Article

Optimal Design of Water Distribution System Using Improved

Life Cycle Energy Analysis: Development of Optimal
Improvement Period and Unit Energy Formula
Yong min Ryu 1 and Eui Hoon Lee 2, *

1 Department of Civil Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea;
rmfl45@naver.com
2 School of Civil Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea
* Correspondence: hydrohydro@chungbuk.ac.kr; Tel.: +82-043-261-2407

Abstract: Water distribution systems (WDSs) are crucial for providing clean drinking water, requiring
an efficient design to minimize costs and energy usage. This study introduces an enhanced life
cycle energy analysis (LCEA) model for an optimal WDS design, incorporating novel criteria for
pipe maintenance and a new resilience index based on nodal pressure. The improved LCEA model
features a revised unit energy formula and sets standards for pipe rehabilitation and replacement
based on regional regulations. Applied to South Korea’s Goyang network, the model reduces energy
expenditure by approximately 35% compared to the cost-based design. Unlike the cost-based design,
the energy-based design achieves results that can relatively reduce energy when designing water
distribution networks by considering recovered energy. This allows designers to propose designs
that consume relatively less energy. Analysis using the new resilience index shows that the energy-
based design outperforms the cost-based design in terms of pressure and service under most pipe
failure scenarios. The implementation of the improved LCEA in real-world pipe networks, including
Goyang, promises a practical life cycle-based optimal design.

Keywords: water distribution system; life cycle energy analysis; energy consumption; unit energy
formula; new resilience index
Citation: Ryu, Y.m.; Lee, E.H. Optimal
Design of Water Distribution System
Using Improved Life Cycle Energy
Analysis: Development of Optimal
1. Introduction
Improvement Period and Unit Energy
Formula. Water 2024, 16, 3300. The supply of uncontaminated drinking water to consumers is essential for human
https://doi.org/10.3390/w16223300 life, and a water distribution system (WDS) is critical infrastructure to fulfill this neces-
sity. The design of a WDS is complex because of its operational conditions and related
Academic Editors: Katarzyna
uncertainties [1,2]. The design process involves determining several variables such as the
Pietrucha-Urbanik and Janusz Rak
pipe diameter, the pipe length between nodes, the pipe material, pumps, and tanks [3–6].
Received: 8 October 2024 Various metaheuristic optimization algorithms have been used to derive optimal WDS
Revised: 13 November 2024 designs [4,7–10]. Most of these studies have focused on minimizing the cost of designing a
Accepted: 15 November 2024 WDS [11–13]. Cost minimization studies aim to derive optimal designs based on the initial
Published: 17 November 2024 construction cost of a WDS but do not consider factors such as energy consumption during
network construction. However, to construct a large-scale social infrastructure (such as
a WDS), an optimal design should consider the entire life cycle, including maintenance
and decommissioning.
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
The life cycle includes the entire process from fabrication to the disposal of any
This article is an open access article
item or facility [14,15]. The major stages to be considered during the WDS life cycle
distributed under the terms and
are fabrication, maintenance, and disposal. While the fabrication and disposal stages
conditions of the Creative Commons analyze the static condition of the entire facility, the maintenance stage considers the
Attribution (CC BY) license (https:// aging and destruction of pipes over time. Shamir and Howard (1979) confirmed that
creativecommons.org/licenses/by/ pipe destruction occurs exponentially and proposed a failure rate formula [16]. Sharp and
4.0/). Walski (1988) derived a simple formula for pipe aging over time using the Hazen–Williams

Water 2024, 16, 3300. https://doi.org/10.3390/w16223300 https://www.mdpi.com/journal/water

Water 2024, 16, 3300 2 of 20

and Darcy–Weisbach equations [17]. Mononobe (1960) proposed a destruction estimation

formula based on existing WDS data [18]. Shamir and Howard (1979) proposed a method
for planning pipe replacement cycles in a WDS based on the degree of destruction, and
Male et al. (1990) suggested a cost-effective method for renewal and replacement cycles
in a WDS [16,19]. Studies on the maintenance stages of WDSs and those considering
environmental and economic factors based on WDS life cycle analysis have also been
conducted [16,19]. Subsequently, the life cycle energy analysis (LCEA) model has been
applied to WDSs [12,20]. Representative WDS optimal design studies using LCEA include
the study by Filion et al. (2004) and the study by Lee et al. (2015) [14,21].
In this study, a new LCEA was proposed that improved the shortcomings of Filion
et al. (2004) and Lee et al. (2015), which are representative LCEA studies [14,21]. In the
case of the newly proposed LCEA, to apply it without modifying the basic data of the pipe
network to be applied, the C value of the existing pipe network was used, and the C value
of the newly buried pipe was equally applied during rehabilitation and replacement. To
enhance applicability, a method was employed to calculate rehabilitation and replacement
times, considering regional characteristics based on local regulations and pipe C values.
In addition, to improve the accuracy of the unit energy calculation formula in the process
of improving applicability, a new optimal unit energy calculation formula was proposed
by analyzing various types of trend lines and R2 according to the trend lines. Addition-
ally, a novel resilience index was formulated and applied to assess the performance of
the proposed water distribution system design using the new LCEA model. The new
resilience index, developed based on Todini’s (2000) and Cimellaro et al.’s (2016) resilience
indices primarily used in water distribution systems (WDSs), was introduced [22,23]. The
previously proposed resilience index integrated factors like the affected population in a
system failure, the tank capacity in the WDS, and water quality through calculations [22,23].
The new resilience index focuses on the need to restore water pressure at each node to meet
WDS standards for a return to the original state after a failure. The new resilience index pre-
sented in this study employs an approach that assesses the overall system performance by
considering hydraulic pressure at each node during failure events. Through the utilization
of this new resilience index, a comparative analysis was conducted between the cost-based
optimal design plan and the energy-based optimal design plan.

