Abstract

Usage of the appropriate model of water distribution systems (WDS) enables easier everyday operations and management decisions. Creating a reliable model of WDS requires a large amount of system response data for different case scenarios. Commonly used software for creating models of WDS is EpaNet. Ongoing processes in WDS, such as pipe bursts, permanently closed valves which are not registered in the data base and other inconsistencies will change WDS network topology, so WDS validation tests are to be applied from time to time. This paper presents the WDS network topology validation test conducted on one district metered area of Belgrade with two inflows. The pressure drop test combined with genetic algorithm and ant colony optimization are simple hydroinformatic tools available for network topology validation. The system's reaction under a pressure change during the isolation test was measured at two observation points. Obtained results are then compared with assumed WDS topology using 55 potential locations of inconsistencies in the EpaNet model. This step is repeated until a good enough match between results from the real system and the created model's version is obtained. Heuristic optimization algorithms are used for speeding up the process of finding a satisfactory match (unknown locations of inconsistencies) by minimizing or maximizing the defined criteria function.

INTRODUCTION

Having a reliable mathematical model of water distribution systems (WDS) enables the user more easily to operate and optimally manage the water supply system. When the appropriate simulation algorithm is implemented, it is possible to detect unplanned changes in WDS such as pipe bursts and pumps out of service (Giustolisi et al. 2008; Bicik et al. 2014; Jung & Lansey 2014; Wright et al. 2014; Laucelli et al. 2016) or to detect leakage (Wu 2008). However, the development of the WDS mathematical model is a challenging task. Early stages of mathematical model development require a number of simplifications and conceptualizations especially in the network layout (network topology) that lead to a number of differences between model and real system. A proper calibration of the WDS model can reduce the influence of those differences, but to gain confidence in the model, it has to be validated after the calibration, by comparing its performance with the real system state. The significance of the knowledge of water distribution network (WDN) topology can be seen in the research by Giudicianni et al. (2018), where detailed taxonomy of both synthetic and real systems is presented. Topology has significant impact on the hydraulic performance of water supply systems. Therefore, Torres et al. (2016) analyzed this problem through graph theory. Detection of the primary network in original WDN topology that can guarantee minimum hydraulic requirements in order to reduce investment in network extent is presented by Di Nardo et al. (2018). Here, knowledge of the original WDN topology is crucial, which confirms the need for topology validation.

Leakage detection and other changes in the water distribution network are inferred by measuring pressures or flows at certain locations in the network (Giorgio Bort et al. 2014). Significant changes in pressure or flow are considered as indicators of the leakage presence and/or other problems in the water distribution network.

WDS topology validation can be performed by introducing large pressure or flow changes and measuring the reaction of the WDS to these generated scenarios. The changes could be made by closing the isolating valves in the water distribution network or by increasing water ‘consumption’ (opening hydrants or drain outlets) at a selected number of nodes (Morrison et al. 2007). Comparison of the results obtained on the real system and results obtained from the WDS model can be used to search for real inconsistencies in the network. Applying heuristic optimization algorithms (HOA) leads to the problem solution much faster than using brute force search algorithms, which seek for the solution by testing all possible combinations (Rao 2009).

HOA are well applied in solving different problems in WDS. Babayan et al. (2006) and Marques et al. (2015) show the application of HOA in optimal design of the WDS, and Nicolini et al. (2011) proposed calibration methods using HOA. The solving of leakage detection problems in WDS is presented in Nasirian et al. (2013) and Huang et al. (2015). Optimal sensor placement was the research topic in Weickgenannt et al. (2009), Casillas et al. (2015) and Zhao et al. (2016). These algorithms also find application in pressurized network sectorization (Di Nardo et al. 2013) and in determining efficient operational procedures with reduced energy costs (Costa et al. 2010). The genetic algorithm is one of the most common heuristic algorithms used for optimization in water supply systems. However, the ant colony optimization algorithm also finds its place in WDS optimal design (Maier et al. 2003; Zecchin et al. 2006; Tong et al. 2011) and optimal pumping operations (López-Ibáñez et al. 2008; Ostfeld & Tubaltzev 2008).

This paper presents the methodology of the pressure drop test combined with HOA to validate WDS model topology. The hydroinformatic tool used for solving this problem on a real pressurized network combines the pressure drop test with the genetic algorithm and ant colony optimization. It is based on comparing the results of the pressure change obtained on the real system and results obtained from the WDS model. Modeled data are obtained by an initial randomly generated variant of topology which is later improved through the iterations using the genetic algorithm or ant colony optimization. The algorithm can detect changes in the network's topology, and alert the user of potential model vs real network inconsistencies. Since WDS topology is dynamic and can be changed during time, the validation step has to be repeated from time to time.

