10
CHAPTER 2
LITERATURE REVIEW
Water distribution systems consist of pipeline networks and
associated components, most of which is underground and exposed to soil
corrosion and mechanical stress from the surrounding soil, surface traffic,
and internal water pressure (Ahammed and Melchers 1997). Pipe failure in
water distribution systems disrupts the water supply to consumers and reduces
the reliability of the system. It is found that about 35% to 60% of the
supplied volume is wasted due to pipe leakages (Babovic et al 2002).
Therefore, inspection, control and planned maintenance and rehabilitation
programs are necessary to properly operate existing water distribution
systems (Saegrov et al 1999).
This chapter reviews the applications of various methods, tools and
techniques for the design and performance evaluation of water supply systems
and the optimization models in water distribution systems. Section 2.1
presents several optimization models, techniques and heuristics used for the
optimal design of water distribution systems that have been given appreciable
attention in the published literature. A literature survey on optimal operational
strategies of urban water distribution systems is given in Section 2.2. The
literature on topics such as failure analysis and prevention, reliability-based
design, and risk assessment and control in water distribution systems are
presented in Section 2.3. A review of literature on the maintenance,
rehabilitation, strengthening and replacement policies of water distribution
systems is included in Section 2.4.
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2.1 DESIGN OF WATER DISTRIBUTION SYSTEM
A water distribution network must be designed so that it can supply
the desired quantity of water to the consumers at sufficient pressure. The
design involves specifying the sizes of different elements of the distribution
network and checking the adequacy of this network (Mays 2000). Significant
effort has been placed in developing approaches to solve for optimal designs
of water distribution systems.
2.1.1 Pipe Characteristics
A large body of literature exists on the optimization of the pipe
network design, reporting the application of classical optimization methods
(including linear programming, dynamic programming and nonlinear
programming). These methods have been used, sometimes at the cost of
considerable simplifications of the optimization models. One of the earliest
optimization approaches, the linear programming gradient method was
proposed by Alperovits and Shamir (1977). Other authors followed this
innovative course and introduced alternative derivations from the linear
programming-based gradient expressions (Quindry et al 1981, Fujiwara
et al 1987, Lansey and Mays 1989, Kessler and Shamir 1989, Fujiwara and
Khang 1990). These approaches lead to solutions in which pipes have one or
two fixed diameter segments. For practical implementation this type of
solution is unrealistic.
The state-of-the-art principles and methods of pipe network
optimization are presented by Walski (1985). Su et al (1987) presented a basic
framework for a model that can be used to determine the optimal least-cost
design of a water distribution system subject to conservation of energy and
reliability constraints. The limitation of this model is that the resulting pipe
diameters may not be commercially available pipe sizes and should be
12
rounded of to the appropriate sizes. These approximated diameters might
affect the feasibility of the resulting optimal solution.
Fujiwara and Silva (1990) proposed a heuristic method to obtain a
least-cost water distribution network design with a given reliability. The
method first determines an optimal design without the consideration of
reliability. The reliability of the network design is then assessed. An iterative
feedback procedure is then employed, which improved the reliability with a
small increase in cost.
Nonlinear programming technique has been used as an optimization
approach to solve the design optimization problem of water distribution
networks (Fujiwara and Khang 1990, Fujiwara and Khang 1991 and Varma
et al 1997) in which the diameter is taken to be a continuous variable.
A redundancy-constrained minimum-cost design of water
distribution networks is presented by Park and Liebman (1993). Redundancy
is quantified using the expected shortage due to failure of individual pipes as
a measure of reliability that permits incorporation of some considerations of
frequency, duration and severity of damage.
Developments in the field of stochastic optimization have allowed
the resolution of design optimization problems formulated as nonlinear mixed
integer problems. Genetic algorithms were used by Murphy et al (1993),
Simpson et al (1994), Dandy et al (1996), Savic and Walters (1997),
Keedwell and Khu (2005), and Keedwell and Khu (2006) and Simulated
annealing technique was applied by Cunha and Sousa (1999) and Cunha and
Sousa (2001). The applications of other evolutionary optimization algorithms
such as Ant Colony Optimization (Maeir et al 2003), Shuffled Frog Leaping
Algorithm (Eusuff and Lansey 2003), Tabu Search heuristic (Cunha and
Ribeiro 2004), Scatter Search (Lin et al 2007) and Particle-Swarm Harmony
13
Search (Geem 2009 b) to obtain the least-cost design of water distribution
network are reported in the literature. Evolutionary algorithms have also
enabled researchers to approach water distribution network design
optimization as a multiobjective problem, usually to determine the least cost
design which maximizes the benefits (Halhal et al 1997, Walters et al 1999,
Prasad and Park 2004, Kapelan et al 2005, and Lyroudia et al 2005).
Liong and Atiquzzaman (1994) proposed a powerful optimization
algorithm, Shuffled Complex Evolution (SCE) linked with EPANET, the
network simulation model to solve water distribution network design
optimization problems.
Taher and Labadie (1996) developed a prototype decision support
system WADSOP (Water Distribution System Optimization Program) to
guide water distribution system design and analysis in response to changing
water demands, timing, and use patterns; and accommodation of new
developments. WADSOP integrates a geographic information system (GIS)
for spatial database management and analysis with optimization theory to
provide a computer-aided decision support tool for water engineers. Xu and
Goulter (1999) proposed a fuzzy linear program optimization approach for the
optimal design of water distribution networks.