2. Methodology
2.1. Overview
This study consisted of four main parts. First, metaheuristic optimization algorithms
(MOAs) were selected for the optimal WDS design. Second, optimal improvements and
renewal timing based on the aging of the WDS were established. Third, the LCEA model
was analyzed using a new unit energy calculation method. Finally, a new resilience index
was developed and applied based on the pressure at each node in the water pipe network.
The optimal design search method using the improved LCEA method used in this study is
shown in Figure 1.
According to Figure 1, the first step is to establish the optimal improvement and
regeneration period according to the aging of the WDS. The WDS consists of multiple pipes.
For each pipe, the optimal diameter is selected from among various types of diameters. In
order to establish the optimal rehabilitation, repair, and replacement period, it is necessary
to calculate the degree of aging according to the diameter for each pipe, and the criteria are
presented based on this. The second step is to select MOAs. MOAs have been developed in
the past, but each has its own advantages and disadvantages. For example, there are MOAs
with a small number of parameters and high usability and MOAs with a large number of
parameters and internal operators but low usability but good performance. Among the
MOAs developed previously, MOAs that showed good performance in the WDS optimal
design were selected and applied to the WDS optimal design through parameter sensitivity
analysis. The third step is to develop a new unit energy calculation method. In order to
improve the accuracy of the existing unit energy calculation method, various unit energy
Water 2024, 16, 3300 3 of 20

calculation formulas were established, and the optimal unit energy calculation formula
was proposed through accuracy analysis. Finally, a new resilience index was developed.
Based on the optimal design produced through the proposed method, a new resilience
Water 2024, 16, x FOR PEER REVIEW 3 of 22
index was developed, applied, and evaluated to analyze the resilience of the design when a
disaster occurs.

Figure1.1.Optimal
Figure Optimaldesign
designsearch
searchmethod
methodusing
usingimproved
improvedLCEA
LCEAmodel.
model.

2.2. Metaheuristic
According to Optimization
Figure 1, the Algorithm
first step forisOptimal Waterthe
to establish Distribution System Designand re-
optimal improvement
generation period
The optimal according
design to theconsists
of a WDS aging ofof the WDS. The
deriving WDS consists
an optimal designofplan multiple pipes.
according
toFor
theeach pipe, thepurpose
designer’s optimalwhilediameter is selected
satisfying the from
user’samong various types
requirements such as of diameters.
appropriateIn
orderquality
water to establish the optimal
and demand. rehabilitation,
Traditionally, repair, and
this approach hasreplacement
relied on trial period, it is based
and error neces-
on user
sary experience,
to calculate thewith
degree additional
of aging mathematical
according to the techniques
diameter applied
for each [24].
pipe, Since
and the 1981,
cri-
research
teria arehas been conducted
presented usingThe
based on this. linear and step
second nonlinear functions
is to select MOAs. to design
MOAs have WDSsbeen to
minimize the cost of branched pipe networks [25–27]. However,
developed in the past, but each has its own advantages and disadvantages. For example, in the case of linear and
nonlinear
there are functions,
MOAs with anaoptimal design of
small number could not be derived
parameters and high due to nonlinear
usability elements
and MOAs withina
the simulation
large numberprocess and dependence
of parameters and internal on the initial solution
operators but low group [6,28,29].
usability but To overcome
good perfor-
the limitations
mance. Among of the
these mathematical
MOAs developed techniques,
previously, metaheuristic
MOAs that algorithms
showed good have been used
performance
for
in WDS
the WDS optimization
optimal design[11,30–32]. Among various
were selected and appliedmetaheuristic
to the WDS algorithms,
optimal designthe modified
through
hybrid vision correction algorithm (MHVCA) has demonstrated superior
parameter sensitivity analysis. The third step is to develop a new unit energy calculation performance in
minimizing costs for WDS optimization [10].
method. In order to improve the accuracy of the existing unit energy calculation method,
In this
various study,
unit energyamong various formulas
calculation metaheuristic wereoptimization
established, algorithms,
and the optimal the modified hy-
unit energy
brid vision correction
calculation formula was algorithm
proposed (MHVCA)
throughproposed
accuracyby Ryu and
analysis. Lee (2023)
Finally, a new was used [10].
resilience in-
The
dexMHVCA is a metaheuristic
was developed. Based on the optimization
optimal design algorithm that consists
produced throughof thesix parameters
proposed that
method,
must
a new beresilience
set by the index
user. According
was developed, to Ryuapplied,
and Lee and(2023), the MHVCA
evaluated showed
to analyze thegood resultsof
resilience
inthe
the optimal design of six
design when a disaster occurs. WDSs (Goyang network, Hanoi network, Pescara Network,
Zhejiang network, Modena network, and Balerma network) and showed better results than
metaheuristic optimization
2.2. Metaheuristic Optimizationalgorithms
Algorithm such
foras Harmony
Optimal Watersearch and the System
Distribution GeneticDesign
algorithm,
which have fewer parameters than the MHVCA [10]. In this study, the effectiveness of
The optimal design of a WDS consists of deriving an optimal design plan according
the MHVCA in WDS optimization was used to explore the optimal design of WDSs to
to the designer’s purpose while satisfying the user’s requirements such as appropriate
minimize energy consumption. Table 1 provides a description of each important internal
water quality and demand. Traditionally, this approach has relied on trial and error based
operator and parameter used in the MHVCA.
on user experience, with additional mathematical techniques applied [24]. Since 1981, re-
According to Table 1, the CGS, CGSR, and DR are probability parameters for operator
selection,has
search beenthe
while conducted
CF, AF, MTF, using
and linear
MHRand arenonlinear
parameters functions
utilized toto design
fine-tune WDSs to mini-
the solution
during iterative calculations. The optimal solution search process of the MHVCA isnon-
mize the cost of branched pipe networks [25–27]. However, in the case of linear and as
linear functions,
follows in Figure 2. an optimal design could not be derived due to nonlinear elements in the
simulation process and dependence on the initial solution group [6,28,29]. To overcome
the limitations of these mathematical techniques, metaheuristic algorithms have been
used for WDS optimization [11,30–32]. Among various metaheuristic algorithms, the
modified hybrid vision correction algorithm (MHVCA) has demonstrated superior per-
formance in minimizing costs for WDS optimization [10].
In this study, among various metaheuristic optimization algorithms, the modified
Water 2024, 16, 3300 4 of 20