METHODS

EpaNet model

The WDS model is created in EpaNet 2.0 (Rossman 2000). The EpaNet is used since it is open source software and can be linked with any programming language through an adequate dynamic link library (dll) file. To present the methodology, the network topology used in this paper is kept as simple as possible and only the pipe status is considered: pipe status can be either OPEN (1) or CLOSED (0). Changing these parameters as optimization variables and changing model topology accordingly, the optimization problem is created.

Optimization algorithms

The proposed methodology for water distribution network topology validation is based on measuring the system reaction to intentionally (artificially) generated changes by applying the pressure drop test, which is described in the next section. First iteration topology is assumed by setting all potential locations of inconsistencies to a random value of pipe status (OPEN – 1 or CLOSED – 0). The measured data obtained from the real system is then compared with the reaction of the first iteration EpaNet model. EpaNet model topology is then modified in order to find a better match between the obtained data that describes real system reaction and results obtained by the EpaNet model.

HOA, the genetic algorithm (GA) and ant colony optimization algorithm (ACO) are used for speeding up the process of finding the best WDS model solution. The optimization variable is pipe (link) status: 0 (closed pipe with no flow) and 1 (open pipe with full capacity flow) (Figure 1). Parameters which affect the results of the optimization process are population size and number of generations (iterations) in which algorithms find the best solution (Rao 2009).

Figure 1

Pipe status as optimization variable: (a) 1 – open; (b) 0 – closed.

Figure 1

Pipe status as optimization variable: (a) 1 – open; (b) 0 – closed.

Criteria function

The proposed algorithm is based on: (1) the EpaNet model of the WDS, (2) pressure measurements at several points of the real system, and (3) optimization algorithms (GA and ACO) used to change the status of the model elements. A simple objective function, F, that is used for evaluation of the ‘proposed’ solution given by the optimization algorithm is the squared error between pressures obtained by the field measurements and pressures calculated by the model: 
formula
(1)
where F is the criteria function, pi,field is measured pressure data at a specific moment and is calculated pressure, modified by limiting its value to the lower physical limit of 0.0 Pa and N is the number of time steps in which field pressures were obtained. This is necessary, since the used EpaNet model is demand-driven, which creates a problem when part of the pressurized network is isolated: base demand does not depend on the pressure in the consumption node, so during the implementation of the pressure drop test in the model, large negative pressures could be obtained.
The criteria function can also be defined as root-mean-square error (RMSE), Equation (2). The main difference between the two criteria functions is that squared error gives more ‘weight’ to the greater errors between modelled and measured data than the RMSE. This should provide easier elimination of the ‘bad’ solutions in the optimization process. 
formula
(2)

Pressure reduction method (pressure drop method)

The pressure reduction method, or pressure drop testing, is based on closure of valves, one by one, until the complete isolation of the selected area is achieved (Morrison et al. 2007). Simultaneously, observation is made of pressures at specific nodes of the network for a certain period of time. Between two closures, enough time is needed to compensate for network dynamics. Inconsistencies found in the pressure data indicate undocumented changes of the WDS that need to be identified.

CASE STUDY

The proposed methodology is tested on one WDS district metered area (DMA) of Belgrade (Serbia). The DMA is an old part of Belgrade's WDN and was often subjected to reconstruction without proper documentation, hence the network topology can be considered as suspicious. The pressure drop test is implemented by closing eight selected valves and isolating this DMA from the rest of the WDS. The DMA consists of 196 junctions, where each junction represents the real consumption location. The network was extracted from the rest of the Belgrade WDS by minimizing the number of inflows. By using this criterion, the DMA was created with two inflow points, simulated by two fictive reservoirs. These fictive reservoirs represent boundary conditions and interaction between the DMA and the rest of the WDS. Reservoir elements in the EpaNet model are defined with constant head multiplied by head pattern. Head patterns for this case study were determined by 24-hour field pressure measurement at the locations of two fictive reservoirs. Head patterns are shown in Figure 2 as 12 averaged 2-hour intervals.

Figure 2

(a) Case study: Belgrade water distribution system district metered area; (b) consumer demand pattern and head patterns at locations of the fictive reservoirs represented as 12 averaged 2-hour intervals.

