Method for acquiring water leakage amount of leakage area in water distribution system

Abstract

The present invention relates to a method for acquiring the water leakage amount of a leakage area in a water distribution system. In the method, a hydraulic model is coupled with monitored data, and the water leakage amounts of different areas in the water distribution system are obtained through inversion by optimizing the spatial distribution of water leakage amounts. In addition to the coupling of the hydraulic model with the monitored data, virtual sectorization and pipe leakage risk assessment are used. By using a minimum difference between a simulated value and a monitored value at a pressure measurement point as a target, the water leakage amounts of different areas in the water distribution system are calculated by an optimization algorithm. Compared with the prior art, the present invention actualizes the effective identification of leakage areas in a water distribution system with a high leakage rate (i.e., with many leakage points).

Claims

1. A method for acquiring a water leakage amount of a leakage area in a water distribution system, which is used for acquiring the water leakage amount of an area to be measured, wherein the method comprises the following steps of: 1) using pressure sensors to measure a time sequence of monitored values of a free head at pressure measurement points, inputting data of the water distribution system, including a hydraulic model, an actual water leakage amount, a leakage risk value of each of a plurality of nodes and the area to be measured, and establishing a pipe leakage risk assessment model so as to acquire a leakage risk of each of the plurality of nodes; 2) reading indexes of nodes, indices of two endpoints of pipes of a pipe network and pipe lengths from the pipe leakage risk assessment model, and using the pressure sensors as sectorization centers and searching a shortest path by a Dijkstra algorithm on the basis of a weighted graph variable that is established based on a topology of the pipe network and by using the pipe lengths as weights, and dividing the pipes into virtual areas; and 3) selecting a target function and setting two penalty functions, i.e., a minimum free head penalty function and a water leakage amount penalty function, and searching an optimal spatial distribution of water leakage amounts to acquire water leakage amounts of different virtual areas.

2. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 1, wherein, in the step 3), a minimum difference between a monitored value and a simulated value of a pressure at a pressure measurement point is selected as a target function.

3. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 2, wherein the optimal spatial distribution of water leakage amounts is searched by a genetic algorithm to acquire the water leakage amounts of different virtual areas.

4. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 1, wherein acquiring a leakage risk of a node comprises following specific steps: 11) establishing the pipe leakage risk assessment model, and calculating a leakage risk value of each of the pipes, wherein the pipe leakage risk assessment model is expressed by:
h(u,Z)=h.sub.0(u)e.sup.βZ where h(u,Z) is the leakage risk value of a pipe; h.sub.0(u) is a reference risk function for pipe leakage; u is a pipe age; Z is another available factor (i.e., a co-variable) related to pipe leakage, except for the pipe age; and β is a coefficient matrix for the co-variable; and 12) equally distributing the leakage risk value of each of the pipes to two endpoints, and summing risk values of the endpoints to acquire a leakage risk value k of a node.

5. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 4, wherein establishing the pipe leakage risk assessment model specifically comprises following steps: 111) grouping, according to pipe material, pipes in a water distribution system and establishing pipe leakage risk assessment models for different groups, respectively; 112) using a leakage frequency as the reference risk functions for pipe leakage, and fitting results of calculation based on pipe repair records and Geographic Information System (GIS) information through a quadratic function, to obtain the reference risk function for pipe leakage: $h_0\left(u\right)=\frac{\underset{i=1}{\overset{m}{.Math.}}\frac{n\left(u_i{y}_i\right)}{W\left(y_i\right)}}{m}$ where n(u,y.sub.i) is a number of leakages of a pipe having an age of u within a period of time y.sub.i on a monthly basis, m means a total number of months in the calculated data; and W(y.sub.i) is a total length of pipes within the period of time y.sub.i; 113) calculating, together with information about a pipe diameter and pipe age in pipe repair records, a coefficient matrix p for the co-variable Z by Cox regression.

6. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 5, wherein dividing the pipes of the pipe network into the virtual areas specifically comprises following steps: 21) establishing, based on the indexes of nodes, the indices of two endpoints of pipes and pipe lengths, which are read in the step 1), a pipe network adjacency matrix, i.e., the weighted graph variable; and if there are N nodes and M pipes in the pipe network model, determining elements in the adjacency matrix A according to the following formula: $A_{ab}=\{\begin{array}{cc}\omega & \mathrm{if}\mathrm{node}a\mathrm{is}\mathrm{adjacent}\mathrm{to}\mathrm{node}b\\ \inf & \mathrm{if}\mathrm{node}a\mathrm{is}\mathrm{not}\mathrm{adjacent}\mathrm{to}\mathrm{node}b\end{array}$ where a is an index of a node, a=1, 2 . . . , N; b is an index of a pipe, b=1, 2 . . . , M; and ω is a pipe length; 22) by considering some or all of pressure measurement points input in the step 1 as the sectorization centers, on the basis of the adjacency matrix A, searching the shortest path from each of the N nodes to each of the sectorization centers by the Dijkstra algorithm to obtain a shortest path matrix D.sub.C×N, where C is a number of the sectorization centers; and 23) based on the shortest path matrix D.sub.C×N, finding a minimum value D.sub.c,a among elements in the a.sup.th column, wherein the node a belongs to a virtual area c containing a respective sectorization center, where c=1, 2 . . . , C.

7. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 3, wherein the minimum difference between the monitored value and the simulated value at a pressure measurement point selected as the target function is expressed by:
minΔp=[Σ.sub.f=1.sup.BΣ.sub.t=1.sup.T|p.sub.r,f,t−p.sub.x,f,t|]+H.sub.1+H.sub.2 where B is a number of pressure measurement points; T is a simulation duration; p.sub.r,f,t is a monitored value of a pressures at the pressure measurement point f at moment t; p.sub.x,f,t is a simulated value of the free head at the pressure measurement point f at the moment t when an emitter coefficient g.sub.a=k.sub.ax.sub.a of a node is set in the hydraulic model, where k.sub.a is a leakage risk value of the node a and x.sub.a is a value of a decision variable at the node a; H.sub.1 is the minimum free head penalty function; and H.sub.2 is the water leakage amount penalty function.

8. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 7, wherein three termination conditions are set for searching the optimal spatial distribution of water leakage amounts by the genetic algorithm, and the searching terminates if any one of the conditions is satisfied: condition 1: a limit value F of the target function is obtained, and the searching terminates when a minimum target function value calculated by the current population is equal to F; condition 2: the searching terminates, when an average relative change in a target function value of 50 successive generations of populations is less than 10.sup.−6; and condition 3: the searching terminates, when a number of iterations of the algorithm reaches a set maximum iteration number of 500.

9. The method for acquiring the water leakage amount of a leakage area in a water distribution system according to claim 8, wherein, after the searching terminates and an optimal solution is obtained, in the hydraulic model input in the step 1), the emitter coefficient g.sub.a=k.sub.ax.sub.a for each of the nodes is set for simulation, a current flow of each of a plurality of water consumption nodes at each of a plurality of simulation moments is read, and a leakage ratio identification value R.sub.0 of each of the virtual areas to be identified is obtained by the following formula: $R_0=\frac{\left[\underset{t=1}{\overset{T}{.Math.}}\underset{a_c=1}{\overset{N_c}{.Math.}}.Math.{\hat{q}}_{a_c,t}-q_{a_c,t}.Math.\right]}{\left[\underset{t=1}{\overset{T}{.Math.}}\underset{a=1}{\overset{N}{.Math.}}{q}_{a_{,t}}\right]\times 100}\%$ where N.sub.c is a number of water consumption nodes in virtual area c, {circumflex over (q)}.sub.a.sub.c.sub.,t is a current water consumption amount of node ac in the virtual area c at the moment t when the emitter coefficient g.sub.a=k.sub.ax.sub.a of a node is set in the hydraulic model, and q.sub.a.sub.c.sub.,t is a water consumption amount of the node ac in the virtual area c at the moment t.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic flowchart of the method according to the present invention; and