Table 1. Important internal operators and parameters in the MHVCA [10].

Operators
Description
(Full Name)
An operator that proceeds with a search after setting a new search range using the optimal
CGS
value of the current iteration and the median value of the search range
(Centralized Global Search)
-
A method for adjusting the decision variable based on the distance between the best value
MTF
among the existing optimal solutions and the new solution using an operator that mimics lens
(Modulation Transfer Function)
brightness adjustment in the process of manufacturing glasses
Parameters Value of range
Description
(Full name) (General value)
A parameter used in the process of searching for a new solution, a
MHR 0~0.36
probability parameter that determines whether fine-tuning (search method
(Modified Hybrid Rate) (Self-adaptive)
using CF, AF, and MTF) is executed
CGSR 0~1
Probability parameter that determines whether CGS is executed
(Centralized Global Search Rate) (Self-adaptive)
A method of reducing the range of region search as the number of
CF 0~100
iterations increases with an operator that mimics the compression process
(Compression Factor) (30)
in the process of manufacturing glasses
A method of setting and searching the range of region search based on the
AF 0~180
angle of the astigmatism axis set by the user with an operator that mimics
(Astigmatic Correction) (45)
the astigmatism correction process in the process of manufacturing glasses
Water 2024, 16, x DR
FOR PEER REVIEW A probability parameter that determines the direction to be searched 0~1 5 of 22
(Division Rate) within the search range during the process of searching for a new solution (0.1)

Figure2.2.Flowchart
Figure FlowchartofofMHVCA.
MHVCA.

According to Figure 2, the MHVCA does not search for the number of solution com-
binations equal to the number of parent generations like the Genetic algorithm in one op-
timal solution search, but it instead searches for one solution combination (glasses in
MHVCA terminology).
Water 2024, 16, 3300 5 of 20

According to Figure 2, the MHVCA does not search for the number of solution
combinations equal to the number of parent generations like the Genetic algorithm in one
optimal solution search, but it instead searches for one solution combination (glasses in
MHVCA terminology).

2.3. Establishment of Optimal Improvement Period

In the pursuit of cost minimization, the optimal WDS design requires alternatives with
minimal initial installation costs. However, to analyze the WDS life cycle, it is essential
to consider the energy required for maintenance over time after pipeline installation.
Therefore, to simulate the maintenance of a WDS, it is crucial to proactively model the
aging of pipes over time. Lee et al. (2015) quantified the Hazen–Williams coefficient (C)
based on the equation proposed by Mononobe (1960) and the coefficient proposed by Baek
(2002), which is expressed as follows [14,18,33]:
√  −0.0660117
(0.0961659D + 1.15507) y 0.723076D