Figure 2

(a) Case study: Belgrade water distribution system district metered area; (b) consumer demand pattern and head patterns at locations of the fictive reservoirs represented as 12 averaged 2-hour intervals.

The consumers are the general population, with no industry. Their demand behavior is described by 11 demand patterns. The average demand pattern can be seen in Figure 2, with appropriate range.

Instead of using regulating valves in the EpaNet model, eight pipes represented isolation valves. The pressure drop test in the model was simulated by changing a link's (pipe's) status from 1 to 0. Pipe roughness for all the pipes is constant and has the value of 1.2 mm, as suggested by WDS experts. This parameter is used for head loss calculations in the Darcy–Weisbach equation. The pipe material is iron.

The closing valve (CV) schedule during the pressure drop test is presented in Table 1 and the locations of isolating valves are presented in Figure 3. Two measuring points were used for pressure monitoring during one day (24 hours), Junction J134 and Junction J105. Locations of measuring points are also presented in Figure 3. CV7 broke after closing so it remained closed during the experiment.

Table 1

Closing and opening isolation valves schedule (see Figure 4)

TimeTime from beginning of observation [min]ValveLinkStatus
9:40 am 580 CV1 Pipe 64 Closed 
10:20 am 620 CV2 Pipe 182 Closed 
10:42 am 642 CV3 Pipe 65 Closed 
10:50 am 650 CV4 Pipe 67 Closed 
11:20 am 670 CV5 Pipe 179 Closed 
12:04 pm 724 CV6 Pipe 77 Closed 
12:35 pm 755 CV7 Pipe 78 Closed 
1:00 pm 780 CV8 Pipe 131 Closed 
2:45 pm 885 CV6 Pipe 77 Open 
4:40 pm 1,000 CV4 Pipe 67 Open 
6:00 pm 1,080 CV5 Pipe 179 Open 
7:02 pm 1,142 CV3 Pipe 65 Open 
7:07 pm 1,145 CV2 Pipe 182 Open 
7:20 pm 1,160 CV1 Pipe 64 Open 
7:30 pm 1,170 CV8 Pipe 131 Open 
TimeTime from beginning of observation [min]ValveLinkStatus
9:40 am 580 CV1 Pipe 64 Closed 
10:20 am 620 CV2 Pipe 182 Closed 
10:42 am 642 CV3 Pipe 65 Closed 
10:50 am 650 CV4 Pipe 67 Closed 
11:20 am 670 CV5 Pipe 179 Closed 
12:04 pm 724 CV6 Pipe 77 Closed 
12:35 pm 755 CV7 Pipe 78 Closed 
1:00 pm 780 CV8 Pipe 131 Closed 
2:45 pm 885 CV6 Pipe 77 Open 
4:40 pm 1,000 CV4 Pipe 67 Open 
6:00 pm 1,080 CV5 Pipe 179 Open 
7:02 pm 1,142 CV3 Pipe 65 Open 
7:07 pm 1,145 CV2 Pipe 182 Open 
7:20 pm 1,160 CV1 Pipe 64 Open 
7:30 pm 1,170 CV8 Pipe 131 Open 
Figure 3

(a) Isolation (closing) valve locations (green stars), measuring points (blue squares) and potential locations of inconsistencies between the real system and EpaNet model (red dots); (b) pressure data obtained at measuring points during the pressure drop test. Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/ws.2018.095.

Figure 3

(a) Isolation (closing) valve locations (green stars), measuring points (blue squares) and potential locations of inconsistencies between the real system and EpaNet model (red dots); (b) pressure data obtained at measuring points during the pressure drop test. Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/ws.2018.095.

The WDS network validation test was implemented by assuming 55 locations of potential inconsistencies between the real system and EpaNet model (Figure 4). Locations of these potential inconsistencies were determined and suggested by network operators. The main criteria were to check the locations where reconstructions were performed, locations at street crossings and short pipes between consumers (shorter than 5 m).

Figure 4

Detected inconsistencies in WDS network topology for parameter combinations (a) I, (b) II, (c) III, (d) IV, (e) V, (f) VI. Red dots – detected inconsistencies with criteria function F (Equation (1)), blue crosses – detected inconsistencies with criteria function RMSE (Equation (2)). Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/ws.2018.095.

