Available via license: CC BY 4.0
Content may be subject to copyright.
Leakage detection in water distribution networks by the use of analytical and
experimental models
Ali Nasiriana,*, Mahmoud F. Maghrebiband Ali Mohtashamic
a
Civil Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran
b
Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
c
Civil Engineering, Water Resources Management, University of Sistan and Baluchestan, Zahedan, Iran
*Corresponding author. E-mail: a.nasirian@birjand.ac.ir
ABSTRACT
Recently, calibration based methods are considered to determine the quantities and locations of all leakages in a Water
Distribution Network (WDN), simultaneously. In this paper, the accuracy of detecting leakages using Ant Colony Optimization
(ACO) in two networks including a hypothetical and a laboratorial network is investigated. A novel method is introduced to ana-
lyze the effects of measurement errors on demand calibration in an under-determined problem. The results confirm the ability
of the optimization-based method detecting the exact locations and values of the leakages in a WDN. Also, it is emphasized that
merely suitable fitnesses cannot provide sufficient confidence in result accuracy. To overcome this difficulty, the correctness of
leakage detection can be verified in a sampling design problem. Moreover, to check the reliability of leakage detection an
alternative method based on various results is introduced in this research.
Key words: ACO, calibration, leakage detection, uncertainty analysis, water distribution network
HIGHLIGHTS
•A New method is presented.
•Both experimental and analytical method is investigated.
INTRODUCTION
Leakage reduction in a WDN is essentially needed to have an economic, reliable, and safe network. Low quality
of pipeline and junction materials, design errors, improper maintenance, high pressure and also random failures
are the main reasons cause a serious damage within a network (Lay-Ekuakille et al. 2009). Currently many
methods such as acoustic equipment, mass balance technique, thermography, ground-penetrating radar, tracer
gas, and video inspection are used for detecting and locating leakages within networks (Covas & Ramos
2010). Although these approaches provide reliable and precise measurements in some conditions, they are econ-
omically expensive, labor intensive and often inaccurate. Amongst these approaches, the equipped acoustic is
extensively used by the water industry that properly measures leakages for metal pipes but gives inaccurate results
for other pipe materials such as plastic or PVC pipes (Hunaidi et al. 1998,1999).
Recently model base methods such as transient-based (Liggett & Chen 1994;Brunone 1999;Covas & Ramos
1999;Brunone & Ferrante 2001;Covas et al. 2005) and steady state techniques (Carpentier & Cohen 1991;
Pudar & Liggett 1992;Andersen & Powell 2000;Poulakis et al. 2003;Abhulimen & Susu 2004;Cheng & He
2011) have been considered by many researchers to cope with the shortcoming caused by the conventional detec-
tion techniques concisely outlined above. However, transient based methods can find leakage location more
accurate than steady based methods. Noticed that, it has some drawbacks like generation of negative wave
and make this method difficult for complex networks. Also, it cannot be used for a large network, simultaneously.
Pudar & Ligget (1992) used the inverse steady state analysis method for detecting leakages in pipe networks
(Pudar & Liggett 1992). Almandoz et al. (2005) and Walski et al. (2006a,2006b) developed an approach for
detecting leakages by network hydraulic modeling (Almandoz et al. 2005;Walski et al. 2006a). Wu & Sage
(2006) proposed an optimization-based method for locating and sizing the water losses obtained for the WDN
through the calibration process (Sage & Wu 2006). In this method, the demand multiplier factors have been
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying,
adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).
© 2021 The Authors Water Practice & Technology Vol 00 No 0, 1 doi: 10.2166/wpt.2021.071
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
adjusted for nodes groups using a genetic algorithm optimization method. In this leakage detection method, leak-
age is modeled as additional demands in the nodes, and then total nodal outflows are adjusted for all nodes. The
base demand is subtracted from the adjusted demand and the leakage is defined. Based on this research, one
logger is needed for each 200 houses in this method. To cope with this problem, next investigations are focused
on pressure dependent analysis for leak detection (Giustolisi et al. 2008;Wu et al. 2010). In this case, the nodal
demands can be estimated using demand patterns and the leakage value can be computed based on the orifice
area and nodal pressure by the use of specific equation. In this method, a SCADA system provide a large
number of observations using few loggers while the pressure dependent analysis prevents increasing the
number of unknowns. Todini (1999) developed a Kalman filter approach by converting the WDN model formu-
lation to a linear estimation problem (Todini 1999). Based on his work, in a looped system, the network
observability cannot be guaranteed using a unique set of steady-state data even all the nodal heads and demands
are measured.
Often there is a few number of leakage in WDS and many of nodes there are not leaked. Using this fact can
minify the space search. Wu et al. (2010) assumed that the number of leakages are limited to a specified value
(N). Nasirian & Maghrebi 2011 limitd the space search using a novel algorithm (Nasirian et al. 2011).
Most previous works in network calibration and leakage detection are used Genetic Algorithm (GA) (Savic &
Walters 1995;Sage & Wu 2006;Jamasb et al. 2008;Behzadian et al. 2009;Pérez et al. 2011). GA is a revolution
base algorithm that used pervious answer result to find correct direction for next generations. Calibration pro-
blem in steady state is inherently an ill-posed problem (Giustolisi & Berardi 2010;Ostfeld et al. 2012) and
because of low sensitivity of the nodal pressure to demand variation, the results in the first analysis with relatively
high fitness cannot guide to the correct direction. Wu et al. (2010) assumption could help to get better answers.
ACO have the especial parameter named ‘pheromone’which use pervious answers. Additionally, it can be
guided by another factor named ‘heuristic guidance’. This parameter can be used by analyzer to lead to correct
answers. Using this parameter to apply the number of potentially leakage can decrease the time of program
execution and accuracy of the results. Measured pressures and flows in WDS is different with model. Some of
this discrepancy may be caused by leakage. Other sources of this error include measurement errors, modeling
errors and search space discretization error. Pressure, flow rate, pipe diameter, pipe material and node elevation
are example for measurement errors. Some assumption in WDS modeling enter error in modeling. It is assumed
that consumption and demand happened in nodes. Minor loss in WDS component apply in friction coefficient.
Most of search method used for WDS, separate the search space. When the solution space is discretized, it is
possible that the exact answer is not existed in the answer’s set. The effects of these errors appear in the measured
pressure and flow. Therefore, it is difficult to detect a small leak in WDS. In other hand, inverse steady state
method can detect and locate areas with high leakage. Also, it is important to investigate the effect of measure-
ment errors on accuracy of results. When the relation between two parameters is determined, it is simple to
estimate the error of one parameter due to the error of other parameter. Most of the sensitivity analysis methods
are developed for even determined state (Kang et al. 2009;Kang & Lansey 2010,2011;Cheng & He 2011;Cheng
et al. 2014). This paper presents a method to investigate the existence of unique answer in difference cases. How-
ever, applying the method in a real situation is the best way to evaluate the model. Then, a laboratory scale
network can clarify the ability of the method in a real situation. It provides opportunity to check the location
and value of detected leakages with real leaks. It is clear that a real network is more complicated than a labor-
atorial one however in a real network it is not possible to check the results exactly. Up to now, laboratory
networks are tested for network calibration e.g. Walski et al. (2006a,2006b) or in leakage detection using tran-
sient analysis e.g. Covas & Ramos (2010) and Lay-Ekuakille et al. (2009) and there is no laboratorial examination
for leakage detection in steady state analysis.