Wu and Simpson (2001) applied a Genetic Algorithm to the
optimal design and rehabilitation of a water distribution system. Two
benchmark problems of water pipeline design and a real water distribution
system are presented to demonstrate the application of the proposed
technique.
A Fuzzy linear programming model is formulated by Bhave and
Gupta (2004) for minimum cost design of water distribution networks. Future
water demands being difficult to predict with any uncertainty are considered
14
as fuzzy demands and modeled by trapezoidal possibility distribution
function. The proposed linear programming model avoided iterative
procedure and also provided a cheaper solution.
A self-adaptive fitness formulation for solving constrained design
optimization of water distribution networks is presented by Farmani
et al (2005). The method has been formulated to ensure that slightly infeasible
solutions with a low objective function value remain fit. The method does not
require an initial feasible solution, this being an advantage in real-world
applications having many optimization variables.
Vairavamoorthy and Ali (2005) proposed a methodology for the
optimal design of water distribution systems based on Genetic Algorithms.
The objective of the optimization is to minimize the capital cost, subject to
ensuring adequate pressures at all nodes during peak demands. The method
involves the use of a pipe index vector to control the genetic algorithm search.
The method has been tested on several networks, including networks used for
benchmark testing least cost design algorithms, and has been shown to be
efficient and robust.
A least-cost design of water distribution networks under demand
uncertainty is developed by Babayan et al (2005). A new approach to
quantifying the influence of demand uncertainty is proposed. The original
stochastic model is reformulated as a deterministic one, and it is coupled with
an efficient genetic algorithm solver to find robust and economic solutions.
Khu and Keedwell (2005) formulated a multi-objective
optimization problem for water distribution network design and results are
compared with optimization using a single-objective Genetic Algorithm and
two-objectives optimization using a non-dominated sorted Genetic
Algorithm-II (NSGAII). Atiquzzaman et al (2006) suggested a scheme to
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assist decision makers in selecting the best alternative water distribution
network design solution which is within the available budget and tolerated
pressure deficit. A multi objective optimization algorithm, NSGA-II is
coupled with water distribution network simulation software-EPANET
(Rossman, 2000) to demonstrate the application of the same.
Geem (2006) presented a cost minimization model using Harmony
Search (HS) algorithm for the design of water distribution networks. The
model is applied to five water distribution networks and the results showed
that the Harmony Search-based model is suitable for water network design.
Zecchin et al (2006) proposed an advanced Ant Colony Optimization (ACO)
algorithm known as Max-Min Ant System (MMAS) for the water distribution
system optimization problem.
Branch and Bound integer linear programming technique is used by
Samani and Mottaghi (2006), for optimum design of municipal water
distribution networks. The constraints include pipe sizes, reservoir levels, pipe
flow velocities and nodal pressures. This procedure helped to design a water
distribution network that satisfies all required constraints with a minimum
total cost.
Lin et al (2007) have proposed an optimization procedure using
Scatter Search (SS) heuristic to solve the design optimization problem of
water distribution networks. The computational results obtained with the three
example networks indicate that SS is able to find solutions comparable to
those provided by some of the most competitive algorithms published in the
literature. Perelman and Ostfeld (2007) presented an adaptive stochastic
algorithm for optimal design of water distribution systems based on the
heuristic cross-entropy method for combinatorial optimization. Immune
Algorithm (IA) inspired by the defense process of the biological immune
16
system is proposed by Chu et al (2008) to obtain the optimal design of water
distribution networks.
Reca et al (2008) evaluated the performance of metaheuristic
techniques such as Genetic Algorithms, Simulated Annealing, Tabu Search
and iterative local search used in the design optimization of water distribution
networks. It is observed that Genetic Algorithm is more efficient when
dealing with a medium-sized network, but other methods outperformed it
when dealing with a real complex one.
A modified Harmony Search algorithm incorporating ‘particle
swarm’ concept is developed by Geem (2009 a) for optimal design of water
networks. Pierro et al (2009) have introduced two hybrid algorithms,
ParEGO and LEMMO, to solve a multi-objective design optimization
problem of water distribution networks. A real medium-size network in
Southern Italy and a real large-size network in United Kingdom under a
scenario of a severely restricted number of function evaluations are tested on
the design problem. Banos et al (2010) have analyzed the performance of a
new memetic algorithm for the optimal design of water distribution systems.
2.1.2 Network Layout
The joint problem of layout and component design of water
distribution networks is addressed by Rowel and Barnes (1982). A two-level
hierarchically integrated system of models is developed for the layout of both
single and multiple source water distribution systems. Bhave and Lam (1983)
proposed a Dynamic Programming approach to obtain a less costly
distribution layout. An integrated model for the least cost layout and design of
water distribution networks is developed by Goulter and Morgan (1985). The
model consists of two linked linear programming formulations. One linear
program determines the least cost layout of a distribution network given an
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initial pressure distribution. The other program determines the least cost
component design given an initial pipe layout.
Goulter and Coals (1986) developed two quantitative approaches to
the incorporation of reliability measures in the least-cost design of water
distribution networks. In both approaches Linear Programming technique is
used to obtain an optimal layout design.
A model for the layout optimization of water distribution networks
under single loadings is presented by Awumah et al (1989). The zero-one
integer programming model is used to select the pipes that should form the
network, while satisfying redundancy and hydraulic requirements. A network
component optimization step, using well established design models is then
applied to this solution to refine the pipe sizes and pressure heads, thus giving
a layout and component optimal solution.