Figure 4

Detected inconsistencies in WDS network topology for parameter combinations (a) I, (b) II, (c) III, (d) IV, (e) V, (f) VI. Red dots – detected inconsistencies with criteria function F (Equation (1)), blue crosses – detected inconsistencies with criteria function RMSE (Equation (2)). Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/ws.2018.095.

The genetic algorithm and ant colony optimization algorithms were compared by implementing the same parameters for population size and number of generations. In the genetic algorithm the crossover operator was set as uniform crossover with mutation rate at 1. Performance of the ACO algorithm depends on pheromone trail evaporation. This operator is defined by the parameter of decrease in pheromone intensity, which was set at 0.2. The reproduction operator when GA was implemented and ant searching path behavior when ACO algorithm was implemented were carried out by using roulette wheel selection.

RESULTS AND DISCUSSION

Figure 3(b) presents the observed pressures during a pressure drop test at two observation nodes which are used for the WDS network topology validation.

Different parameters (population size and number of generations or iterations) for GA and ACO algorithms produce different solutions. Table 2 contains criteria function results for three parameter combinations for GA and three parameter combinations for the ACO algorithm. Two criteria functions were implemented. WDS network topology inconsistencies detected by the described optimization algorithms for each parameter combination are presented in Figure 4. Pressure changes calculated by the EpaNet model for each optimization parameter combination are presented in Figure 5.

Table 2

Criteria function values for each optimization parameter combination

CombinationOptimization algorithmPopulation sizeNumber of generations (iterations)Criteria function value – FCriteria function – RMSE
GA 100 100 87,131.76 17.45 
II GA 200 100 96,838.24 18.73 
III GA 50 70 82,225.59 17.71 
IV ACO 100 100 67,283.00 16.74 
ACO 200 100 78,977.00 15.30 
VI ACO 50 70 80,600.00 18.60 
CombinationOptimization algorithmPopulation sizeNumber of generations (iterations)Criteria function value – FCriteria function – RMSE
GA 100 100 87,131.76 17.45 
II GA 200 100 96,838.24 18.73 
III GA 50 70 82,225.59 17.71 
IV ACO 100 100 67,283.00 16.74 
ACO 200 100 78,977.00 15.30 
VI ACO 50 70 80,600.00 18.60 
Figure 5

Comparing pressure changes between measured data and model for parameter combinations (criteria function F): (a) I, (b) II, (c) III, (d) IV, (e) V, (f) VI.

Figure 5

Comparing pressure changes between measured data and model for parameter combinations (criteria function F): (a) I, (b) II, (c) III, (d) IV, (e) V, (f) VI.

According to the criteria function given by Equation (1), as can be seen in Table 2, the best value is obtained by ACO algorithm with combination IV (the appropriate WDS network topology is presented in Figure 4(d)). When RMSE is used as the criteria function (Equation (2)), the minimal value is calculated by using parameter combination V with the ACO algorithm. Solutions (detected inconsistencies) obtained by six algorithm parameter combinations and two criteria functions show some similar results, but there are also some significant differences, in locations and number of the identified changes in the network's topology. Figure 4 shows that the number of these locations is greater when RMSE is used as the criteria function. From Figure 4 it can be seen that some of the solutions of the detected inconsistencies are located closer to the observation points than others. When Equation (1) is used as the criteria function there are more solutions detected closer to the observation point J134. This can indicate that the real problem in the network is one of these detected inconsistencies. Also, it can be seen that there is a certain amount of overlapping, ‘suspicious’, locations when Equation (1) or Equation (2) were used as criteria functions. All of these overlapping locations are nearby observation points. This indicates that changes in WDN topology in some parts of the tested network do not effect pressure changes at two monitoring points. Hence, the range of detected inconsistencies spreads, especially in the areas further from monitoring points. Reducing the range of detected inconsistencies could be implemented through optimal sensor placement, in order to find the largest sensitivity area for each sensor and/or through increasing the number of sensors. However, the case study used for this paper had the limitation of just two observation points.

The criteria function defined in Equation (1) gives more weight to greater errors between measured and modeled data, and it should be easier to eliminate bad solutions in the optimization process. Hence, Figure 5 represents pressure change in two observation points just for the squared error criteria function (Equation (1)). However, neither of the proposed criteria functions should be thrown away. The final solution can be given as a combination of the solutions obtained by several optimization parameters and criteria functions.

From the obtained results, it can be seen that the calculated pressure drop during the isolation process is faster than the pressure decrease from the real system. The main reason for that difference is the used demand-driven model, where base demand in every node does not depend on pressure in the same node. To overcome this problem a pressure-driven model should be tested.