(2) FIG. 2 is a schematic view showing the pipe network and pressure measurement points according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

(3) The present invention will be described below in detail with reference to the accompanying drawings by specific embodiments. Apparently, the embodiments to be described are some but not all of embodiments of the present invention. All other embodiments obtained based on the embodiments in the present invention by a person of ordinary skill in the art without paying any creative effort shall fall into the protection scope of the present invention.

(4) The present invention relates to a method for acquiring the water leakage amount of a leakage area in a water distribution system. The method includes following steps.

(5) Step 1: Data of the water distribution system, including a hydraulic model, an actual water leakage amount, a time sequence of monitored values of the free head at pressure measurement points, a leakage risk value of each node and an area to be measured, is input to establish a pipe leakage risk assessment model so as to acquire a leakage risk of each node. The actual water leakage amount may be calculated by water balance analysis. If it is impossible, the water amount may be estimated by the formula in this method.

(6) Step 2: Sectorization centers are selected and the shortest path is searched by a Dijkstra algorithm on the basis of a weighed graph variable that is established based on the topology of the pipe network and by using the pipe length as a weight, and the pipe is divided into virtual areas.

(7) By using pressure sensors as sectorization centers, and the pipe length as a weight, the shortest path from a node to each sectorization center is searched to realize the division into virtual areas. The virtual partitions can constrain decision variables of nodes outside the range of pressure monitoring.

(8) Step 3: A minimum difference between a monitored value and a simulated value of the pressure at a pressure measurement point is selected as a target function, two penalty functions, i.e., a minimum free head penalty function and a water leakage amount penalty function, are set, and an optimal spatial distribution of water leakage amounts is searched by a genetic algorithm to calculate water leakage amounts of different areas in the water distribution system.

(9) To verify the effectiveness of the method of the present invention, in this case, actual experiments are conducted by taking actual data of the water distribution system in a certain region as an example. The operating process includes following steps.

(10) 1. Inputting and Reading Parameters

(11) An inp file of the hydraulic model of the water distribution system in a certain region, which is established by the real-time data and related meter reading data from August 6 in a certain year to August 12 in this year and then get verified, the indices of five pressure measurement points, the time sequence of monitored values of the free head, and the areas to be identified are input.

(12) Information about nodes, water pools, pipes and modes are read from the inp file. Information about nodes includes indices, coordinates, elevations, basic water consumption amounts and water consumption mode indices of nodes. As to water pools, it includes indices, coordinates, average gross heads and water supply mode indices of water pools. Information about pipes contains indices, indices of two endpoints and lengths of pipes. Information about modes consists of indices of modes and the time sequence values.

(13) According to the monitored data, the total water supply amount of this region within this period is about 266015 tons. Together with the production-and-sale difference ratio of this region of about 14.85%, the actual water leakage amount of this region within this period is estimated as 23149.98 m.sup.3±9.72%.

(14) Depending upon the pipe material, the pipes in this region are classified into six categories, i.e., galvanized steel pipes, plastic pipes, steel pipes, cast iron pipes, ductile iron pipes and pipes made of other materials. In accordance with the pipe leakage repair records in 2012-2017 and together with the pipe information in the GIS system, a water supply pipe leakage risk assessment model of this region is established by quadratic function fitting and Cox regression, as shown in Table 1.