Lejano (2006) developed a method for determining an optimal
layout for a branched pipeline irrigation water distribution system given only
the spatial distribution of potential customers and their respective demands. A
mixed integer linear programming (MILP) algorithm is applied to optimize an
empirically derived objective function.
Genetic Algorithm approach is presented by Afshar (2007) for the
simultaneous layout and component size optimization of water distribution
networks. The method starts with a predefined maximum layout which
includes all possible and useful connections. An iterative design-float
procedure is then used to move from the current to a cheaper layout satisfying
a predetermined reliability set by the user.
Tanyimboh and Setiadi (2008) presented a multi-criteria maximum-
entropy approach to the joint layout, pipe size and reliability optimization of
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water distribution systems. The capital cost of the system is taken as the
principal criterion, and so the trade-offs between cost, entropy, reliability and
redundancy are examined sequentially in a large population of optimal
solutions.
2.2 OPERATION OF WATER DISTRIBUTION SYSTEM
2.2.1 Leak Detection and Monitoring
Leakage in water supply networks can represent a large percentage
of the total water supplied, depending on the age and deterioration of the
system. As a result of water losses and increasing population, urban areas may
experience shortages of water. Coulbeck and Orr (1993) presented a
reliability perspective of the required systems and activities for control of
water distribution networks with an objective of cost control, quality control
and leakage control. The ways in which computers are being used for control
purposes are described.
Reis et al (1997) have addressed the problem of appropriate
location of control valves in a water supply pipe network and their settings via
Genetic Algorithm to obtain maximum leakage reduction for given nodal
demands and reservoir levels.
Vitkovsky et al (2000) used Genetic Algorithm technique in
conjunction with the inverse transient method to detect leakage locations and
magnitudes while simultaneously finding the friction factors in water
distribution systems.
A new method for detecting the magnitude of leaks in small
residential service zones of a drinking water distribution system is proposed
by Buchberger and Nadimpalli (2004). Several examples, based on observed
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and simulated pipe flows are presented to demonstrate the application of the
leak detection method.
Almandoz et al (2005) presented a methodology for evaluation of
water losses based on discrimination of the two components of uncontrolled
water in a water distribution network; physical losses in mains and service
connections, and the volume of water consumed. An extended period
simulation of a water distribution network is employed in the study.
A model to support decision systems regarding quantification,
location and opening adjustment of control valves in a network system, with
the main objective to minimize pressure and consequently leakage levels is
developed by Araujo et al (2006). EPANET model (Rossman 2000) is used
for hydraulic network analysis and Genetic algorithm optimization method for
pressure control and leakage reduction. A case study is presented is used to
show the efficiency of the system by pressure control through valves
management.
Alvisi and Franchini (2009) have presented a procedure for optimal
medium-term scheduling of rehabilitation and leakage detection interventions
in a water distribution system given predetermined budget constraints. The
objectives are to minimize the lost volumes of water and break repair costs.
The optimizer used is the NSGA II multi-objective genetic algorithm.
2.2.2 Pumping Mains Operations
The problem of daily controlling a water distribution network,
including pumping devices, and storage capacities, in order to supply the
consumers at the lowest cost is addressed by Joalland and Cohen (1980).
Discrete Dynamic Programming approach is used to solve the problem.
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Walski (1982) made an economic comparison of the cost between the lining
of main and the associated savings in the energy costs of pumping.
Chen (1988) considered a network without tanks and determined
the optimal allocation of supply between the pump sources. Dynamic
programming approach was used to select the actual pumps given the optimal
continuous outflows.
Kim and Mays (1994) described how to minimize the pumping
costs by including the rehabilitation action for each main of the hydraulic
model as a decision variable. This system cost, subject to a hydraulic
constraint formulation is minimized using a nonlinear optimization package.
Klempous et al (1997) presented a multilevel two algorithms for finding
optimal control in a static water distribution system based on the idea of
aggregation technique. The first is a simulation algorithm of the pipeline
network and the other is an algorithm for finding an optimal control at the
pumping station.
A hybrid expert system called EXPLORE has been developed by
Leon et al (2000), to manage the Seville City water supply system.
EXPLORE reduces the cost of the operation of pumping the water to the
different storage tanks. For this task EXPLORE employs the water demand
forecast to obtain an optimal daily pumping schedule. A prototype has been
tested and has provided great improvement in the electrical costs.
Sakarya and Mays (2000) used a mathematical programming
approach for determining the optimal operation of water distribution system
pumps with water quality considerations. The methodology is based upon
describing the operation as a discrete time optimal scheduling problem that
can be used to determine the optimal operation schedules of the pumps in
distribution systems.
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Cembrano et al (2000) proposed an optimal supervisory control
system which can be used as an efficient means of scheduling water transfer
operations to achieve management goals, such as cost minimization and
quality improvement. The case study presented showed that significant
savings may be achieved by using the optimal control procedures to compute
the strategies for pumping and water transfer operation.
An optimal pump scheduling problem in water supply systems is
addressed by McCormick and Powell (2003). Medium term maximum
demand policies are assumed to be represented in daily scheduling by
constraints on power use or by penalty costs. The problem is formulated as a
Dynamic Program in which variations in daily demand for water are modeled
as a Markov process.
Zyl et al (2004) proposed the use of a hybrid Genetic Algorithm for
operational optimization of water distribution systems. Two hill-climber
strategies, the Hooke and the Jeeves and Fibonacci methods are investigated.