The method is examined for two networks. The first network is considered as a hypothetical network selected
from well-known papers in the literature and the second network comprises the laboratory-scale network built for
this work. Additionally, a novel sensitivity analysis technique is employed to exactly evaluate the relationship
between the amount and the location of the leakage and the number and accuracy of sensors used for the
pressure measurements. An in-house computer program in MATLAB has been written for the optimization
part. This computer program is coupled with the EPANET 2 (Rossman 2000) to compute the discharges
within the pipes and the pressure heads for the nodes.
Water Practice & Technology Vol 00 No 0, 2
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
METHODS
Leakage detection using network calibration is investigated with some assumptions: (1) A roughly calibrated net-
work is provided before demand calibration, (2) A few numbers of simultaneous leakages occur in the network,
(3) Base demands are detected for all nodes and (4) The uncertainty analysis is performed in the presence of one
leakage in the network.
Calibration problem
The WDN calibration is generally used to determine the different model parameters needed to provide a reason-
able accordance between the measured and calculated pressures and/or flows in a network. Parameters of
calibration usually comprise nodal demand and pipe roughness coefficient. Nodal demand includes nodal
based demand, hourly and daily multiplayers, and nodal leakage value. Nodal base demand can be recorded
by customer consumption. In this work, the unknown parameters are nodal leakages (Li). The formulation of
the objective function of the WDN hydraulic model is defined based on a weighted least squares problem:
Search for:
x¼(Li)i¼1, ...,N(1)
To minimize:
f(x)¼min X
N
j¼1
(HobsjHsimj)2(2)
Under constraint:
LLiLand XLi¼NRW(Non Revenue Water) (3)
where xis the vector of leakages Liat various nodes, f(x) is the fitness function that should be minimized, Hobsj
and Hsimjare the observed and simulated total heads at node j, respectively, N is the number of nodes in the
network and Land Lare the upper and lower bounds of the possible nodal leakages. Usually, lower bound is
zero that means no leakage happens and upper bound can be estimated by the analyzer. Maximum of Lcan
be the total leakage in the network or DMA. If the total inflow to the network is defined, by subtracting the
total customer consumption then NRWis detected as a constraint. It is expected that if the calculated fitness
for an answer (a set of demand for all nodes) is smaller than the calculated one for another answer, the detected
leakage will be closer to the other. To evaluate and compare various results obtained in optimization process, the
sum of absolute differences between the real and the simulated leakages is calculated. It divided by the total
inflow in the network to be obtained a unit less parameter:
ft(d)¼
P
N
j¼1
jLobs
jLsim
j,tj
Qin
(4)
where ft(d) is the sum of absolute difference between the simulated and observed leakage in iteration t, Lobs
jis the
real leakage value at node j, Lsim
j,tis the simulated leakage in iteration t at node j, N is the node number in the
network and Qin is the total inflow in the network. If the leakage quantities and locations are detected exactly,
ft(d) is zero. If the leakage locations and/or quantities are not exact, it takes a nonzero value. Equation (4) can be
evaluated when Lobs
jis defined.
Uncertainty analysis
Measurement devices are not perfect and the field measurements of pressures and flows in the WDN suffer from
some uncertainties. Measurement errors are propagated to the determined values of the calibration parameters.
Because of the fact that WDN simulation results depend on calibration parameters, error in the measured values
influences the model predictions dominantly. In the previous research works usually the First-Order Second
Water Practice & Technology Vol 00 No 0, 3
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
Momentum (FOSM) estimation method calculated based on the Taylor series expansion is employed for uncer-
tainties prediction (Kapelan et al. 2003,2005;Behzadian et al. 2009; Kang, 2009; Jung et al. 2014;Jung et al.
2016b). This method can be used for the even-determined problems. A particular type of uncertainty predictor
for under-determined problems is introduced in this paper. For an even-determined problem, uncertainty in
any unknown parameter can be obtained as a scalar value based on the measurement errors but if the problem
would have some freedom degrees, it has no unique answer and a solution space would been obtained. When
measurement error is added to the problem, the problem will be more complicated.
For an even determined problem:
J:dD ¼dP (5)
dD ¼J1:dP (6)
where Jrepresents the Jacobian matrix of derivatives @pi=@dkwhere i¼1, ...,Npand k¼1, ...,Nd,dis the
vector of Ndnodal demands, and Pis the vector of Nppressure measurement of interest location. Ndand Np
are the number of unknown presenting demand parameters and number of observations (number of pressure
measurements), respectively. And finally, dD and dP are the vectors of perturbation of demands and pressures.
Here, the elements of these two matrices are calculated by using the finite difference method (Bush & Uber
1998;Lansey et al. 2001;Kapelan et al. 2003,2005;Behzadian et al. 2009):
@pi
@dk
¼pD
ipi
(dkþDd)dk
(7)
where pD
iis the calculated pressure with respect to the change in the demand value (dkþDd), pishows the
pressure calculation with an assumed demand dk, and Dddenotes the deviation value added to dk. The Jacobian
matrix elements can be computed based on the following steps: (1) the values of the base demand are assumed
and the hydraulic model is built, (2) the hydraulic model is simulated by adding some perturbed values Ddto the
base demand dkfor k¼1, (3) the derivatives @pi=@dkare computed by applying Equation (6) which provides the
first row of the Jacobian matrix; (4) steps 2 and 3 are repeated for k¼1, ...,Nd(Behzadian et al. 2009).
The Jacobian matrix can be inversed if the matrix is squared; in other words, the number of measurements
should be equal to the number of unknown parameters. For the systems posed for the WDN, the number of
equations is less than the number of unknown parameters which leads to under-determined systems. To cope
with this difficulty some researchers use pipes and nodes grouping to reduce the number of unknown and/or
run the studied network for the different load conditions (Kapelan et al. 2005;Behzadian et al. 2009).
In the current paper this revision has not been used and an under-determined system is considered. For this
purpose, it is assumed that there is a leakage at node jand the pressures are measured at nodesi¼1, ...,Np.
So, we have;
Ddk,i¼1
Ji,k
:Dpi
Ddk,i¼1
Ji,k
:Dpi
Ddk,i¼1
Ji,k
:Dpi
(8)
where Dpiis the variation in the pressure in the junction idue to the leakage at node j.Dpiand Dpiare the upper
and lower bounds of the variation of the pressures respectively due to measurement errors, ( Dpi,Dpi¼Dpi+s).
The accuracy of pressure measurement depends on the accuracy of sensors and the precision topographic map-
ping and for each WDS should be estimated by analyzer. Ji,kis one row of Jacobian matrix that shows the
relationship between variation in pressure of node idue to changing in the demand of node k(k¼1, ...,N)
where N is the node number in the network. Ddk,iis the vector of demand changing because of the difference
in pressure of node iand Ddk,i,Ddk,iare the perturbation in upper and lower bounds due to the existence of
error with the amount of +sin pressure measurement.
Water Practice & Technology Vol 00 No 0, 4
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
If there is only one pressure sensor in the network, the amount of leakage is between Ddk,i,Ddk,i. If there is
some other pressure sensor, the answer bound for leakage at node kis limited. Equation (9) compute this bound.
