed through another path. With the re-routing, the path taken by the water may be longer. This results in decrease in the pressure at the point of consumption. For maintaining the pressure at the point of consumption, an additional energy is to be provided in the alternate path that is taken by the water. The additional energy to be provided is related to the impact of a failed pipe on the operation of water distribution network. Thus, for identifying the pipes that have higher impact on failure, an alternate path centrality metric for all the pipes p is computed considering the pipes, individually, have failed. The alternate path centrality metric for a failed pipe is a measure of pressure head loss at all the nodes n due to the failure of the pipe. The pressure head loss qualitatively defines the impact and the additional energy to be provided for the alternate path when a pipe has failed. For the purpose of the description herein, the alternate path centrality metric for an i^th pipe pi, when failed, is denoted as APC(pj).

[0053] Initially, based on the network topology of the water distribution network, the computation module 1 12 generates the adjacency matrix [A] with elements Aj_jS of the adjacency matrix [A] taking the values as per equation (1). Based on the adjacency matrix [A], the computation module 1 12 computes the current-flow centrality metric Mp for all the pipes p of the water distribution network as described above through equation (7). Further, based on the computed current- flow centrality metric MF for all the pipes p, the analysis module 1 14 computes the total pressure heads H for all the nodes n as described above through equation (8) and equation (9).

[0054] For computing the alternate path centrality metric APC(pi) for the i^lh pipe p., the pipe pi is removed from the network topology. The removal of pipe p, governs the failure of the pipe p;. Now, for the revised network topology of the water distribution network without the pipe p,, the computation module 112 generates the adjacency matrix [Α'] with elements A'jjS of the adjacency matrix [Α'] taking the values as per equation (1 ). Based on the adjacency matrix [Α'], the computation module 112 computes the current-flow centrality metric M'F for all the pipes p of the water distribution network as described above through equation (7). Further, based on the computed current-flow centrality metric M'F for all the pipes p, the analysis module 114 computes the total pressure heads H' for all the nodes n as described above through equation (8) and equation (9). The total pressure heads H' are the total pressure heads for the nodes when the pipe pj not present in the water distribution network.

[0055) Now, the analysis module 114 computes the alternate path centrality metric APC(pi) based on equation (10) below:

where the summation is over all the nodes n. The alternate path centrality metric APC for all the pipes p are computed in a similar manner.

[0056] After the alternate path centrality metric APC for all the pipes are computed, the analysis module 114 processes the alternate path centrality metric APC to rank the pipes in accordance with the values of alternate path centrality metric APC. The ranking is indicative of which pipes have higher impact upon failure. Based on the ranking, the analysis module 114 identifies the pipes that are important for positioning meters and/or sensors.

[0057] In an example, the pipes are ranked according to the descending order of values of alternate path centrality metric APC, and a predefined percentage of pipes in top of the order are identified as the pipes for positioning meters and/or sensors. The predefined percentage may be in a range from about 10 % to about 50 %.

Identification of nodes more suitable for detection of bursts

[0058] When a pipe bursts, the pressure at the point of burst reduces. The reduction in pressure generates transient pressure waves that travel through the adjacent pipes along the surface of the pipes. Further, burst detection sensors, if placed in the path of these transient pressure waves, can determine the magnitude and the time of the reduction in pressure due to the burst. Based on these determinations, the locations of the burst can be detected. For the detection of burst, it is important to position burst detection sensors at specific nodes. The nodes which are closest to other nodes can be considered as important nodes for positioning burst detection sensor so that the transient pressure waves can be sensed in a substantially short time. Thus, for identifying the nodes that are more suitable for detection of burst, the closeness centrality metric Mc for all the nodes n is computed.