The objective is to find the optimal operating strategy to provide an
acceptable level of service to the customer within system constraints, while
minimizing the operational cost.
Farmani et al (2005) investigated the application of multi-objective
evolutionary algorithms to the identification of the payoff characteristics
between total cost and reliability of a water distribution system. The pipe
rehabilitation decisions, tank sizing, and pump operation schedules are the
decision variables considered.
Broad et al (2010) have proposed the application of meta-models,
which can act as a surrogate or substitute for simulation models, for optimal
operation of water distribution networks. The study considered average daily
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pumping costs and chlorine costs and demonstrated the effectiveness of the
approach by applying it to an actual distribution network.
2.3 RELIABILITY OF WATER DISTRIBUTION SYSTEM
2.3.1 Failure Analysis and Prevention
The deterioration of pipes may be classified into structural
deterioration which diminishes their structural resiliency and their ability to
withstand various types of stress, and internal deterioration resulting in
diminishing hydraulic capacity, degradation of water quality. The
deterioration processes as well as pipe structural failure models are therefore
very complex and difficult to model. Although significant work has been done
in modeling the physical process of pipe deterioration and failure (Doleac
et al 1980, Ahammed and Melchers 1994, Rajani et al 1996), the complex
processes, lack of pertinent data and highly variable environmental conditions
posed severe challenges to these research efforts and a comprehensive model
is required.
Damelin et al (1972) considered water supply pump inter-failure
times and repair times as random variables, and assumed them to be
exponentially distributed and lognormally distributed respectively. They
studied pumps with different capacities and presented statistical data on mean
time to failure (MTTF) and mean time to repair (MTTR). The failure data
were based on inter-arrival times of working hours, not including times when
the pumps were inoperative due to scheduled outages for maintenance.
Shamir and Howard (1981) used these data for computing mean annual
number of failures, presuming that pump operates 8400 h per year with some
20 to 44 h per month for preventive maintenance and other scheduled outages.
Shamir and Howard (1979) applied regression analysis to obtain a
relationship for the breakage rate of a pipe as a function of time. Walski and
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Pellicca (1982) developed an exponential pipe failure prediction model based
on investigation of the correlation between pipe age and break frequency.
They adopted Shamir and Howard’s (1979) model for predicting break rates.
O’Day (1982) has presented an overview of the various causes of
water-main breaks and leaks, and listed the rate of water main breaks in
15 U.S. cities. Clark et al (1982) suggested a model that combines two
equations, one to predict the time of first break and the second to predict the
number of subsequent breaks, which are assumed to grow exponentially over
time in an attempt to account for the relative impacts of various external
agents. Kettler and Goulter (1985) proposed regression equations for the
number of breaks versus diameter and time for cast iron and asbestos-concrete
mains. They observed a linear relationship between pipe breaks and age.
Andreou et al (1987) used two different approaches for modeling a pipe
failure pattern: a proportional hazard model for early states of deterioration,
and a Poisson-type model for later stages.
Quimpo and Shamsi (1991) showed that the time of failure of water
pipes follows the exponential probability density function. Many failure
probability models have also been proposed to relax the assumption of
constant failure rate. Goulter et al (1993) further examined pipe breakage
patterns with respect to both time and space. They developed a methodology
for quantifying the variation in pipe failure rates associated with temporal and
spatial clustering of water-main failures.
A practical way of assessing the impact of various pipe failure
conditions on water distribution networks is described by Jowitt and
Xu (1993). The method assesses the vulnerability of the network to the loss of
any particular pipe element, and provides a quantitative estimate of the impact
on each nodal demand, and the post-failure utilization of nodal sources and
24
pipe elements. The results of the method can be combined with pipe failure
probabilities to provide measures of network reliability.
Constantine and Darroch (1993) proposed a time-dependent
Poisson distribution, in which the cumulative number of breaks in the pipe is
a power function of the pipe age. Herz (1996) developed a new probability
distribution function to be applied in a cohort survival model to an entire
stock of pipes in a distribution system. Deb et al (1998) applied the
Herz (1996) model to several water distribution systems.
Mays (2000) reported current and future needs in the analysis of
water distribution system reliability along with a review of concepts,
techniques, and methodologies for the evaluation of water distribution
systems. The use of advanced data mining methods in order to determine the
risks of pipe bursts is proposed by Babovic et al (2002). The database of
already occurred pipe bursts has been used to establish a risk model as a
function of associated characteristics of bursting pipe (its age, diameter, pipe
material etc.), soil type in which a pipe is laid, and traffic loading.
Various studies (Rajani and Makar 2000, Katano et al 2003) have
reported different methodologies used to predict the lifespan of metallic
underground pipeline networks and all of them are dependent on data related
to corrosion attack of the pipes. Visual inspection of the metallic surface,
characterization of the pitting attack, and metallurgical analysis are required
to complete the data necessary to establish a data driven pipeline maintenance
program (Doyle and Grabinsky 2003, Srikanth et al 2005).
Misiunas et al (2005) have proposed a new continuous monitoring
approach for detecting and locating breaks in water pipelines. The continuous
monitoring technique uses a modified two-sided cumulative sum (CUSUM)
algorithm to detect abrupt break-induced changes in the pressure data.
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Several strategies have been evaluated to obtain appropriate
predictions of pipeline condition and consequently to establish where to invest
maintenance resources to avoid failures (Doglione and Firrao 1998, Babovic
et al 2002, Sadiq et al 2004, Tesfamariam et al 2006). The lack of precise
information about failure causes and pipeline conditions are among the
primary difficulties associated with proper pipeline maintenance (Saegrov
et al 1999, Babovic et al 2002, Sadiq et al 2004).