Ddk¼Mini(Ddk,i):H(Maxi(Ddk,i)Mini(Ddk,i))
Ddk¼Maxi(Ddk,i):H(Maxi(Ddk,i)Mini(Ddk,i))
(9)
where Ddkand Ddkare the upper and lower bounds for the demand variation in the junction kbecause of error in
the pressure measurement at nodes i¼1, ...,Np, respectively. H is the Heaviside step function that is zero
when the value is negative or zero, and one if it is positive (Abramowitz 1972). The space solution for the leakage
is located between upper and lower bound of demand perturbation. For example, if the demand perturbation is
caused by a leakage, the interval between Ddkand Ddkcan be the correct options as the leakage value and it can
cause the observed pressure in the measurement points.
Optimization methodology
The optimization methodologies can be classified into three different categories: mathematical, statistical and sto-
chastically methods. Among the stochastic methods, heuristic and meta-heuristics methods are used in several
fields of science as well as problems related to the WDN (Sage & Wu 2006;Kapelan et al. 2007;Behzadian
et al. 2009;Rezaei et al. 2014;Yazdi et al. 2014). The ACO, as one of the heuristic methods, is introduced in
1992 by Dorigo (1992).Simpson et al.(2001) discussed the parameters used in the ACO algorithm for the net-
work optimization problems. More recently, Maier et al. (2003) developed an ACO method for an optimal
design in two case studies and compared the results with GA. Their results indicated more preference of ACO
than GA in two benchmarks of WDN. Afshar (2007,2010) proposed a new transition rule for ACO algorithms
using elitist strategies and applied the method to network optimization problems. Maghrebi et al. (2012) com-
pared ACO with Darwin calibrator WaterGems3 in the leakage detection. Their results have shown that ACO
provides more accurate results with rapid convergence as well as significantly improvement in terms of time
and accuracy when compared to the GA.
In this paper, calibration of demands is carried out in the following steps: (1) The hydraulic model of the network
is simulated in EPANET. (2) The interval between minimum (L) and maximum (L) that is the solution space for
unknown leakage as a continuous region, is discretized in a numbers of Liwith a number of AN. On the other
hand, ANis the number of options that leakage value gets in each node. In other words, Lifor each node is selected
from the set of {L,LþD,Lþ2D,... ,L}andD¼(LL) (An 1). This set is fixed for all nodes and the base
demand for each node is added to the set to obtain a set of nodal demands (d1,... di,... ,dn). This procedure
will be performed for each node. Then ACO is implemented to select one of (d1,... di,... ,dn) as the correct
demand at each node, (3) ACO parameters are adjusted, (4) the program is run. In this step, each artificial ant
selects a demand for each node. Pressures of all nodes using these demands are computed by EPANET, and
then fitness value is calculated using Equation (2). (5) Pheromone for different paths based on these fitnesses is
updated. It means that the pheromone of the demand option of each node that is placed in a patch with better fit-
ness is increased, while the pheromone of the other demand options in that node are decreased because of
evaporation parameters. (6) Steps 4 and 5 are repeated until the interest fitness is achieved and (7) adjusted
demands are manually compared with the base demands to identify leakage locations and values.
In this method, selection probability of demand options in each node is not equal. The probability of choosing
each value as demand for a node is the most important part of this method and is obtained by the following
equation:
pij(k,t)¼[
t
ij(t)]
a
[
h
ij]
b
P
k
[
t
ik(t)]
a
[
h
ik]
b
(10)
where pij(t) is the probability of choosing the value difor the ant kas demand at node jin iteration tth .
t
ij(t) is the
amount of pheromone for the nodal demand iat node jin the iteration tth which is updated after each iteration,
h
ij is the heuristic factor favoring option is called ‘heuristic guidance’which is a constant value allocating based
on the researcher estimation for demand option iat node j. For instance, a few leakage numbers usually occur in
Water Practice & Technology Vol 00 No 0, 5
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
a network, simultaneously (Wu et al. 2010) and most of nodes show no leakage, then the selection possibility of
the no leakage option can be multiplied. αand βare two parameters that regulate the comparative weight of
pheromone series and heuristic guidance, respectively.
As mentioned above, pheromone updating is an important step in ACO method. In this work, if calculated fit-
ness is better than the best fitness in comparison to the fitnesses pervious steps, the pheromones are updated by
following equation:
t
ij(tþ1) ¼
rt
ij(t)þD
t
ij (11)
where
t
ij(t þ1) and
t
ij(t) are the values of pheromone in iteration tand tþ1, D
t
ij is the updating value which is
added to the pheromone value of the local best answer,
r
is the evaporation rate of pheromone which is ranged
between zero and one and it decreases the pheromone value of all solution space. These two parameters
take constant values defined by trial and error by analyzer. In the current paper D
t
ij and
r
are 0.1 and 0.98,
respectively. It should be noted that pheromones for all demand options in every node are chosen equal to
one in the first analysis. Then the ACO is run for a few times with this regulation to acquire a number of finesses.
Next, the obtaining results are sorted. Finally, D
t
ij is added to the selected value of demand causing the best
achieving fitness, meanwhile for other demand options in each node, the pheromones are fixed. However,
because of the evaporation function, corresponding pheromones are diminished. In other words, in each phero-
mone updating, the pheromone of answer with good fitness is increased while the pheromone of other answers is
decreased.
RESULTS AND DISCUSSION
In this study, as the first and second networks are benchmark and experimental, the consumption pattern is not
considered and the analysis were carried out in steady condition. It should be noticed that this method is exten-
sible for EPS condition.
Case 1
To examine the reliability of the calibration method, the Anytown network which is known as a small network is
created to investigate the leakage detection based on ACO and uncertainty methodology (Figure 1). It should be
noted that this network was widely used in the literatures to specify the optimal sensor placement (Ferreri et al.
1994;Kapelan et al. 2003;Kapelan et al. 2005;Kapelan et al. 2007;Behzadian et al. 2009). The optimal places for
installation of the pressure measurement devices are proposed at nodes 90, 120, 110 and 40 (Kapelan et al. 2005;
Behzadian et al. 2009). Also, the optimal number of pressure measurements are suggested as 7 and 6 by
Behzadian et al. (2009) and Kapelan et al. (2005), respectively when the accuracy of pressure measurement is
equal to 0.1 m. Both of them classified the demands and load conditions within five groups. The relative accuracy
of calibration with various number of pressure measurements for 2, 4 and 8 pressure observations are 0.2, 0.6 and
0.85, respectively. The fitness function in Behzadian et al. (2009) and Kapelan et al. (2005) is weight mean square
error (Kapelan et al. 2005;Behzadian et al. 2009). The relative accuracy means the accuracy if N nodes pressure
are observed relative to the case that all nodes pressure are measured (Kapelan et al. 2003). It should be noted
that attaining to the accuracy of 0.1 m is difficult in some aspects in real networks. Pressure sensor has about 1%
error in the best condition. Topography map error is added to the pressure sensor error as well. The HGL
1
almost
has 0.1–1 m accuracy. In this benchmark case, the assumptions of previous studies are implemented. The other
error which is added to the measurements is the inflow parameter. The flowmeters which are measure the inflow
rate, usually have an accuracy about 0.05–0.1 l/s. In this case, 0.05 l/s was assumed for flowmeter.