[0059] For this, based on the network topology of the water distribution network, the computation module 112 generates the adjacency matrix [A] with elements Aj_jS of the adjacency matrix [A] taking the values based on equation (11) below:

Ay = L/v : for a pair of i'^h and j"¹ nodes (η,, n_j)

directly connected to each other; and

Aj_j = co : for a pair of i^th and j^th nodes (ni, n_j) (1 1)

not directly connected to each other,

where L is the length of the pipe connecting the nodes (n,, n_j), v is the velocity of transient pressure wave through the pipe connecting the nodes (nj, n_j), and i and j take values from 1 to V (number of nodes). As mentioned earlier, a pair of nodes (nj, n_j) is considered to be directly connected if the nodes are connected through a single pipe without any other node in between. A single pipe may be understood as one physical pipe or one pipe equivalent to multiple parallel physical pipes between the pair of nodes. If a pair of nodes (nj, n_j) is connected through multiple parallel physical pipes, without any other node in between, the single pipe is an imaginary pipe that offers a resistance equivalent to that offered by the multiple pipes. A pair of nodes (n,, n_j) is considered to be not directly connected if the nodes are not connected through a single pipe.

[0060] The value of velocity of transient pressure wave v(pj) through the i^th pipe pj is defined by equation (12) below:

K

(12)

where K is the bulk modulus of elasticity of water, p is the density of water, E_Pi is the Young's modulus of elasticity of walls of pipe pi, R is the radius of pipe pi, is the thickness of wall of pipe pi, and θ_ρι is the a predefined parameter based on anchoring of pipe pi in the water distribution network.

[0061] By incorporating values of L/v for pipes in the adjacency matrix [A], connectivity information between the adjacent nodes, with respect to generation transient pressure waves in the pipes, is captured in adjacency matrix [A]. This facilitates in computing the closeness centrality metric Mc and identify important nodes in the water distribution network for installation of meters and/or sensors with substantial accuracy.

[0062] Based on the adjacency matrix [A], the computation module 112 computes the closeness centrality metric Mc for all the nodes n of the water distribution network. For computing the closeness centrality metric Mc(n,) for an i^th node n_i; the shortest paths from the node η,· to all the other nodes are identified and the distances of the shortest paths from the node nj to all other nodes are determined. The distance of the shortest path between the node n, and the t^th node n_t is denoted as 5_ni,_m. The shortest path between the nodes nj and n_t is identified as a path for which sum of the values of the elements of the adjacency matrix [A] governing the path is minimum. The value of 5_{ni nt} is considered as the distance of such identified path. The distance 6 of the path may be understood as the hydraulic distance between the nodes ni and n_t. [0063] After determining the distances δ of the shortest paths between the node n; and the other nodes, the closeness centrality metric Mc(n,) is computed based on equation (13) below:

where V is the number of nodes, and the summation is over all the nodes except the node n,. The closeness centrality metric Mc for the nodes n are computed in a similar manner.

[0064] After the closeness centrality metric Mc for all the nodes are computed, the analysis module 114 processes the closeness centrality metric to rank the nodes in accordance with the values of closeness centrality metric Mc. The ranking is indicative of which nodes are suitable for positioning burst detection sensors and detecting the bursts. Based on the ranking, the analysis module 114 identifies the nodes that are important for positioning meters and/or sensors.

[0065] In an example, the nodes are ranked according to the descending order of values of closeness centrality metric Mc, and a predefined percentage of nodes in top of the order are identified as the nodes for positioning meters and/or sensors. The predefined percentage may be in a range from about 10 % to about

50 %.

[0066] In an implementation, the instrumenting may be done by a utility for a new water distribution network or for updating an existing water distribution network. In an implementation, the instrumenting may be done by a utility for calibrating a new hydraulic model of a water distribution network or for updating the calibration of an existing hydraulic model of a water distribution network.

[0067] Figure 2 illustrates a method 200 for instrumenting a water distribution network, according to an implementation of the present subject matter. The order in which the method 200 is described is not intended to be construed as a limitation, and any number of the described method blocks can be combined in any order to implement the method 200, or an alternative method. Additionally, individual blocks may be deleted from the method 200 without departing from the spirit and scope of the subject matter described herein.

[0068J Furthermore, the method 200 can be implemented by processor(s) or computing devices in any suitable hardware, non-transitory machine readable instructions, or combination thereof. It may be understood that steps of the method 200 may be executed based on instructions stored in a non-transitory computer readable medium as will be readily understood. The non-transitory computer readable medium may include, for example, digital data storage media, digital memories, magnetic storage media, such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media.