Cy = C0 1− (1)
D

where Cy denotes the C value over time, C0 denotes the initial C value, D denotes the
diameter of the pipe (mm), and y denotes the year after burial or replacement.
A previous study used Equation (1) to propose the rehabilitation and replacement pe-
riod for pipes, which were suggested based on the value of the Hazen–Williams coefficient
(C). When C was ≤ 90, the pipe was rehabilitated; after two rehabilitations, if C was ≤80,
the pipe was replaced. It was assumed that C recovered to 90–110 after rehabilitation and
to 130 after replacement because of the installation of new pipes. However, in this study,
the rehabilitation and replacement periods of pipes were not set uniformly based on a fixed
value of C. Instead, a method was proposed to consider the Hazen–Williams coefficient
(C) of the WDS under consideration. The service life of the water supply and sewage
facilities was specified based on the regulations of the Office of Waterworks in South Korea.
The WDS used in this study was the Goyang network. In order to estimate the head loss
of a pipe, the Darcy–Weisbach or Hazen–Williams formula is used. In the case of the
Goyang network, which is the water pipe network applied in this study, the head loss was
estimated using the Hazen–Williams formula as a result of analyzing the initially proposed
literature and the literature in which the optimal design was conducted [4,10,13,34,35].
Therefore, in this study, the Hazen–Williams formula was also used to conduct the optimal
design. The material of pipe that constitutes the Goyang network is assumed to be made
of steel according to the existing literature, and the useful service life of the pipe is set to
30 years [10,13,34,35]. Therefore, based on the diameter of the pipes, rehabilitation and
replacement criteria were established using the C value after 30 years (useful life for the
service of steel pipes). Figure 3 shows the variation in C values by diameter over time.
As shown in Figure 3, after 30 years, the C values for each pipe range from approx-
imately 60 to 68. To establish criteria for rehabilitation and replacement, the average C
value for pipes after 30 years was set to about 65 in this study. Furthermore, based on the
existing replacement criteria, replacement was performed after two rehabilitation sessions.
To determine the recovered C values following rehabilitation and replacement, an approach
similar to that proposed in previous studies was adopted. Similarly to previous research, it
was assumed that after rehabilitation, the C value of pipes recovered to approximately 85%
of their initial C values (130 out of 110).
 duct the optimal design. The material of pipe that constitutes the Goyang network is as-
sumed to be made of steel according to the existing literature, and the useful service life
of the pipe is set to 30 years [10,13,34,35]. Therefore, based on the diameter of the pipes,
rehabilitation and replacement criteria were established using the C value after 30 years
Water 2024, 16, 3300 6 of di-
20
(useful life for the service of steel pipes). Figure 3 shows the variation in C values by
ameter over time.

Figure3.3.Convergence
Figure Convergence curve
curve of
of CC by
bydiameter
diameter over
over time
time (red
(redbox
boxisisdistribution
distributionof
ofCCaccording
accordingto
to
diameter after 30 years.).
diameter after 30 years.).

2.4. The
AsLCEA
shownModel Using3,a after
in Figure New Unit Energy
30 years, theEquation
C values for each pipe range from approxi-
mately
The60 to 68. To
proposed LCEAestablish
modelcriteria for rehabilitation
can be divided and phases—Phase
into three main replacement, the average C
1 determines
value
the for pipes after
rehabilitation 30 years
period of eachwas setusing
pipe to about 65 in thison
information study. Furthermore,
the WDS based on
to be optimized the
(pipe
existing replacement
diameters) criteria,
and regulations replacement
specific to the region;wasPhase
performed after the
2 calculates twounit
rehabilitation ses-
energy for each
pipe
sions.using the WDS information
To determine the recoveredtoCbevalues
optimized (nodes,
following pipes, pressures,
rehabilitation etc.); Phasean
and replacement, 3
isapproach
further divided
similar tointo
thatthree stagesin
proposed (fabrication, maintenance,
previous studies and disposal).
was adopted. Similarly During the
to previous
fabrication
research, itstage, the fabrication
was assumed energy
that after of all pipes inthe
rehabilitation, theCWDS
valuecanof be calculated
pipes using
recovered to the
ap-
unit energy. The maintenance stage involves estimating
proximately 85% of their initial C values (130 out of 110). the maintenance energy over the
intended life cycle by considering pipe destruction simulations and the rehabilitation period
determined
2.4. The LCEA in Phase
Model 1. Finally,
Using a NewtheUnit
disposal
Energy stage involves calculating the disposal energy
Equation
for allThe
pipes
proposed LCEA model can be divided improved
in the WDS using unit energy. The into three LCEA model was simulated
main phases—Phase 1 deter-
using
mines the rehabilitation period of each pipe using information on the Demand-Driven
Visual Basic 6.0 and EPANET 2.0 (US EPA, 2000) [36]. In this study, WDS to be opti-
Analysis (DDA)
mized (pipe and Pressure-Driven
diameters) and regulationsAnalysis (PDA)
specific were
to the used Phase
region; in the 2process of applying
calculates the unit
EPANET to optimally design the WDS. DDA was used to simulate normal situations for
energy for each pipe using the WDS information to be optimized (nodes, pipes, pressures,
optimal design, and PDA was used to simulate abnormal situations for resilience index
etc.); Phase 3 is further divided into three stages (fabrication, maintenance, and disposal).
analysis [10,37–40]. This study calculated the resilience index based on the optimal design
During the fabrication stage, the fabrication energy of all pipes in the WDS can be calcu-
and optimal design plan. In the process of conducting the optimal design, the optimal
lated using the unit energy. The maintenance stage involves estimating the maintenance
design plan was derived using the DDA method. PDA was used to calculate the disaster
energy over the intended life cycle by considering pipe destruction simulations and the
resilience index of each optimal design plan. The demand at each node of the WDS to be
rehabilitation period determined in Phase 1. Finally, the disposal stage involves
applied was set as a fixed value, and the temporal distribution pattern of demand was
not applied. The optimal WDS design using the LCEA model can be used to calculate the
annual energy consumption. Using this, the year with the lowest energy consumption can
be set to be the optimal life cycle. The objective function of the optimal WDS design using
the LCEA model can be expressed as follows:
h i
Eall = E f ab + ( Emain − Erec ) + Edis + Penalty /LC (2)