Restrepo et al (2009) evaluated the current condition of a water
distribution system and a large amount of data for both the soil and the
corresponding pipeline section were collected. Statistical techniques have
been used to establish the sampling design and a mathematical expression for
pitting depth as a function of several experimental variables. The approaches
and techniques employed provide a useful tool for structuring maintenance
programs.
2.3.2 Reliability Analysis
Reliability analysis of a water distribution system is concerned with
measuring its ability to meet consumer’s demands in terms of quantity and
quality, under normal and emergency conditions. In the past, various concepts
of reliability and approaches for reliability assessment have been proposed
and used for analyzing the reliability of water distribution networks. The
analytical methods developed for reliability analysis of water distribution
networks considered two states: working condition and shutdown condition.
Kettler and Goulter (1985) introduced reliability constraint – the probability
of breakage should not exceed a specified acceptable level- in a least-cost
network design model. Mays (1985) reviewed many analytical techniques for
reliability estimation and concluded that cut-set method and path enumeration
method were most promising.
26
Based on the topology of the network, Goulter and Coals (1986)
introduced the probability of simultaneous failure of all links connected to a
node, which is termed as the probability of node isolation. Su et al (1987)
used minimum cut-set approach to obtain nodal and system reliabilities and
integrated these reliabilities in the least-cost design of water distribution
networks.
A review of reliability considerations and measures for water
supply systems is presented by Wagner et al (1988 a). Two probabilistic
reliability measures, reachability and connectivity, are explored for use in
water distribution systems. An algorithm is developed for the calculation of
this measure, which combines a capacitated network with a method to
efficiently search through network configurations involving multiple link
failures.
Wagner et al (1988 b) also presented simulation as a complementary
method for analyzing the reliability of water distribution networks. It is found
that simulation method enables computation of much broader class of
reliability measures than do analytical methods and also allows the detailed
modeling of the hydraulic behavior of the system.
Jacobs and Goulter (1988) made evaluation of various graph theory
approaches for their applicability to reliability analysis of water distribution
networks. Bao and Mays (1990) proposed a methodology to estimate the
nodal and hydraulic reliabilities of water distribution system that account for
uncertainties. The method is based on a Monte Carlo simulation which can be
used for the assessment of existing systems, the design of new systems or the
expansion of existing systems.
A least-cost methodology is presented by Ormsbee and
Kessler (1990) for use in upgrading existing single-source water-distribution
27
networks in order to sustain single component failure. The methodology is
developed by casting the network-reliability problem in terms of an explicit
level of system redundancy.
Deshpande (1990) presented an analytical method based on loss-of-
demand probability for reliability analysis of pumping systems. Duan and
Mays (1990) proposed a new methodology for the reliability analysis of
pumping stations for water supply systems. The methodology considers both
the mechanical failure and hydraulic failure and models the availability
capacity of a pumping station as a continuous-time Markov process.
Walski (1993) summarized the state-of-the-art in providing
reliability in water distribution and gave some practical tips for improving
reliability. The measures to improve reliability, design considerations,
operation and maintenance considerations are discussed. A review and new
concepts for incorporating reliability in optimal design of water distribution
networks is presented by Ostfeld and Shamir (1993). Methods based on
decomposition, chance constrained approach and graph theory procedures are
discussed.
The concept of hydraulic reliability has been widely used in
determining system reliability (Hobbs and Beim 1988, Duan and Mays 1990,
Fujiwara and Silva 1990, Fujiwara and Tung 1991, Fujiwara and
Ganesharajah 1993, Gupta and Bhave 1994, 1996, Prasad and Park 2004).
Taking into consideration the hydraulic requirements, the basic concept of
system reliability commonly perceived is that the water should be provided
from sources to each demand point at the desired time, at the desired pressure
and at the desired flow rate.
Kansal et al (1995) have emphasized the need of computing
mechanical reliability of the water distribution system and its various
28
components that are subjected to breaks or failures. In the connectivity
analysis presented by Yang et al (1996 a), the mechanical reliability of a water
distribution network is determined under a static condition. Yang et al (1996 b)
also applied stochastic simulation in a reliability analysis of a regional water
distribution network. The proposed simulation technique is aimed at
evaluating the impacts of component failures on meeting demand at a certain
quantity level.
Quimpo and Wu (1997) suggested a capacity-weighted reliability
surface as a tool to assess the condition of deteriorating water supply
infrastructure. The method considered the reliability to meet demands at
nodes to depend on the reliability and hydraulic capacity of all the network
elements leading from the sources.
Gargano and Pianese (2000) presented a methodology to evaluate
the reliability of water distribution systems that can be used in the design
phase and for identifying repair works to be carried out on existing systems.
The system’s overall reliability (mechanical and hydraulic) is estimated using
the overall reliability index, which is defined by the weighted mean of the
hydraulic performance indices obtained for various operating conditions.
Ostfeld et al (2002) have demonstrated an application of stochastic
simulation for reliability analysis of water distribution systems, taking into
account the quality of the water supplied, as well as hydraulic reliability
considerations. The model is limited to one random component failure at a
time, uniform time to failure and time to repair probability distribution
functions.