Figure 5 presents solutions of WDS network topology for the performed pressure drop test. Because it is likely that two observation points cannot give us a unique solution for WDS network topology, another isolation test should be done, with a different isolation schedule, in order to reduce the number of potential inconsistencies in the EpaNet model.

CONCLUSIONS

The proposed methodology for WDS network topology validation can be a valuable first step in detecting potential inconsistencies in the EpaNet model. After that, standard field methods for detecting inconsistencies, such as acoustic or correlation methods, should be used, but the search area can be significantly narrowed by the proposed methodology.

It should be mentioned that the results obtained in the presented case study show a similar behavior of the genetic algorithm and ant colony optimization algorithm. It is suggested to perform the second field experiment with different isolation schedules. The number of observation locations should also be increased because it can produce a higher correlation between measuring data and WDS network topology.

ACKNOWLEDGEMENTS

The authors express their gratitude to the Serbian Ministry of Education, Science and Technological Development for financial support through the project TR37010.

REFERENCES

REFERENCES
Babayan
A. V.
,
Kapelan
Z. S.
,
Savic
D. A.
&
Walters
G. A.
2006
Comparison of two methods for the stochastic least cost design of water distribution systems
.
Engineering Optimization
38
(
3
),
281
297
.
https://doi.org/10.1080/03052150500466846
.
Bicik
J.
,
Kapelan
Z.
,
Makropoulos
Ch.
&
Savic
D. A.
2014
Pipe burst diagnostics using evidence theory
.
Igarss
2014
(
1)
,
1
5
.
Casillas
M. V.
,
Garza-Castañón
L. E.
&
Puig
V.
2015
Optimal sensor placement for leak location in water distribution networks using evolutionary algorithms
.
Water
7
(
11
),
6496
6515
.
https://doi.org/10.3390/w7116496
.
Costa
L. H. M.
,
Ramos
H. M.
&
de Castro
M. A. H.
2010
Hybrid genetic algorithm in the optimization of energy costs in water supply networks
.
Water Science and Technology: Water Supply
10
(
3
),
315
326
.
https://doi.org/10.2166/ws.2010.194
.
Di Nardo
A.
,
Di Natale
M.
,
Santonastaso
G. F.
,
Tzatchkov
V. G.
&
Alcocer-Yamanaka
V. H.
2013
Water network sectorization based on a genetic algorithm and minimum dissipated power paths
.
Water Science and Technology: Water Supply
13
(
4
),
951
957
.
https://doi.org/10.2166/ws.2013.059
.
Di Nardo
A.
,
Di Natale
M.
,
Giudicianni
C.
,
Santonastaso
G. F.
&
Savic
D.
2018
Simplified approach to water distribution system management via identification of a primary network
.
Journal of Water Resources Planning and Management
144
(
2
),
4017089
.
https://doi.org/10.1061/(ASCE)WR.1943-5452.0000885
.
Giorgio Bort
C. M.
,
Righetti
M.
&
Bertola
P.
2014
Methodology for leakage isolation using pressure sensitivity and correlation analysis in water distribution systems
.
Procedia Engineering
89
,
1561
1568
.
https://doi.org/10.1016/j.proeng.2014.11.455
.
Giudicianni
C.
,
Di Nardo
A.
,
Di Natale
M.
,
Greco
R.
,
Santonastaso
G. F.
&
Scala
A.
2018
Topological taxonomy of water distribution networks
.
Water
10
(
4
),
444
.
https://doi.org/10.3390/w10040444
.
Giustolisi
O.
,
Kapelan
Z.
&
Savic
D.
2008
Detecting topological changes in large water distribution networks
.
Water Distribution Systems Analysis
2008
.
https://doi.org/10.1061/41024(340)75
.
Huang
Y.-C.
,
Lin
C.-C.
&
Yeh
H.-D.
2015
An optimization approach to leak detection in pipe networks using simulated annealing
.
Water Resources Management
29
(
11
),
4185
4201
.
https://doi.org/10.1007/s11269-015-1053-4
.
Jung
D.
&
Lansey
K.
2014
Burst detection in water distribution system using the extended Kalman filter