where Eall denotes the total annual energy (GJ/year), E f ab denotes the fabrication energy
(GJ/year), Emain denotes the maintenance energy (GJ/year), Erec denotes the recycle energy
(GJ/year), Edis denotes the disposal energy, Penalty denotes the penalty function, and LC
denotes the optimal life cycle (year). The penalty function can be used to exclude design
proposals that do not satisfy the minimum required hydraulic pressure of each node during
the process of optimal WDS design. On the one hand, if the minimum required water
Water 2024, 16, 3300 7 of 20

pressure is satisfied, the penalty is zero; on the other hand, if the minimum required water
pressure is not satisfied, a penalty is assigned, as follows:

tot
Penalty = ∑ 1020 × hminP − h jc + 107 , (i f h jc < hminP )


jc=1 (3)


Penalty = 0, i f h jc > hminP

where tot denotes the total number of nodes in the WDS, hminP denotes the minimum water
pressure of the nodes in the WDS, and h jc denotes the water pressure of jc.

2.4.1. New Unit Energy Equation

For an optimal WDS design using the LCEA model, the energy generated at each
stage (fabrication, maintenance, and disposal) must be analyzed, which is based on the
length of the pipe. To calculate the unit energy based on diameter, it is essential to ensure
accuracy by building on the previously suggested values. In this study, various formulas
for unit energy calculations were expressed using trend equations, and an optimal formula
for the unit energy calculation was proposed. The trend equation was established using
previously studied data, and the diameter data of the Goyang pipe network were utilized
to analyze the possibility of additional use. Table 2 presents unit energy equations using
existing unit energy equations and various proposed equations and is a table showing the
R2 value for each equation.

Table 2. Previously proposed unit energy formula and various other formulas.

Previous Function [14] R2

e f ab = 4.206 × D1.9959 × Conv


Fabrication 0.9962
edis = 0.2974 × D2.0248 × Conv


Disposal 0.9952
Linear function R2
Fabrication e f ab = (27.053 × D − 35.659) × Conv 0.9788
Disposal edis = (1.9904 × D − 2.6401) × Conv 0.9789
Log function R2
Fabrication e f ab = (78.805 × ln( D ) − 31.34) × Conv 0.9298
Disposal edis = (5.8014 × ln( D ) − 2.326) × Conv 0.9308
Exponential function R2
e f ab = 4.2905 × D1.9677 × Conv


Fabrication 0.9992
edis = 0.3035 × D1.9927 × Conv


Disposal 0.9989
2nd-order polynomial function R2
e f ab = 4.3669 × D2 − 2.0038 × D + 3.1002 × Conv


Fabrication 0.9962
edis = 0.3116 × D2 − 0.0831 × D + 0.1258 × Conv


Disposal 0.9952
3rd-order polynomial function R2
e f ab = 2.1678 × D3 − 19.535 × D2 + 65.506 × D − 58.322 × Conv


Fabrication 0.9963
edis = 0.1769 × D3 − 1.476 × D2 + 5.427 × D − 4.8875 × Conv


Disposal 0.9979
4th-order polynomial function R2
e f ab = 1.2748 × D4 − 15.24 × D3 + 62.27 × D2 − 107.33 × D + 64.24 × Conv


Fabrication 1.0000
edis = 0.1116 × D4 − 1.3474 × D3 + 5.9498 × D2 − 9.7072 × D + 5.8445 × Conv


Disposal 1.0000

In this table, D denotes the pipe diameter (m), and Conv denotes a unit conversion
factor that converts m units to GJ/m. As shown in Table 2, the R2 values for the previ-
ously proposed unit energy formulas are 0.9962 and 0.9952. For the previously proposed
function, regression analysis was performed based on five data points, and the function
was expressed as an exponential function [14,21]. In this study, various analyses were
Water 2024, 16, 3300 8 of 20