Kalungi and Tanyimboh (2003) presented a quantified measure for
assessing the redundancy of water distribution networks. The importance of
adopting both redundancy and reliability as the basis foe assessing system
29
performance has been demonstrated. Both performance indices are calculated
using a method based on head driven simulation, which combines the
probability that components of the network are operational at any given time
and the network’s ability to meet consumer demands.
Tolson et al (2004) demonstrated the application of Genetic
Algorithms (GA) for reliability-based optimization of water distribution
networks. The approach links genetic algorithm as the optimization tool with
the First-Order Reliability Method (FORM) for estimating network capacity
reliability. The correlations between nodal demands are shown to significantly
increase distribution network costs designed to meet a specific reliability
target.
2.3.3 Availability Assessment
The availability of the pipe network is an important criterion when
establishing maintenance policy in water distribution networks. Depending on
the network under consideration, water authorities might select either
maintenance cost or availability/reliability as their objective in the
maintenance policy. However, for primary levels of water distribution
networks, which include large pipes with very high supply capacity, pipe
breaks might cause severe supply deficiency and the use of availability
measure seems more appropriate.
Cullinane et al (1992) have presented a practical measure for
distribution system reliability, based on hydraulic availability and
incorporated in an optimal design procedure for component sizing. The
measure combines hydraulic and mechanical availability in a form that
defines the proportion of the time that the system will satisfactorily fulfill its
function. Li and Haimes (1992 a) have considered this objective in the
30
proposed model, where the deterioration behavior of a pipe is represented by
the use of a semi-Markov process.
Li and Haimes (1992 b) proposed the use of system availability,
which is defined as the weighted sum of nodal availabilities as an objective
function to find the optimal repair/replacement policy based on a set of
predefined maintenance actions at all states of a deteriorating network. The
model proposed is difficult to apply in actual water distribution networks due
to the complex relationship between nodal availability and availability of a
network’s pipes, especially when the network is rather large.
Lansey et al (1992) summarized various factors which affect the
performance of the water distribution system and also discussed about various
alternatives for the maintenance of the piping network. Reliability analysis on
two water distribution networks in Arizona by linking reliability model to a
steady state simulation model to calculate the availability of the network is
presented.
Reliability and availability analysis are performed by Shinstine
et al (2002) on two large-scale municipal water distribution networks in the
Tucson Metropolitan area in Arizona. Reliability is computed using a
minimum cut-set method and simulation model. Availability is defined as the
proportion of time the system adequately satisfies the nodal demands and
pressure heads for various possible pipe breaks in the distribution system.
A mathematical model is developed by Luong and Nagarur (2005)
that aims to support the decision to allocate funds among pipes of the water
distribution network as well as the decision to repair or replace the pipes in
the state of failure. The objective function of the model is to maximize the
total weighted long-run availability of the whole system. The concept of
hydraulic reliability is employed to determine the weight of pipes in the
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maintenance program. The deterioration behavior of the pipe is depicted by a
semi-Markov process.
2.3.4 Risk Assessment and Control
Deb et al (1998) have proposed a framework called ‘crisis model’,
a group of prioritized models in which renovation program is determined
based on the risk of pipe breaks and the critical effects of these accidents on
the network.
Environmental assessment and Geographic Information System
(GIS)-based models are used to evaluate the impact or performance of
different phenomena on the surrounding environment. Recently, Vairavamoorthy
et al (2007) have developed a GIS-based risk analysis tool for simulation and
management of water distribution networks.
Lim et al (2010) considered an urban water infrastructure
optimization problem to reduce environmental impacts and costs. The
proposed mathematical model decreases average concentrations of the
influents supplied for drinking water, which can improve human health and
hygiene; total consumption of water resources, reducing overall
environmental impacts and the life cycle cost.
2.4 MAINTENANCE OF WATER DISTRIBUTION SYSTEM
2.4.1 Rehabilitation
Since the performance of the water distribution system depends on
the performance of every single pipe, the decision on pipe rehabilitation or
renewal should consider the individual pipe in the context of the network
performance. The literature provides a variety of models that can assist the
decision maker in scheduling rehabilitation of a water distribution system.
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Woodburn et al (1987) combined a nonlinear programming procedure with a
hydraulic simulation program in a model designed to determine which pipes
should be replaced, rehabilitated or left alone in order to minimize cost.
The various techniques for installation, renovation and
rehabilitation of water distribution systems have been reviewed by Marshall
et al (1990). A detailed account of the development of new methods is
presented. Male et al (1990) addressed the structural deterioration of water
mains over time. A procedure is applied to New York water distribution
system that incorporates the costs of replacing water mains and those of
repairing main breaks to determine least-cost rehabilitation planning strategies. A
net present value analysis is used to investigate the best replacement policy.
A nonlinear optimization model is proposed by Lansey et al (1992)
for optimal scheduling of maintenance for water distribution systems
encompassing a wide range of alternatives. The methodology considered
major piping alternatives of replacing and cleaning, and relining. It also
considered the potential of pumping improvements while accounting for the
costs of maintenance, failure and operations for a multiple-period planning
horizon.
Kim and Mays (1994) proposed a Branch and Bound scheme to
improve the Su et al (1987) model. Arulraj and Rao (1995) introduced the
concept of Significance Index (SI) which is an optimality criterion that can be
applied heuristically to prioritize pipe rehabilitation. Halhal et al (1997)
identified the rehabilitation problem as a multi-objective one, the two
objectives being minimizing cost and maximizing benefits. The benefits to the
system included economics, flexibility, and water quality. A cost-based
approach is employed by Kleiner et al. (1998) to construct a long-term
rehabilitation strategy for water distribution networks.