The hypothetical network has 16 nodes, 34 pipes, 3 pumps as well as 2 tanks and 1 reservoir with the elevation
of 71.6 and 3.04 m. Length, diameter and Hazen-Williams (H-W) coefficient are denoted above each pipe and
elevation and consumption of each node is represented in box next to the node. The other properties can be
found in mentioned references. It should be mentioned that the hydraulic analysis is carried out in EPANET
2. and the Hazen-Williams formula is used in the analysis.
1
Hydraulic Gradient Line
Water Practice & Technology Vol 00 No 0, 6
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
In this research, the network analysis is carried out without demand grouping and also no-load condition
(demand grouping decreases the unknown parameters. Using several load conditions increase the number of
observations). The demands are ranged from zero to 50 l/s with an increment of 10 l/s and the maximum iter-
ation is 1,000. The heuristic guidance values based on statistics and trial and error are selected. They are for
one and two leakages are considered 30 and 20, respectively. Table 1 shows 8 different scenarios for calibration.
The network is analyzed for different scenarios applying the pressure measurements and total inflow to the net-
work. The pressure measurements are needed to calculate the fitness function, while the total inflow is applied as
a physical constraint. Table 1 presents the results of 8 calibration scenarios. According to Table 1 column 2, nodal
pressures are measured 100% accurately in the first 4 analyses. However, the pressure measurement pertur-
bations are assumed 0.1 m in the next 4 analyses. Also, the next two columns represent the locations and
values of leakages located at nodes 70 and 140 in various scenarios. The next five columns show the observa-
tional states of pressures and flow, the locations and sizes of the leakages obtained in calibration, the fitness
value and finally the total iterations, respectively. And final column is present the run-time for each scenario.
Based on Table 1, it is clearly observed that the calibrations in scenarios 1 and 3 that tried to find one and two
leakages using one and two pressure measurements do not attain the correct results. However, scenario 2 which
is used 2 pressure measurements for finding one leakage has reached perfect answers. Also, scenario 4 that is
utilized 3 pressure and inflow measurements, is attained the correct answer. The observations in scenario 5
are subjected to some errors. In this case, although the leakage location is found exactly, some errors can be
observed in the quantity of leakage. Two simultaneous leakages are investigated in scenario 6. Although, an excel-
lent fitness is achieved, the consequence demonstrates significant variation. Likewise, scenario 7 can lead to
successful outcomes with additional observations. The last analysis is performed with duplicating the quantities
of leakages in scenario 8. The results of this case show a dramatically improvement in the leakage detection in
comparison to scenario 7. To investigate the relationship between the number of observations, measurement
error and the accuracy of the obtained results in the different scenarios, the uncertainty analysis is carried out.
In order to clarify the behavior of the proposed method in detecting the leakage, the results of all scenario
are investigated. Based on the results of scenario 4 which is correspond to the exact solution and also its
number of iterations, this scenario is chosen and its results presented in Figure 2. As shown in this figure, the
difference between the leakages in the real and calculated answers f(d) for 63 checking answers is plotted against
the fitness f(x).
This figure shows a positive correlation between f(x) and f(d). By decreasing f(x), f(d) is also decreased which
shows a kind of improvement to the real answer. Most of the optimization approaches use fitness as a criterion to
Figure 1 |The anytown network.
Water Practice & Technology Vol 00 No 0, 7
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
Table 1 |8 Different scenarios for calibration
12
3
4
5
678
Real leakage Calculated leak
Analysis case Measurement error (m) Position Value (l/s) Observation Position Value (l/s) Fitness (m
2
) Iteration Time (sec)
Scenario 1 0 70 30 P90
inflow
20
40
70
10
10
10
2.9E-06 43 6
Scenario 2 0 70 30 P90
P120
70 30 1.8e-005 532 86
Scenario 3 0 70
140
30
20
P90
P120
110 20 0.007547 157 35
Scenario 4 0 70
140
30
20
P90
P120
P110
inflow
70
140
30
20
3.46E-05 63 26
Scenario 5 0.1 70 30 P90
P120
70 20 0.004699 92 42
Scenario 6 0.1 70
140
30
20
P90
P120
P110
inflow
100
140
160
20
20
10
1.42E-02 871 181
Scenario 7 0.1 70
140
30
20
P90
P120
P110
P40
P170
inflow
60
70
140
10
20
20
0.001969 914 325
Scenario 8 0.1 70
140
60
40
P90
P120
P110
inflow
160
70
140
10
50
40
0.00087 694 289
Figure 2 |The difference between the leakages in the real and calculated answers.
Water Practice & Technology Vol 00 No 0, 8
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
check the correct trend of progress towards the final best results. When the correlation between f(x) and f(d)is
weak, the optimization methods will not be able to find the correct answer. In ACO, pheromone updating in is
applied to the fitness of previous answers to select new direction towards the correct answer. This property is
similar to the evolutionary based optimization methods. However, ACO is equipped with another device
named heuristic guidance that helps in finding the correct direction towards the real answer. In this paper,
leaks are defined at a few numbers of unidentified nodes. Then, naturally, the existence of leakage probability
for each node is decreased which is fulfilled by the heuristic guidance. By the use of this technique, it will be poss-
ible to find the correct answer among 19,344 possible solutions only by performing 63 iterations in this scenario.
Uncertainty analysis
It is assumed that one pressure sensor is placed at node 90 and one leakage with the amount of 30 l/s is intro-
duced at node 70. The magnitude of pressure decrement at node 90 due to this leakage is 0.33 m. This
reduction may happen by some other leakages in other nodes. Figure 3 shows some other results that only
with one leaking node can reduce the pressure of node 90 to an amount of 0.33 m. For instance, a flow rate
of 10 l/s at node 90 can cause similar reduction. It means there are several choices to set true value in the
pressure of this node.
The leakage in this case is about 7.5 percent of total consumption. If the leakage is decreased to 10 l/s, the
pressure reduction in observed node is 0.11 m. With pressure measurement errors, this method will be inaccurate
for small leaks.
With some technique it is possible to attain better results. For example, in the minimum night flow the con-
sumption is significantly low and both pressure and leakage over consumption are high. To ascertain better
results, it is proposed to stop the pressure management in the measurement night. Also, this method can help
to detect the zone with high leakage or pipe burst. Using EPS data can increase the accuracy of the methods.
To attain the unique answer, the observational pressure at node 120 is added to the pressure measurements set.
When the pressure at nodes 120 and 90 has been measured accurately, the only choice which can adjust the
pressures at two junctions is the leakage at node 70 of 30 l/s (see Figure 4 and Table 2).
In the anytown network, the number of unknowns were considered 16 node consumption and the number of
pressure observation considered among 2–6.
The common method in real WDNs which is used extensively in studies is classifying the consumption in
nodes. For instance, the network could be divided in to 4 or 5 parts. With this technique the number of unknowns
decrease however, the accuracy of finding the location reduces.
When the measurements are associated with some uncertainties, the points shown in Figure 3, are depicted by
vertical lines. Figure 5 shows the leakage range in various nodes that cause 0.33 m reduction in the pressure of
Figure 3 |The results with leaking node.