performed based on the five given data points in the same way as the method used in
the existing literature. However, when various functions (linear, log, exponential, and
polynomial) were used to calculate the unit energy, the 4th-order polynomial function
had the highest R2 value of 1.0000 for the unit fabrication and disposal energy. However,
because of the uniqueness of the polynomial function, when calculating the unit energy
using pipes from locations other than those proposed by Filion et al., the energy decreased
as the pipe diameter increased [21]. In the case of individual pipes forming a constant pipe,
as the diameter increases, the energy required to manufacture the pipe increases. However,
in the case of the 4th-order polynomial presented in Table 2, when data other than the
given data are input, the energy required to manufacture the pipe decreases. Consequently,
considering the specific nature of the polynomial function, it was excluded from the unit
energy formula. An exponential function that realized the highest R2 value was chosen for
the new unit energy formula. The proposed unit fabrication and disposal energy formula
can be expressed as follows:
 
e N_ f ab = 4.2905 × D1.9677 × Conv (4)
 
e N_dis = 0.3035 × D1.9927 × Conv (5)

where e N_ f ab denotes the new fabrication unit of energy, e N_dis denotes the new disposal
unit of energy, D denotes the pipe diameter (m), and Conv denotes a unit conversion factor
that converts m units to GJ/m.

2.4.2. Energy Calculation for Design of Water Distribution System

As mentioned in Section 2.4.1, for the optimal design of WDSs employing LCEA, it
is imperative to calculate the energy generated during the fabrication, maintenance, and
disposal stages. In this study, the energy for each stage, as suggested by Lee, was computed
using the newly proposed unit energy calculation formula based on the diameter [41]. The
energy calculation formula for each stage, which integrates the newly proposed unit energy
calculation formula, is presented in Table 3.

Table 3. Energy calculation formula and description for each stage [41].

Stage Formula Description

This stage includes various processes such as raw
Tot material extraction, material processing and production,
Fabrication E f ab = ∑ Li × 4.2905 × D1.9677 and pipe fabrication. The energy consumed in these
i =1
  processes can be defined as the fabrication energy.
Emain = Ereh + Erep + Erpi − Erec
The maintenance process of a WDS comprises the
Tot
Ereh = ∑ Li Nreh × 0.65 × 4.2905 × D1.9677

rehabilitation, repair, and replacement of pipes, owing
i =1 to aging or pipe failure. Maintenance energy defines all
Tot the energy consumed during the maintenance stage. Lee
Erep = ∑ Li Nrep × 4.2905 × D1.9677


Maintenance
i =1 et al. (2015) defined recycling energy as the benefit
Tot obtained from the improved flow rate resulting from the
Erpi = ∑ Li × N (t) × 2 × Lb × 4.2905 × D1.9677


i =1
rehabilitation of pipes during the maintenance
Tot  p  process [41].
1
Erec = pump ∑ E p,i − E ap,i
e
i =1
The disposal stage involves the disposal of pipes that
constitute the WDS. Disposal energy is the energy
Tot consumed purely for the disposal of pipes, which
Disposal Edis = ∑ Li × 0.3035 × D1.9927 × (1 + Nreh ) includes the energy required for the disposal of pipes
i =1
during replacement as well as that consumed during the
disposal of pipes in the maintenance stage.
Water 2024, 16, 3300 9 of 20

In this table, E f ab denotes the fabrication energy consumption (GJ), Tot denotes the
total number of pipes, Li denotes the length of the ith pipe (m), D denotes the diameter
of the pipe, Emain denotes the maintenance energy consumption (GJ), Ereh denotes the
rehabilitation energy (GJ), Erep denotes the replacement energy (GJ), Erpi denotes the
repair energy (GJ), Erec denotes the recycled energy (GJ), Nreh denotes the number of
pipe rehabilitations, Nrep denotes the number of pipe replacements, N(t) denotes the pipe
failure probability function, Lb denotes the typical breakage length, pumpe denotes the
p
efficiency of the pump, E p,i denotes the pump energy required when the pipe is rough
before rehabilitation, and E ap,i denotes the pump energy required when the pipe is smooth
after rehabilitation.

2.5. Development of New Resilience Index Using Insufficient Pressure

A new resilience index was proposed to evaluate and compare the performance of the
proposed design using the improved LCEA. Using the new resilience index, we evaluated
the performance of the WDS design through scenarios such as system failure caused by
natural disasters. The proposed new resilience index is an index that can indicate the
performance of the system based on the pressure per node within the WDS, based on the
resilience proposed by Cimellaro et al. (2016) [23]. The proposed new resilience index is
as follows.
R = R1 × R2 × R3 × R P (6)
∑ nip,e (
LC 1− i LC h(t)
n Tot F(t) ≤ hreserve
h Reserve h
R1 = ∑ TL for i = 1, 2, · · · , n, R2 = ∑ TL , F(t) = ,
TL =0 TL =0 1 h > hreserve
(7)
∑ Nan
j (hmin −h jun )
LC Q(t)
LC 1− ∑ Ntn hmin
Q* j
R3 = ∑ TL , RP = ∑ TL
TL =0 TL =0