33
A survey of research needs and on-going efforts in the area of
rehabilitation of water networks is presented by Saegrov et al (1999). The use
of statistical methods for estimating existing and future rehabilitation needs
and the use of software tools for prioritizing actions have been discussed. The
development on technologies for detecting leaks and for measuring pipe wall
thinning is commented.
Engelhardt et al (2000) presented a literature review on the
rehabilitation strategies for water distribution networks. Numerous
rehabilitation decision making approaches have been discussed. The review
emphasized the need to operate water networks efficiently based on a
rehabilitation strategy in order to minimize the total life-cycle cost.
UtiNets, a Decision Support System (DSS) for rehabilitation
planning and optimization of the maintenance of underground pipe networks
of water utilities, is developed by Hadzilacos et al (2000). The DSS performs
reliability based life predictions of the pipes and determines the consequences
of maintenance.
A dynamic Programming approach, combined with partial and
implicit enumeration schemes, has been used by Kleiner et al (2001), to
determine the most cost-effective plan in terms of what pipes in the water
network to rehabilitate, by which rehabilitation alternative and at what time in
the planning horizon, subject to the constraints of service requirements.
Clark et al (2002) have proposed equations that can be used to
estimate the cost of system construction, expansion, and rehabilitation and
repair for drinking water infrastructure. Equations have been developed to
estimate the cost of cement mortar lining, slip lining and corrosion control.
Selvakumar et al (2002) discussed the various types of technologies that can
be used for rehabilitation and repair of drinking water distribution
34
components. A representative costs that can be used by utility managers to
estimate order-of-magnitude budgetary costs for rehabilitation and
replacement of distribution system components are also presented.
A procedure based on a multi-objective genetic algorithm to search
for a near-optimal rehabilitation scheduling is proposed by Alvisi and
Franchini (2006). With reference to a fixed time horizon, the goal is to
minimize the overall costs of repairing and/or replacing pipes, and to
maximize the hydraulic performances of the water network.
A few methodologies for the prioritization of maintenance actions
in relation to several pipes within a water distribution network are mentioned
(Quimpo and Shamsi 1991, Arulraj and Rao 1995, Quimpo and Wu 1997). A
new prioritization approach to the problem of rehabilitation of water
distribution systems is presented by Saldarriaga et al. (2010). The proposed
algorithm selects the most important pipes to be replaced in order to achieve
two main objectives: first, to reduce loss of water due to leakage and second,
to reduce the dissipated energy in the system, making it more efficient and
reliable.
Tabesh et al (2010) presented a methodology to manage the
rehabilitation and replacement of water distribution network using hydraulic
and geospatial information systems models. The proposed indices consist of
pipe breaks and leakage analysis, hydraulic and quality performance and
mechanical reliability of the network. A novel approach is also introduced to
calculate leakage values throughout the network.
2.4.2 Strengthening and Expansion
When an existing water distribution network is deficient, several
pipes together would need strengthening. The literature related to
35
strengthening of an existing network to enhance its capability; and its
expansion to cover additional localities is presented below.
Morgan and Goulter (1985) proposed a heuristic linear
programming based procedure for the least cost layout and design of water
distribution networks. The methodology is capable of wide range of demand
pattern and pipe failure combinations. The procedure can also be extended for
use in the expansion or reinforcement of existing network systems.
Bhave (1985) used a criterion to increase the capability of the
network by optimally selecting links to be strengthened by parallel piping and
expansion of the network to cover additional localities.
Boulos and Wood (1990) proposed a method for determining
explicitly different parameters for upgrading and enhancing water distribution
networks. The method can directly determine a variety of design parameters
such as pipe diameter, pipe length, pump power, pump head, storage level and
valve characteristics; and operating parameters such as pump speed, control
valve setting and specified flow or pressure requirements.
Martin (1990) proposed a Dynamic Programming based pipeline-
capacity expansion model minimizing the cost of initial construction and
subsequent capacity expansion. The proposed design algorithm has an ability
to specify the number and size of pump stations, and the length, diameter and
pressure class of pipes to be added at the beginning of each staging interval
over the design period.
WADISCO (Water Distribution Simulation and Optimization)
computer software is developed by Walski et al (1990) which can be used for
optimal design or strengthening and expansion of a network. The algorithm
enumerates all possible pipe size combinations within the user specified size
36
ranges and tests them for feasibility against pressure requirements. The
program can handle any number of links and nodes; booster pumps and check
and pressure reducing valves.
Stochastic search method is applied to optimal strengthening and
expansion of existing networks by Savic and Walters (1997) using genetic
algorithm. Two network examples, one of a new network design and one of
parallel network expansion, illustrate the potential of the proposed computer
model GANET as a tool for water distribution network planning and
management.
Barros et al (2008) developed an optimization model for the
management and operation of a large-scale, multi-reservoir water distribution
system with preemptive priorities. When the water supply is insufficient to
meet the planned demand, appropriate rationing factors are applied to reduce
water supply. The model and its user-friendly interface form a decision
support system, which can be used to configure a water distribution system to
facilitate capacity expansion and reliability studies.
2.4.3 Repair and Replacement
A few analytical methods have been published to assist in making
pipe replacement and repair decisions. Shamir and Howard (1979) derived an
equation which computes the optimal replacement time of a water main by
equating the expected maintenance cost for repairs and the replacement cost.