.
Procedia Engineering
70
,
902
906
.
https://doi.org/10.1016/j.proeng.2014.02.100
.
Laucelli
D.
,
Romano
M.
,
Savi
D.
&
Giustolisi
O.
2016
Detecting anomalies in water distribution networks using EPR modelling paradigm
.
Journal of Hydroinformatics
18
(
3
),
409
427
.
https://doi.org/10.2166/hydro.2015.113
.
López-Ibáñez
M.
,
Devi Prasad
T.
&
Paechter
B.
2008
Ant colony optimization for optimal control of pumps in water distribution networks
.
Journal of Water Resources Planning and Management
134
(
4
),
337
346
.
https://doi.org/10.1061/(ASCE)0733-9496(2008)134:4(337)
.
Maier
H. R.
,
Simpson
A. R.
,
Zecchin
A. C.
,
Foong
W. K.
,
Phang
K. Y.
,
Seah
H. Y.
&
Tan
C. L.
2003
Ant colony optimization for design of water distribution systems
.
Journal of Water Resources Planning and Management
129
(
3
),
200
209
.
Marques
J.
,
Cunha
M.
&
Savić
D. A.
2015
Multi-objective optimization of water distribution systems based on a real options approach
.
Environmental Modelling & Software
63
,
1
13
.
https://doi.org/10.1016/j.envsoft.2014.09.014
.
Morrison
J.
,
Tooms
S.
&
Rogers
D.
2007
District Metered Areas: Guidance Notes.
Water Loss Task Force, IWA
,
London, UK
.
Nasirian
A.
,
Maghrebi
M. F.
&
Yazdani
S.
2013
Leakage detection in water distribution network based on a new heuristic genetic algorithm model
.
Journal of Water Resource and Protection
5
(
3
),
294
303
.
https://doi.org/10.4236/jwarp.2013.53030
.
Nicolini
M.
,
Giacomello
C.
&
Deb
K.
2011
Calibration and optimal leakage management for a real water distribution network
.
Journal of Water Resources Planning and Management
137
(
1
),
134
142
.
https://doi.org/10.1061/(ASCE)WR.1943-5452.0000087
.
Ostfeld
A.
&
Tubaltzev
A.
2008
Ant colony optimization for least-cost design and operation of pumping water distribution systems
.
Journal of Water Resources Planning and Management
134
(
2
),
107
18
.
Rao
S. S.
2009
Engineering Optimization: Theory and Practice
.
Wiley
,
Hoboken, NJ, USA
.
Rossman
L. A.
2000
EPANET 2 Users Manual
.
EPA/600/R-00/057, US Environmental Protection Agency
,
Washington, DC, USA
.
Tong
L.
,
Han
G.
&
Qiao
J.
2011
Design of water distribution network via ant colony optimization
. In:
Proceedings of the 2nd International Conference on Intelligent Control and Information Processing
,
IEEE, Piscataway, NJ, USA
, pp.
366
370
.
Torres
J. M.
,
Duenas-Osorio
L.
,
Li
Q.
&
Yazdani
A.
2016
Exploring topological effects on water distribution system performance using graph theory and statistical models
.
Journal of Water Resources Planning and Management
143
(
1
),
1
16
.
https://doi.org/10.1061/(ASCE)WR.1943-5452.0000709
.
Weickgenannt
M.
,
Kapelan
Z.
,
Blokker
M.
&
Savic
D. A.
2009
Optimal sensor placement for the efficient contaminant detection in water distribution systems
.
Water Distribution Systems Analysis
2008
.
https://doi.org/10.1061/41024(340)99
.
Wright
R.
,
Stoianov
I.
&
Parpas
P.
2014
Dynamic topology in water distribution networks
.
Procedia Engineering
70
,
1735
1744
.
https://doi.org/10.1016/j.proeng.2014.02.191
.
Wu
Z. Y.
2008
Innovative optimization model for water distribution leakage detection
.
Bentley Systems Inc.
,
Watertown, CT, USA
.
Zecchin
A. C.
,
Simpson
A. R.
,
Maier
H. R.
,
Leonard
M.
,
Roberts
A. J.
&
Berrisford
M. J.
2006
Application of two ant colony optimisation algorithms to water distribution system optimisation
.
Mathematical and Computer Modelling
44
(
5–6
),
451
468
.
https://doi.org/10.1016/j.mcm.2006.01.005
.
Zhao
Y.
,
Schwartz
R.
,
Salomons
E.
,
Ostfeld
A.
&
Vincent Poor
H.
2016
New formulation and optimization methods for water sensor placement
.
Environmental Modelling & Software
76
,
128
136
.
https://doi.org/10.1016/j.envsoft.2015.10.030
.