[00691 Further, although the method 200 may be implemented in any computing device; in an example described in Figure 2, the method 200 is explained in context of the aforementioned system 100, for the ease of explanation.

[0070] Referring to Figure 2, at block 202, an adjacency matrix [A] is generated for the network topology of a water distribution network having pipes and nodes. The adjacency matrix [A] is generated by the system 100 based on static physical properties related to the water distribution network. The adjacency matrix [A] is generated depending on the centrality metric that is to be computed for identifying the pipes and/or the nodes for positioning or installing meters and/or sensors. In an example, if the current-flow centrality metric Mp for the pipes is to be computed, the adjacency matrix [A] is generated based on the length and the diameter of the pipes in accordance with equation (1) as mentioned earlier. In an example, if the closeness centrality metric Mc for the nodes is to be computed, the adjacency matrix [A] is generated based on the length of the pipes and the velocity of transient pressure waves in the pipes in accordance with equation ( 11) as mentioned earlier.

[0071 J At block^j204, based on the adjacency matrix [A], a centrality metric is computed for at least one of the pipes and the nodes. The centrality metric is computed by the system 100 depending on the basis or the criterion of identifying the pipes or the nodes that are important. In an example, for identifying which pipes carry more water-flow, or which nodes experience more pressure, or which pipes, upon failure, have higher impact on the operation of water distribution network, the current-flow centrality metric MF for the pipes is computed in accordance with equation (7) as mentioned earlier. In an example, for identifying which nodes are more suitable for positioning burst detection sensors or detection of bursts, the closeness centrality metric Mc for the nodes is computed in accordance with equation (13) as mentioned earlier.

[0072] After computing the centrality metric, the values of the centrality metric are processed and at least one of pipes and nodes, from amongst the pipes and the nodes, which are important for installation or positioning of meters and/or sensors are identified at block 206. The processing and the identification are performed by the system 100.

[0073] 1° a° example, for identifying the pipes that carry more water- flow, the pipes are ranked based on the computed values of current-flow centrality metric MF for the pipes. The order of ranking is indicative of pipes which carry more water-flow and thus are important for installation or positioning of meters and/or sensors.

[0074] In an example, for identifying the nodes that experience more pressure, the total pressure heads H for all the nodes are computed based on the current- flow centrality metric Mp for the pipes as described earlier, and the nodes are ranked based on the computed values of total pressure heads H for the nodes. The order of ranking is indicative of which nodes experience more pressure and thus are important for installation or positioning of meters and/or sensors.

[0075] In an example, for identifying the pipes that have higher impact upon failure, the alternate path centrality metric APC for all the pipes is computed based on the current-flow centrality metric Mp and based on the total pressure heads H as described earlier, and the pipes are ranked based on the computed values of alternate path centrality metric APC for the pipes. The order of ranking is indicative of which pipes have higher impact upon failure and thus are important for installation or positioning of meters and/or sensors. [0076] In an example, for identifying the nodes that are more suitable for detection of bursts, the nodes are ranked based on the computed values of closeness centrality metric Mc for the nodes. The order of ranking is indicative of which nodes are more suitable for detection of bursts and thus are important for installation or positioning of meters and/or sensors.

[0077] Although implementations for the methods and the systems have been described in language specific to structural features, it is to be understood that the invention is not necessarily limited to the specific features described. Rather, the specific features are disclosed and explained in the context of a few implementations for the methods and the systems.

[0078] Other advantages of the methods and the systems of the present subject matter will become better understood from the description and claims of an exemplary implementation of the methods and the systems. The methods and the systems of the present subject matter are not restricted to the implementations that are mentioned above in the description.

[0079] Although the subject matter has been described with reference to specific implementations, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed implementations, as well as alternate implementations of the subject matter, will become apparent to persons skilled in the art upon reference to the description of the subject matter. It is therefore contemplated that such modifications can be made without departing from the spirit or scope of the present subject matter as defined.

Claims

I/We claim:

1. A method for instrumenting a water distribution network, the method comprising:

generating, by a processor (102), an adjacency matrix for network topology of the water distribution network having pipes and nodes, wherein the adjacency matrix is generated based on static physical properties related to the water distribution network;

computing, by the processor (102), a centrality metric for at least one of the pipes and the nodes based oh the adjacency matrix; and

identifying, by the processor (102), based on the centrality metric, at least one of pipes and nodes, from amongst the pipes and the nodes, for installation of at least one of meters and sensors.