O’Day (1982) presented a similar analysis to determine whether a pipe should
be relined to extend its useful life or replaced. Walski (1982) developed a
relation between the expense of increasing pump capacity and its energy
requirement, and the cost of relining a water main to determine which of the
alternatives is more cost effective.
37
The options available to utilities when trying to correct for
excessive pipe breakage are limited; they can continue to repair the breaks
as they occur or replace the offending main segment. Quimpo and
Shamsi (1991) proposed a strategy for prioritizing decisions for the
maintenance of a water distribution system. The specific components that
must be repaired or replaced are determined using a component importance
criterion that measures the overall effect of component maintenance on the
system reliability. The procedure is applied to one hypothetical and two real-
life water distribution systems.
Li and Haimes (1992 a) have developed a Semi-Markovian model
to capture the dynamic evolution of the failure mode of a deteriorating main
pipe, thus facilitating the determination of the optimal replacement/repair
decision at various deteriorating stages. An example problem is solved to
demonstrate the proposed methodology and to show the trade-off between the
system availability and the expected maintenance cost.
A comprehensive review of pipe replacement analysis is presented
by Loganathan et al (2002), from which an economically sustainable
threshold break rate for replacement of pipelines in deteriorating water
distribution systems is derived. Design charts to determine the optimal
threshold break rate as a function of pipe diameter and discount rate are also
presented.
Dandy and Engelhardt (2006) demonstrated the use of Genetic
algorithms to generate trade-off curves between cost and reliability for pipe
replacement decisions. Curves for two planning scenarios are generated. The
first identifies the trade-offs necessary for the current conditions. The second
allows the water authority to determine the required levels of future
expenditure, given funding constraints, to meet a specified level of service
over the entire planning horizon.
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A framework for devising a short-term decision support tool for
pipe replacement is developed by Giustolisi and Berardi (2009). The approach
considered economic, technical, and management rationales as separate
objectives to produce a pipe-wise prioritization scheme which is achieved by
ranking pipes selected during a multi-objective evolutionary optimization of
replacement scenarios.
2.5 OBSERVATIONS MADE FROM THE REVIEW
The literature survey on the various Water Distribution System
(WDS) optimization models and the review of topics related to the design,
operation, reliability and maintenance of water distribution systems reveal the
following facts:
A large body of literature exists on the water distribution
system optimization, reporting the application of classical
optimization methods such as linear programming (Goulter
and Morgan 1985), non linear programming (Li and
Haimes 1992 b) and dynamic programming (Kleiner
et al 1998). On most occasions, models are deliberately
simplified to make the application possible. Some of them
have been linearized to facilitate the use of linear
programming. In others, the discrete nature of the variables is
disregarded, remaining non linear but no longer combinatorial
(Lansey et al 1992). Deterministic methods were unable to
cope up with the non linear water distribution network
problems. The stochastic optimization algorithms are quite
successful in solving such problems, though requiring large
number of evaluations (Mohan and Babu 2010).
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Literature reveals that many researchers have addressed the
water distribution system design optimization problems.
Several studies have considered the hydraulic
availability/reliability as a performance measure for the
optimal design of water distribution systems (Bhave 2003).
All these studies assumed that a water main was structurally
sound which is not true in real-life water distribution systems.
Surveys carried out in different countries reveal that
35 – 60 % of the water is wasted in leakages in the pipelines
(Babovic et al 2002). In the literature, there appears to be only
a few decision models that address water distribution system
maintenance problems.
It is observed from the literature that the maintenance policies
in most of the proposed maintenance models are evaluated and
compared with respect to cost-effectiveness and hydraulic
reliability characteristics (Luong and Nagarur 2005, Dandy
and Engelhardt 2006). The studies on the maintenance of
water distribution systems that consider infrastructure
availability as a performance measure are not much reported
in the literature.
Several WDS maintenance models available in the literature
have investigated only pipe replacement decisions and did not
include other maintenance/rehabilitation options (Male
et al 1990, Lansey et al 1992). Also to simplify the analysis,
the replacement problems considered are limited to the case of
each pipe being replaced with the same diameter (Dandy and
Engelhardt 2006). Moreover, the studies which considered
rehabilitation problems with decision variables like tank sizing
40
and number of pumps did not consider time value of money
(Farmani et al 2005).
Actually, different failure characteristics in various pipes will
also have an effect on the optimal maintenance policy. This
aspect is not considered (Luong and Nagarur 2005). Though a
few models have incorporated failure probabilities of pipes in
the system, it is found that the maintenance models reported in
the literature have not considered the failure characteristics of
the junction joints in the pipe network and also the failure
behavior of the pumping components in the system, which
would lead to the disruption of water supply to the consumers.
The cost terms which are relevant to the WDS maintenance
problem are usually described by a set of equations, which are
non linear. The development of powerful computing systems
has enabled to carry out simulation studies for the distribution
network to evaluate the maintenance alternatives. Nevertheless,
determination of optimal maintenance strategy even for simple
networks remains difficult. To keep close to reality, this
problem must be considered in combinatorial form, whose
resolution in real-world conditions, via classical optimization
techniques, will, in general, be difficult. The use of stochastic
search algorithms to solve WDS maintenance optimization
problem has been seldom investigated in the literature.
In this study, the application of stochastic search techniques such as
Simulated Annealing, Tabu Search and Genetic Algorithm to determine the
near-optimal maintenance strategy for a real-life urban water distribution
system has been demonstrated. The deficiencies in the maintenance decision
models reported in the literature are overcome in this study.