Water Practice & Technology Vol 00 No 0, 9
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
node 90. Also, Figure 6 has shown the different leakage values that possibility caused the pressure with pertur-
bation amount +0:1mat nodes 90 and 120. These two charts indicate that 16 possible node in Figure 4 is
limited to 9 nodes in Figure 5 that can consider as the leakage location. By adding the total inflow measurement
as a constraint, the candidate nodes limited to 3 nodes. Likewise, the pressures of nodes 110 and 40 are joined to
the observational set. Figure 7 has clearly shown the analysis has reached exact value. In Figures 6 and 7, the
flowmeter error (0.05 l/s) is shown.
Following issues can be concluded from these investigations. (1) It is clearly shown that the locations and
values of leakages can be obtained by a steady state analysis and an optimization method. (2) ACO can find opti-
mum answers of a problem with a few iterations. It should be noted that in this example, if the inflow is not used
Figure 4 |The achieved results for node 90 and node 120.
Table 2 |The archived results for node 90 and node 120
Node No. 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
Leak at node 90 (l/s) 330 36.7 17.4 13.2 330 30 10.3 4.9 30 110 55 41.2 11.4 23.6 330 10.6
Leak at node 120 (l/s) 45 30 12.9 10 90 30 9 15 22.5 4.3 0.3 0.9 7.5 1.3 90 10
Figure 5 |Leakage range in various nodes.
Water Practice & Technology Vol 00 No 0, 10
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
as observation (e.g. scenario 2, 3 and 5) there are 6
16
¼2,821,109,907,456 different options and if the total leak-
age is 50 l/s and used as a constraint, there are 19,344 various cases. Different scenarios can find the correct
answer in 14 to 914 iterations. In the worst case, about 5% of the solution space is checked to find the exact
answer. (3) The leakage detection occasionally has improved with increasing in the leakage amount, number
of the observations and their accuracies. (4) Reaching to the supreme fitness cannot guarantee neither location
nor quantity of leakages; hence, an optimal sensor placement analysis should be accomplished for each network
to understand the capability of the number and quality of observational set in a WDN as well as the calibration
methodology. In other words, the problem is to find the leakage with available equipment. (5) In the previous
researches (Kapelan et al. 2003; Kapelan, 2005; Behzadian et al. 2009) it has emphasized that for a relative accu-
racy of about 0.85 in the calibration of a network, the pressures at 8 nodes among 16 nodes should be measured.
Five load conditions should be implemented and the number of unknown demands should be limited to 5 groups.
In the other word, to find only 5 unknown parameters with relative accuracy of 0.85, 40 observations are needed.
Therefore, it seems that by the use of this method, it is almost impossible to detect the leakage in a real network.
Therefore, using this method seems almost impossible for a real network. However, in this research it is clearly
shown that with a few number of measurements, a suitable result can be gained while neither node/pipe grouping
nor load conditions are used. Actually, by implementing these two facilities better results can be achieved. As a
matter of fact, it should be said that by the use of these techniques results with higher accuracy can be achieved.
Figure 6 |Different leakage values.
Figure 7 |The exact value of leakage.
Water Practice & Technology Vol 00 No 0, 11
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
Case 3: experimental model
To investigate the above-mentioned technique, a laboratory model is set up at the hydraulic laboratory of Ferdowsi
University of Mashhad, Iran for evaluation of explained method. Figure 8 shows some picture and Figure 9 indi-
cates the EPANET model of the network. The height and width of the network are 3.70 m and 10.30 m,
respectively consists eight consumption taps at nodes 1 to 8 for demand simulation and 31 pressure measurement
situations within six loops. Moreover, as shown in Figure 8 to calculate water in the network, water returning pipes,
a pump and a storage tank are used. Additionally, a volumetric measurement tank is used to measure the demand
flow rate. In this model, electronic pressure transducers with the accuracy of 1% in predetermined spots were used
to measure the pressure and then data are transferred to a PC. The pipes were made of Poly Propylene Random Co-
polymer (PPRC) with inner diameter of 16 and 10 mm for loops and returning pipes. A full port ball valve is
Figure 8 |Some pictures of laboratory.
Water Practice & Technology Vol 00 No 0, 12
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
installed in each of loop pipe to change the configuration of the network. Additionally, an electromagnetic flow-
meter was installed in the network entrance to measure the total inflow of the network with an accuracy of
0.03 l/s. As can be seen in Figure 8(d) we have 8 valves. Each valve receives two pipes which ends to a reservoir.
Near the reservoir we have scaled storage that help us to measure the flowrate.
The pump that is used in the WDN is chosen in a way to response the necessary flows and pressures in net-
work. The power, maximum head and flow of the pump are 4 HP, 52 m and 5 l/s respectively. Also, pump
characteristic curve is shown in Figure 10.
Calibration the network
The network is modeled in EPANET with the specification of exact pipes, pump characteristic curve, nodal
elevations, friction factors and minor losses of the pipes. The hydraulic head loss and minor loss coefficients
are determined through several experimental runs. Since in this paper only the demand is considered as unknown
parameter, other parameters of the model should be calibrated at first. The pipe roughness is the most important
uncertain parameter in a network. Nasirian et al. (2011) have considered the best equation to estimate the longi-
tudinal loss as well as the pipe roughness and minor loss coefficients in the experimental network. H-W
coefficient (Walski et al. 2002) is calculated about 150 for pipes (Nasirian et al. 2011) which are confirmed by
Braud & Soom (1981) and Wu & Gitlin (1984). Additionally, they have proved appropriate accuracy of
Darcy-Weisbach (D-W) and H-W’s equations in this network, and then H-W equation is used in the analysis.
The other testing shows that by measuring the pressure at the pump and reservoir, H-W coefficient was measured
about 130 (Nasirian et al. 2011).
The head loss between pump and reservoir is calculated using H-W and D-W equation, and also it is measured
experimentally as shown in Figure 11.
Figure 9 |The EPANET model of the network.
Figure 10 |Pump characteristic curve.
Water Practice & Technology Vol 00 No 0, 13
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
This figure shows the head difference between Darcy-Weisbach method with Colebrok-White roughness in
comparison of other methods. It can be attributed to the effect of minor head loss. A good agreement between
head loss accounting minor head loss and real head loss can be observed. When the Hazen Williams coefficient
is 130 the difference between observed hydraulic head loss and the computed head loss relates to the minor head
losses. The minor head loss for whole path is computed and it is 8.6 m. This value is the summation of all minor
head losses in each connections and valves exist in the path. With calculating the minor head loss and the linear
head loss, the total head loss is derived. This value corresponds to the laboratorial result. Therefore, ignoring the
minor head losses leads to significant errors. So, all the minor head losses must be computed separately. Typi-
cally, minor losses and friction head loss are related to the velocity with different exponents. The flow velocity
doesn’t exceed 1.5 l/s. It has a value lower than 1.5 l/s. Using an equivalent pipe friction factor instead of
head loss coefficient cause an error that for an urban network with long pipes is negligible, but in a laboratory
scale model, it causes a significant error. To prevent propagating this error in the demand calibration, the
minor loss coefficient for each pipe is experimentally examined. Measured pipes roughness and minor loss coef-
ficients are used in model and then the pressures are calculated and compared with the observational pressures.