where TL is the control time (life cycle), nip,e is the number of users receiving insufficient
pressure, n Tot is the number of users in the WDS, n is the number of nodes affected by
the outage, h(t) is the tank water level at time t, h Reserve is the reserve capacity of the tank,
Q(t) is the water quality at time t, Q* is the water quality factor, Ntn is the total number of
nodes, hmin is the minimum required water pressure, Nan is the number of abnormal nodes,
and h jun is the pressure of node j. Additionally, R1 is the number of households affected
by a water outage in the event of a system failure due to a natural disaster, etc., which is
proportional to the system serviceability index proposed by Todini (2000) [22]. In the case
of R1 , if it is assumed that no failure occurs in the WDS when a natural disaster occurs, it
can be represented as 1, and if a failure occurs at all nodes in the WDS, it can be represented
as 0 [22]. R2 is a proposed index based on the water level of the tank in the network, R3 is a
factor for water quality, and R4 is a newly proposed resilience index calculated through all
nodes and abnormal nodes within the WDS. In the case of R2 , if there is a tank in the WDS
and the reserve capacity in the tank is higher than the tank water level at time t, it can be
represented as 1, and in the opposite case, the value of the index is calculated according to
the ratio of the tank water level at time t to the reserve capacity in the tank. R3 is the ratio
of the water quality concentration to the bad concentration at time t due to the occurrence
of a natural disaster. Therefore, if it does not meet the water quality standard, it will have
a value between 0 and 1 depending on the result. R4 is a coefficient that quantifies the
pump energy required to restore a disaster situation according to the reduced pressure at
each node in the WDS due to the occurrence of a natural disaster. R4 has a value less than
1 when the pressure at each node decreases due to a natural disaster and has a value of
0 when the pressure at all nodes is 0%. R1 ~R4 are coefficients for indexing the resilience
of the system to a disaster situation when a natural disaster occurs and a failure occurs
in the WDS, and they always have a value less than 1 for an abnormal situation where a
problem occurs within the WDS. If no failure occurs in the WDS, the resilience index has
 Water 2024, 16, 3300 10 of 20

a maximum value of 1, and if the WDS does not function as intended, it has a minimum
value of 0.

3. Results
3.1. Study Area
Water 2024, 16, x FOR PEER REVIEW
The Goyang network located in South Korea was selected as the target area for the 11 of 22
energy optimization design using the improved LCEA model. The layout of the Goyang
network is shown in Figure 4.

Figure4.4.Layout
Figure Layoutof of Goyang
Goyang network.
network.

The
TheGoyang
Goyangnetwork
networkcomprises
comprises 1 reservoir, 25 25
1 reservoir, nodes, and
nodes, 30 30
and pipes. The
pipes. Hazen–
The Hazen–Wil-
Williams coefficient for calculating the head loss of the Goyang network was
liams coefficient for calculating the head loss of the Goyang network was set to set to 100.
100. The
The minimum water pressure required for each node in the Goyang network was 15 m.
minimum water pressure required for each node in the Goyang network was 15 m. Table
Table 4 lists the pipe diameter and cost per pipe diameter used for the optimal design of
4 lists the pipe diameter and cost per pipe diameter used for the optimal design of the
the Goyang network.
Goyang network.
Table 4. Cost per unit length based on diameter.
Table 4. Cost per unit length based on diameter.
Diameter Cost Diameter Cost Diameter Cost Diameter Cost
(mm) (USD/m) Diameter
(mm) Cost
(USD/m)Diameter
(mm) Cost (USD/m)
Diameter Cost
(mm) Diameter
(USD/m) Cost
80 37.890
(mm)
125
(USD/m)
40.563
(mm) (USD/m)
200
(mm)
47.624
(USD/m)
300
(mm)
62.109
(USD/m)
100 38.933 80
150 37.890
42.554 125 250 40.563 54.125200 47.624
350 300
71.524 62.109
100 38.933 150 42.554 250 54.125 350 71.524
3.2. Optimal WDS Design Using Improved LCEA Model
3.2. In
Optimal WDSthe
this study, Design Using
proposed Improved
LCEA modelLCEA Model
was used to analyze the difference between
energy- In and
this cost-based
study, the optimal
proposed LCEAThere
designs. model was
are usedoftosixanalyze
a total the difference
parameters between
(CG, CGSR,
DR ,
energy-
1 DR , CF, and AF) that need to be set for the MHVCA. Among the parameters
2and cost-based optimal designs. There are a total of six parameters (CG, CGSR, of
the
DRMHVCA, candidate glasses (CG) are the storage space within the algorithm. The
1, DR2, CF, and AF) that need to be set for the MHVCA. Among the parameters of the
parameters of
MHVCA, candidate the MHVCA were
glasses selected
(CG) through
are the sensitivity
storage analysis,
space within theand Table 5 shows
algorithm. The param-
the parameters of the MHVCA set to apply the MHVCA to the Goyang network.
eters of the MHVCA were selected through sensitivity analysis, and Table 5 shows the
parameters of the MHVCA set to apply the MHVCA to the Goyang network.

Table 5. Values for each parameter of MHVCA.

Parameter Value
CG 190
CGSR 0
DR1 0.1
DR2 0.7
CF 30
AG 45
Water 2024, 16, 3300 11 of 20

Table 5. Values for each parameter of MHVCA.