(15) TABLE-US-00001 TABLE 1 Water supply pipe leakage risk assessment model of the region under study Pipe Description of material Pipe leakage risk h(u, d) parameters Galvanized (0.0004u2 − 0.0089u + 0.141) × u: pipe age, a; steel exp(0.124d) d: pipe diameter Plastic (0.0012u2 − 0.044u + 0.4429) × value assignment, exp(0.151d) in following rules: Steel (0.0002u2 + 0.002u + 0.1166) × 1-≤DN80; 2-(DN80, exp(−0.055d) DN100]; 3-(DN100, Cast iron (0.0003u2 − 0.0049u + 0.2415) × DN110]; 4-(DN110, exp(0.05d) DN125]; 5-(DN125, ductile (0.000008u2 − 0.0003u + DN150]; 6-(DN150, iron 0.0107) × exp(0.069d) DN400]; 7-(DN400, Others 0 DN500]; 8-(DN500, DN600]; 9-(DN600, DN700]; 10-(DN700, DN800];

(16) After the leakage risk value of each pipe in the water distribution system of this region is calculated by the model, the leakage risk value of each water consumption node in the model can be obtained.

(17) 2. Division into Virtual Areas

(18) After a pipe network adjacency matrix is established based on indexes of nodes, the indices of two endpoints of the pipes and pipe lengths, which are read in the step 1, five pressure measurement points of this region are selected as sectorization centers, and the shortest path is searched by a Dijkstra algorithm, so that a result of area dividing is obtained.

(19) 3. Solving an Optimal Solution

(20) By invoking the Matlab Genetic Algorithm Toolbox, population initialization, target function calculation, selection, crossover, mutation, reversion of elite individuals and other operations are executed to search an optimal solution until the calculation satisfies the termination condition, and the optimal solution is then outputted. The selection function is @selectionstochunif; the crossover function is @crossoverscattered, and the crossover probability is set as 0.8; the mutation function is @mutationadaptfeasible; and, the number of elite individuals is set as 2, that is, 2 best individuals in each generation of population will be reserved to a next generation.

(21) 4. Calculating the Water Leakage Amount of an Area

(22) By using the optimal solution together with information about the basic water consumption amount of each water consumption node in each area, a leakage ratio of each area to be identified is calculated, as shown in Table 2. Since the age of some pipes in the water distribution system of this region is unknown, the installation date of these pipes is discussed during the calculation of the leakage risk of each node. Although the calculated leakage ratios of areas are slightly different when the value of the installation time of a pipe with unknown age is different, it still can be known by comprehensively considering all results of calculation that the five areas in this region are sorted as A2, A5, A3, A1, A4, by the water leakage amount from the largest to the smallest. This sorting may be used for instructing the leakage control operation in this region.

(23) TABLE-US-00002 TABLE 2 The result of identification of the leakage ratio of each area Value of the installation time of a pipe with unknown age Ductile Galvanized Leakage ratio of each area (%) iron steel Others A1 A2 A3 A4 A5 1994 1970 1970 0.76 4.66 0.62 0.15 1.61 1994 1980 1980 0.49 4.51 0.79 0.10 1.91 1994 1990 1990 0.00 3.92 0.86 0.21 2.80 1994 1999 1999 0.04 3.71 1.28 0.10 2.66 1994 2004 2004 0.04 2.71 0.96 0.00 1.84 Irrespective of the leakage 0.11 2.64 2.05 0.17 2.82 risk of nodes

(24) In the present invention, a hydraulic model is coupled with monitored data to obtain leakage amount of each leakage area in a water distribution system. By coupling the hydraulic model of the water distribution system with the actual monitored data and by using virtual sectorization and leakage risk assessment, a minimum difference between a simulated value and a monitored value at a pressure measurement point is selected as a target function, and water leakage amounts of different areas in the water distribution system are calculated by an optimization algorithm, so that leakage areas in the water distribution system are identified. Accordingly, the leakage can be identified in time, the locations of leakage points can be identified accurately. It is advantageous for instructing the leakage control operation of this region.

(25) The foregoing description merely shows the specific implementations of the present invention, and the protection scope of the present invention is not limited thereto. Various equivalent modifications or replacements can be easily conceived by a person of ordinary skill in the art without departing from the technical scope disclosed by the present invention, and these modifications or replacements shall fall into the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the projection scope defined by the appended claims.