Figure 11 |Differences of the head loss between pump and reservoir between Colbrook-White and other methods.
Figure 12 |Difference between the measured and calculated nodal pressures before and after calibration.
Water Practice & Technology Vol 00 No 0, 14
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
One leakage in the network
In this case, a leakage of 0.262 l/s is introduced at node 9 while the main pipes are opened. Figure 9 shows the
leakage location. Also, the location of pressure sensors used in various scenarios has been shown as hollow cir-
cles. Nodal pressures of nodes 17 and 24 are measured. The demand will be searched within a range of a
minimum of zero to a maximum of 1 l/s with an incremental step of 0.05 l/s in all cases.
Table 3 shows the computational and observational pressures in the considered nodes. The program reaches
true answer in 102th iteration. The results show that the leakage with a quantity of 0.25 l/s happens at node 9
which it is the best possible answer.
In this case an uncertainty analysis is accomplished. Figure 13 represents the solution space for various
pressure observations. Figure 13(a) indicates the solution space when the pressure at node 24 is measured.
Figure 13(b) show the solution space if the pressure at node 17 in measured. Figure 13(c) shows the answer
spaces when the pressures of this two nodes are measured simultaneously. Figure 13(a) and 13(b) illustrate 3
and 4 answers for pressure measurements at nodes 24 and 17, respectively, while the solution space using 2
pressure measurements include 2 answers. In other words, 0.3 l/s of leakages at nodes 5 and 9 can be potentially
Table 3 |The computational and observational pressures in the considered nodes
Node No. Observation pressure (m)
ACO results
Calculated demand (l/s) Simulated pressure (m)
9–0.25 24.35
17 29.96 0 30.30
24 28.72 0 29.07
Figure 13 |The solution space for various pressure observations.
Water Practice & Technology Vol 00 No 0, 15
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
found as the answer, while as mentioned above the leakage location is found in the calibration process at node
9. This analysis is clarified that, although the calibration results in Table 3 have reached the true results, another
potential answer exists. Figure 13(d) presents the solution space after adding the pressures at nodes 24, 17 and 25
to pervious observations. However, no unique value is observed. It should be noted that more analyses with var-
ious observational cases are clarified that reaching a unique answer in this case is impossible. Nevertheless, the
results are considered very satisfactory and promising because solution space is closed to the real leaky point.
Two leakages in a sub-network
In the other case, the network is reconfigured by closing the valves in pipes 8, 12 16, 19, and 22. In other words,
the middle pipes are closed and only the peripheral pipes are opened. The installed taps at nodes 5 and 6 are
opened with the measured leakages of 0.09 and 0.33 l/s, respectively. Also, the pressures of nodes 17, 24 and
27 are measured. The answers are found at 195th iteration and the leakages at nodes 5 and 6 are computed as
0.1 and 0.3 l/s. The final results are shown in the Table 4.
Two leakages in main network
As the final case, leakages at nodes 8 and 6 with the amount of 0.37, 0.526 l/s are introduced to the nodal while
all of the pipes in the network are opened. The pressures at five nodes 20, 33, 25, 14 and 45 are measured. The
network is calibrated using two observational cases. The pressures of nodes, 33, 20 and 25 are used in the first
case, while all of the five pressure measurements are applied in the second case. The leakages are found in
the range of 0 to 0.7 l/s and incremental steps are 0.05 l/s.
To evaluate the errors in the measured data, nodal pressures are calculated using EPANET model applying
measured flows in the leaky nodes. A comparison between the observational and computational pressures
shows that an average discrepancy of about 0.41 m. Therefore, if calibration attains the exact value of leakages,
the obtained fitness will not be less than 0.98. Table 5 presents the measured pressures, EPANET results as well
Table 4 |The final results
Parameter Node No. Observation ACO results
Demand (l/s) 5 0.09 0.1
6 0.33 0.3
Pressure (m) 27 23.96 24.41
24 22.65 22.98
17 25.35 25.87
Table 5 |The acquired results
12345 6
Parameter Node No. Observation Epanet results ACO results with 3 observations ACO results with 5 observations
Demand (l/s) 3 0 0 0 0
40 0 0 0
8 0.37 0.37 0 0.25
6 0.526 0.526 0.4 0.55
9 0 0 0.45 0.1
7 0 0 0.05 0
50 0 0 0
10 0 0 0 0
Pressure (m) 20 34.9 35.54 34.82 35.19
33 32.4 32.84 32.51 32.63
25 34.4 34.93 34.4 34.52
14 37.8 37.54 –37.45
45 36.1 35.92 –35.54
Fitness –– 0.98 0.0185 0.587
Water Practice & Technology Vol 00 No 0, 16
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
as, the ACO optimization results. Table 5 column 5 shows the results using 3 pressure observations. Although the
obtained fitness, 0.0185 is great, the leakages are detected incorrectly and only one of the leakages is partly
defined. The final examination using five pressure observations is presented in column 6 of Table 5. The results
indicate reasonable accuracies in the obtained results.
Due to the fact that the best expected fitness is 0.98, there are several other answers that have shown relative by
good fitnesses. Table 6 displays the best 10 calibrated results for the first observational case. The first column is
expressed the best results in this case. Meanwhile, the other columns show that a number of results are approach-
ing to the best one. The best answer shows that the leakages at nodes 6, 7 and 9 while the second answer shows
leakages at two different nodes 4 and 10 accompanied with a significant reduction in the leakage quantities at
node 9. Likewise, the third answer is completely different from the best answer. In the other word, the results
have shown no convergence or correlation between various results attaining the final solution.
Table 7 shows a number of answers of the second case using five pressure measurements. It is clearly observed
that the calculated answer has greatly approached to the final results. The results elucidate a good convergence
between the three final answers.
Three case studies of leakage detections have shown that increasing in the number of leakages or complexity of
a network increase the difficulty of leakage detection. Also, considering two cases of 3 and 5 observations have
determined the leakage at node 6 which is defined in both cases, while leakage at node 8 is only defined after
using five observations. This confirms a relationship between the value of leakage and the number of obser-
vations. In other words, request number of pressure measurements is increased with increasing in the size and
number of leakages as well as complexity of the network.
Investigating the best 10 results in Tables 6 and 7have illustrated that the leakage at node 6 is correctly
detected in 8 answers as shown in Table 7, while it is obtained only in 5 answers as shown in Table 6. In the
other word, although the leakages of node 6 in both observational cases are correctly determined, leakage
Table 6 |The best 10 calibrated results for the first observational case
Fitness
0.019 0.030 0.098 0.099 0.174 0.432 0.541 1.175 1.533 1.857Node No.