2. The method as claimed in claim 1, wherein the static physical properties comprise lengths and diameters of the pipes in the water distribution network.

3. The method as claimed in claim 2, wherein,

for a pair of nodes connected directly to each other through a single pipe, an element of the adjacency matrix has a value of diameter of the single pipe raised to power five divided by length of the single pipe; and

for a pair of nodes not connected directly to each other, an element of the adjacency matrix has a value of zero.

4. The method as claimed in claim 1, wherein the centrality metric is a current- flow centrality metric for the pipes, wherein the current-flow centrality metric for each of the pipes is indicative of average amount of water passing through the each pipe.

5. The method as claimed in claim 4, wherein the identifying of the pipes is based on pipes that carry more water-flow, and wherein the identifying comprises ranking the pipes based on the current-flow centrality metric for the pipes.

6. The method as claimed in claim 4, wherein the identifying of the nodes is based on nodes that experience more pressure head, and wherein the identifying comprises:

computing total pressure head for the nodes based on the current-flow centrality metric for the pipes; and

ranking the nodes based on the total pressure head for the nodes.

7. The method as claimed in claim 4, wherein the identifying of the pipes is based on pipes that have higher impact of failure on operation of the water distribution network, and wherein the identifying comprises:

computing total pressure head for the nodes based on the current- flow centrality metric for the pipes;

for each of the pipes, comparing the total pressure head with a pressure head for the nodes when the each pipe is removed from the water distribution network;

computing an alternate path centrality metric for each of the pipes based on the comparison; and

ranking the pipes based on the alternate path centrality metric for the pipes.

8. A system (100) for instrumenting a water distribution network, the system (100) comprising:

a processor (102); and

a centrality metric computation module (112) coupled to the processor (102) to:

generate an adjacency matrix for network topology of the water distribution network having pipes and nodes, wherein the adjacency matrix is generated based on static physical properties related to the water distribution network; and

compute a centrality metric for at least one of the pipes and the nodes based on the adjacency matrix; and

an analysis module (114) coupled to the processor (102) to: identify, based on the centrality metric, at least one of pipes and nodes, from amongst the pipes and the nodes, for installation of at least one of meters and sensors.

9. The system (100) as claimed in claim 8, wherein,

10. The system (100) as claimed in claim 9, wherein the centrality metric is a current-flow centrality metric for the pipes, the current-flow centrality metric for each of the pipes is indicative of average amount of water passing through the each pipe.

11. The system (100) as claimed in claim 10, wherein the analysis module (114) ranks the pipes based on the current-flow centrality metric for the pipes.

12. The system (100) as claimed in claim 8, wherein the static physical properties comprise lengths of the pipes in the water distribution network and velocities of transient pressure waves in the pipes in the water distribution network.

13. The system (100) as claimed in claim 12, wherein,

for a pair of nodes connected directly to each other through a single pipe, an element of the adjacency matrix has a value of length of the single pipe divided by velocity of transient pressure wave in the single pipe; and

for a pair of nodes not connected directly to each other, an element of the adjacency matrix has a value of infinity.

14. The system (100) as claimed in claim 12, wherein the centrality metric is a closeness centrality metric for the nodes, the closeness centrality metric for each of the nodes is indicative of degree of closeness of the each node to other nodes in the water distribution network.

15. The system (100) as claimed in claim 14, wherein the nodes are identified based on nodes which are more suitable for positioning burst detection sensors, and wherein the analysis module (114) ranks the nodes based on the closeness centrality metric for the nodes.

16. A non-transitory computer-readable medium comprising instructions executable by a processor to:

generate an adjacency matrix for network topology of a water distribution network having pipes and nodes, wherein the adjacency matrix is generated based on static physical properties related to the water distribution network; compute a centrality metric for at least one of the pipes and the nodes based on the adjacency matrix; and

identify, based on the centrality metric, at least one of pipes and nodes, from amongst the pipes and the nodes, for installation of at least one of meters and sensors.