9 0.45 0.15 0.55 0.6 0 0 0 0 0 0
8 0 0 0 0 0.15 0 0.45 0 0 0.55
7 0.05 0.05 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0.4 0.55 0 0.15 0
4 0000000000
5 0 0.2 0 0 0.1 0 0 0 0.7 0.4
6 0.4 0.4 0 0 0.65 0.55 0 0.5 0.1 0
Table 7 |A number of answers of the second case using five pressure measurements
Node No. 0.59 0.61 0.61 0.73 1.04 1.08 1.88 2.32 2.69 2.69
10 0 0 0 0 0.35 0 0.5 0 0 0
9 0.1 0.05 0 0 0.15 0 0.15 0 0.35 0.35
8 0.25 0.3 0.3 0 0.1 0.15 0 0 0 0
7 0000000000
3 0 0 0 0 0 0 0.05 0.4 0 0
4 0 0 0 0.35 0 0 0 0 0.55 0.55
5 0 0 0 0 0.25 0.1 0 0 0 0
6 0.55 0.55 0.6 0.55 0.05 0.65 0.2 0.55 0 0
Water Practice & Technology Vol 00 No 0, 17
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
detection frequency in Table 7 is higher than Table 6. This comparison between leakage detection frequency at
nodes 8 and 6 in each of observational cases confirm a relationship between frequency of leakage detection and
reliability of answers.
The experimental investigations in two observational cases have illustrated the fact that a good fitness cannot
guarantee attaining a good answer. Based on the results, it is recommended that some good answers are checked
out instead of only on the best result. If the other answers with proximate comparatively good fitness present simi-
lar leakages, the results are reliable. Otherwise, an uncertainty analysis can help to clarify that with a number of
recorded data (obtained from pressure/flow measurement devices) if there is a unique answer set to the problem
or the feasible solution space contains a large number of answer sets.
CONCLUSIONS
In this paper, the leakage detection in a WDN based on calibration and ACO is investigated. Three bases of find-
ing leakage in a network are as the followings: gathering network data, hydraulic analysis of the network and
optimization algorithm. In the current paper, as a main objective it is focused on the improvement of the optim-
ization method. However, in the future works the model will be applied to real networks. It is believed that the
most advanced methods in network analysis such as pressure dependent analysis and EPS should be used. In
addition, it is mandatory to use pipe and node groupings in large networks, which make it possible to solve
the problem. The method is applied to a hypothetical and a laboratorial network without using pipe and/or
node grouping for unknown reduction or implementation at different load conditions to increase the observa-
tional numbers. So, the analyses are accomplished in a fully under-determined state. Also, a novel approach is
used to investigate the uncertainty in an underdetermined problem. This method is successfully applied to
both networks. The solution space is illustrated for a measurement scenario. Also, the effects of measurement
errors on final answers are investigated. Utilization of this method for two networks proves the accuracy of
ACO to find a WDN leakage with a few number of observations. Based on the current investigations, leakage
detection in the studied networks can attain appropriate results with a few number of pressure and flow obser-
vations. Also, this method is succeeded to recognize the sizes and locations of the leaks in the laboratory
network with actual errors. The experimental and computational investigations in two networks have illustrated
that a good fitness cannot guarantee a reliable answer. To cope with this difficulty, it is recommended to check
some answers instead of just looking for the best result. If the answers with comparatively good fitness present
similar leakages, the results are reliable, otherwise, an uncertainty analysis can be used to understand the feasi-
bility of attaining answers with available pressure/flow measurements. Other investigations have shown that the
reliability of the technique has a direct proportionality with the number of correct answers and the total number
of answers. The case studies of leakage detections have shown that increasing the number of leakages in a WDN
or complicating the network needs larger number of observations.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
REFERENCES
Abhulimen, K. E. & Susu, A. A. 2004 Liquid pipeline leak detection system: model development and numerical simulation.
Chemical Engineering Journal 97(1), 47–67.
Abramowitz, M. a. S. I. A. 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th
Printing. Dover, New York.
Afshar, M. H. 2007 Partially constrained ant colony optimization algorithm for the solution of constrained optimization
problems: application to storm water network design.Advances in Water Resources 30(4), 954–965.
Afshar, M. H. 2010 A parameter free continuous ant colony optimization algorithm for the optimal design of storm sewer
networks: constrained and unconstrained approach.Advances in Engineering Software 41(2), 188–195.
Almandoz, J., Cabrera, E., Arregui, F., Cabrera, E. & Cobacho, R. 2005 Leakage assessment through water distribution network
simulation.Journal of Water Resources Planning and Management 131(6), 458–466.
Andersen, J. H. & Powell, R. S. 2000 Implicit state-estimation technique for water network monitoring.Urban Water 2(2),
123–130.
Behzadian, K., Kapelan, Z., Savic, D. & Ardeshir, A. 2009 Stochastic sampling design using a multi-objective genetic algorithm
and adaptive neural networks.Environmental Modelling & Software 24(4), 530–541.
Braud, H. & Soom, A. 1981 Trickle irrigation lateral design in sloping fields.Trans ASAE 24(4), 941–944.
Water Practice & Technology Vol 00 No 0, 18
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
Brunone, B. 1999 Transient test-based technique for leak detection in outfall pipes.Journal of Water Resources Planning and
Management 125(5), 302–306.
Brunone, B. & Ferrante, M. 2001 Detecting leaks in pressurized pipes by means of transients.Hydraulic Research 39(5),
539–547.
Bush, C. & Uber, J. 1998 Sampling design methods for water distribution model calibration.Water Resources Planning and
Management, ASCE 124(6), 334–344.
Carpentier, P. & Cohen, G. 1991 State estimation and leak detection in water distribution networks.Civil Engineering Systems
8(4), 247–257.
Cheng, W. & He, Z. 2011 Calibration of nodal demand in water distribution systems.Journal of Water Resources Planning and
Management 137(1), 31–40.
Cheng, W. P., Yu, T. C. & Xu, G. 2014 Real-Time model of a large-scale water distribution system.Procedia Engineering 89(0),
457–466.
Covas, D. & Ramos, H. 1999 Leakage Detection Single Pipelines Using Pressure Wave Behaviour. In: Water Industry Systems:
Modeling and Optimization Applications (Savic, D. & Walters, G. eds.). Research Studies Press, Hertfordshire, England.
Covas, D. & Ramos, H. 2010 Case studies of leak detection and location in water pipe systems by inverse transient analysis.
Journal of Water Resources Planning and Management 136(2), 248–257.
Covas, D., Ramos, H., Young, A., Graham, N. & Maksimovic, C. 2005 Uncertainties of Leak Detection by Means of Hydraulic
Transients: From the lab to the field. In: Paper Presented at the 8th Int. Conf. on Computing and Control for the Water
Industry (CCWI 2005). Univ. of Exeter, Exeter, UK.
Dorigo, M. 1992 Optimization, Learning and Natural Algorithms. Ph.D. thesis, Politecnico di Milano, Milan, Italy.
Ferreri, G., Napoli, E. & Tumbiolo, A. 1994 Calibration of Roughness in Water Distribution Networks. In: Paper Presented at
the 2nd Int. Conf. on Water Pipeline Systems, Suffolk, U.K.
Giustolisi, O. & Berardi, L. 2010 Water distribution network calibration using enhanced GGA and topological analysis.
Hydroinformatics 13(4), 621–641.
Giustolisi, O., Kapelan, Z. & Savic, D. 2008 Extended period simulation analysis considering valve shutdowns.Water Resources
Planning and Managment, ASCE 527–537.
Hunaidi, O., Chu, W., Wang, X. & Guan, W. 1998 Effectiveness of Leak Detection Methods for Plastic Water Distribution Pipes.
Paper presented at the Workshop on Advancing the State of our Distribution Systems, Denver.
Hunaidi, O., Chu, W., Wang, A. & Guan, W. 1999 Leakage Detection Methods for Plastic Water Distribution Pipes. Paper
presented at the Advancing the Science of Water, Denver.
Jamasb, M., Tabesh, M. & Rahimi, M. 2008 Calibration of EPANET Using Genetic Algorithm Water Distribution Systems
Analysis 2008, pp. 1–9.
Jung, D. & Lansey, K. 2014 Water distribution system burst detection using a nonlinear kalman filter. Journal of Water
Resources Planning and Management
Jung, D., Kang, D., Kim, J. & Lansey, K. 2014 Robustness-based design of water distribution systems. Journal of Water Resources
Planning and Management
Jung, D., Choi, Y. H. & Kim, J. H. 2016a Optimal node grouping for water distribution system demand estimation.Water 8(4),
160.
Jung, D., Yoo, D., Kang, D. & Kim, J. 2016b Linear model for estimating water distribution system reliability. Journal of Water
Resources Planning and Management.
Kang, D. & Lansey, K. 2009 Real-time demand estimation and confidence limit analysis for water distribution systems.Journal
of Hydraulic Engineering 135(10), 12.
Kang, D. & Lansey, K. 2010 Optimal meter placement for water distribution system state estimation.Journal of Water Resources
Planning and Management 136(3), 10.
Kang, D. & Lansey, K. 2011 Demand and roughness estimation in water distribution systems.Journal of Water Resources
Planning and Management, ASCE 137(1), 20–30.
Kang, D. S., Pasha, M. F. K. & Lansey, K. 2009 Approximate methods for uncertainty analysis of water distribution systems.
Urban Water Journal 6(3), 233–249.
Kapelan, Z., Savic, D. & Walters, G. 2003 Multiobjective sampling design for water distribution model calibration.Journal of
Water Resources Planning and Management 129(6), 466–479.
Kapelan, Z., Savic, D. & Walters, G. 2005 Optimal sampling design methodologies for water distribution model calibration.
Journal of Hydraulic Engineering 131(3), 190–200.
Kapelan, Z., Savic, D. & Walters, G. 2007 Calibration of water distribution hydraulic models using a Bayesian-type procedure.
Hydraulic Engineering ASCE 133(8), 927–936.
Lansey, K., El-Shorbagy, W., Ahmed, I., Araujo, J. & Haan, C. 2001 Calibration assessment and data collection for water
distribution networks.Hydraulic Engineering, ASCE 127(4), 270–279.
Lay-Ekuakille, A., Vendramin, G. & Trotta, A. 2009 Spectral analysis of leak detection in a zigzag pipeline: a filter
diagonalization method-based algorithm application.Measurement 42(3), 358–367.
Liggett, J. A. & Chen, L. 1994 Inverse transient analysis in pipe networks.Journal of Hydraulic Engineering, ASCE 120(8),
934–955.
Maghrebi, M., Hassanzade, Y. & Yazdini, S. 2012 Leak detection in water distribution networks based on ant colony
optimization (Case study: golbahar town of mashhad). Journal of Water & Wastewater 85.
Water Practice & Technology Vol 00 No 0, 19
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
Maier, H., Simpson, A., Zecchin, A., Foong, W., Phang, K., Seah, H. & Tan, C. 2003 Ant colony optimization for design of water
distribution systems.Journal of Water Resources Planning and Management, ASCE 129(3), 200–209.
Nasirian, A., Maghrebi, M. & Arshadi, M. 2011 Laboratorial Evaluation of Water Loss in PPRC Pipes. In: Small Diameter Paper
Presented at the 10th Iranian Hydraulic Conference, Rasht, Iran.
Ostfeld, A., Salomons, E., Ormsbee, L., Uber, J., Bros, C., Kalungi, P. & McKillop, R. 2012 Battle of the water calibration
networks.Journal of Water Resources Planning and Management 138(5), 523–532.
Pérez, R., Puig, V., Pascual, J., Quevedo, J., Landeros, E. & Peralta, A. 2011 Methodology for leakage isolation using pressure
sensitivity analysis in water distribution networks.Control Engineering Practice 19(10), 1157–1167.
Poulakis, Z., Valougeorgis, D. & Papadimitriou, C. 2003 Leakage detection in water pipe networks using a Bayesian
probabilistic framework.Probabilistic Engineering Mechanics 18(4), 315–327.
Pudar, R. & Liggett, J. 1992 Leaks in pipe networks.Journal of Hydraulic Engineering 118(7), 1031–1046.
Rezaei, G., Afshar, M. H. & Rohani, M. 2014 Layout optimization of looped networks by constrained ant colony optimisation
algorithm.Advances in Engineering Software 70(0), 123–133.
Rossman, L. 2000 EPANET.2 Users Manual.
Sage, P. & Wu, Z. 2006 Water Loss Detection Via Genetic Algorithm Optimization-Based Model Calibration. In: Paper
Presented at the ASCE 8th Annual Int. Symp. on Water Distribution Systems Analysis, Cincinnati, Ohio.
Savic, D. & Walters, G. 1995 Genetic Algorithm Techniques for Calibrating Network Models (Vol. 95/12). Centre for Systems
and Control Engineering, Univ. of Exeter, Exeter, U.K
Simpson, A., Maier, H., Foong, W., Phang, K., Seah, H. & Tan, C. 2001 Selection of Parameters for Ant Colony Optimization
Applied to the Optimal Design of Water Distribution Systems. In: Paper Presented at the Congress on Modelling and
Simulation, Canberra (Australia).
Todini, E. 1999 Using a kalman filter approach for looped water distribution network calibration. Modelling and Optimisation
Applications 1,9.
Walski, T., Chase, D., Savic, D., Grayman, W. & Beckwith, S. 2002 Advanced Water Distribution Modeling and Management.
Haested Press, Waterbury, CT USA.
Walski, T., Bezts, W., Posluszny, E. T., Weir, M. & Whitman, B. E. 2006a Modeling leakage reduction through pressure control.
AWWA 98(4), 147–155.
Walski, T., DeFrank, N., Voglino, T., Wood, R. & Whitman, B. E. 2006b Determining the Accuracy of Automated Calibration of
Pipe Network Models. In: Paper Presented at the 8th Annual Water Distribution Systems Analysis Symposium, Cincinnati,
Ohio, USA.
Wu, I. & Gitlin, H. 1984 Drip irrigation lateral line network designs. Trans ASAE 25(3), 675–685.
Wu, Z., Sage, P. & Turtle, D. 2010 Pressure-dependent leak detection model and Its application to a district water system.
Journal of Water Resources Planning and Management 136(1), 116–128.
Yazdi, J., Lee, E. & Kim, J. 2014 Stochastic multiobjective optimization model for urban drainage network rehabilitation.
Journal of Water Resources Planning and Management 0(0), 1061–1071.
First received 2 October 2020; accepted in revised form 16 July 2021. Available online 29 July 2021
Water Practice & Technology Vol 00 No 0, 20
Uncorrected Proof
Downloaded from http://iwaponline.com/wpt/article-pdf/doi/10.2166/wpt.2021.071/915774/wpt2021071.pdf
by guest
on 30 July 2021