Parameter Value
CG 190
CGSR 0
DR1 0.1
DR2 0.7
CF 30
AG 45

The optimal design was performed using the MHVCA with parameters set according
to Table 5. The optimal design was performed according to cost- and energy-based optimal
designs, and the results showing the best value after 30 uses of each optimal design were
analyzed. Table 6 shows the results of the optimal design of the Goyang network used
30 times using a cost-based design and energy-based design. Table 6 shows the results of
the optimal design of the Goyang network used 30 times using a cost-based design and
energy-based design.

Table 6. Comparison of cost and energy for each optimal design.

Analysis by Cost Cost-Based Design Energy-Based Design

Mean cost (USD) 177,064.779 177,492.181
Best cost (USD) 177,010.359 177,010.359
Worst cost (USD) 177,020.938 177,141.106
Standard deviation 21.172 130.392
Analysis by energy Cost-based design Energy-based design
Mean energy (GJ) 805.549 578.210
Best energy (GJ) 757.747 478.317
Worst energy (GJ) 788.369 535.783
Standard deviation 9.480 21.034

According to Table 6, in terms of cost, the best cost of the both cost-based design and
energy-based design was the same at 177,010.359, which was the optimal value. However,
the mean cost of the cost-based design was 177,020.938, and that of the energy-based design
was 177,141.106, which was higher than that in the energy-based design. In terms of energy,
the mean energy of the energy-based design was about 252.586 lower than that of the
cost-based design, and the best energy was about 279.429 lower. The standard deviation
was higher in the energy-based design than in the cost-based design, but based on the
comparison of the best energy, worst energy, and mean energy, it can be seen that the energy-
based design shows better results in terms of energy. Figure 5 shows the convergence
curves according to the cost-based and energy-based optimal designs in terms of cost, and
the convergence curves are expressed as the average of the results of 30 uses.
According to Figure 5, in the case of the cost-based design, it can be seen that it
converges quickly and converges after about 2500 iterations. However, it can be seen
that the energy-based design converges after about 6000 iterations. Figure 5 shows that
the purpose of the optimal design is to minimize cost. Therefore, it can be seen that the
cost-based design converges to a lower value than the energy-based design. Figure 6 shows
the convergence curves according to the cost-based and energy-based optimal designs in
terms of energy, and the convergence curves are expressed as the average of the results of
30 uses.
 the cost-based design, and the best energy was about 279.429 lower. The standard devia-
tion was higher in the energy-based design than in the cost-based design, but based on
the comparison of the best energy, worst energy, and mean energy, it can be seen that the
energy-based design shows better results in terms of energy. Figure 5 shows the conver-
Water 2024, 16, 3300 12 of 20
gence curves according to the cost-based and energy-based optimal designs in terms of
cost, and the convergence curves are expressed as the average of the results of 30 uses.

Water 2024, 16, x FOR PEER REVIEW 13 of 22

purpose of the optimal design is to minimize cost. Therefore, it can be seen that the cost-
based design converges to a lower value than the energy-based design. Figure 6 shows
the convergence curves according to the cost-based and energy-based optimal designs in
terms of energy, and the convergence curves are expressed as the average of the results of
Figure5.5.Convergence
Figure Convergencecurves
curvesfor
foroptimal
optimaldesign
designin
interms
termsofofcost.
cost.
30 uses.
According to Figure 5, in the case of the cost-based design, it can be seen that it con-
verges quickly and converges after about 2500 iterations. However, it can be seen that the
energy-based design converges after about 6000 iterations. Figure 5 shows that the

Figure6.6.Convergence
Figure Convergencecurves
curvesfor
foroptimal
optimaldesign
designin
interms
termsof
ofenergy.
energy.

According to Figure 6, in the case of the cost-based design, it can be seen that it con-
verges quickly and then converges after about 4000 iterations. However, in the case of the
energy-based design, it can be seen that it converges after about 8000 iterations, but it can
be seen that it converges to a lower value than the cost-based design. Figure 5 shows that
the purpose of the optimal design is to minimize energy. Therefore, it can be seen that the
energy-based design converges to a lower value than the cost-based design. Table 7 shows
Water 2024, 16, 3300 13 of 20

According to Figure 6, in the case of the cost-based design, it can be seen that it
converges quickly and then converges after about 4000 iterations. However, in the case of
the energy-based design, it can be seen that it converges after about 8000 iterations, but it
can be seen that it converges to a lower value than the cost-based design. Figure 5 shows
that the purpose of the optimal design is to minimize energy. Therefore, it can be seen that
the energy-based design converges to a lower value than the cost-based design. Table 7
shows the pipe diameters by the location of the design plan that showed the best results
among the optimal design results of the cost-based design and energy-based design that
were used to minimize energy.

Table 7. Pipe diameters by location of design plan.

Pipe Diameter (mm) Pipe Diameter (mm)

Location Cost-Based Optimal Energy-Based Optimal Location Cost-Based Optimal Energy-Based Optimal
Design Design Design Design
1 47.624 47.624 16 37.89 37.89
2 40.563 42.554 17 37.89 37.89
3 40.563 38.933 18 37.89 37.89
4 38.933 38.933 19 37.89 37.89
5 37.89 37.89 20 37.89 37.89
6 37.89 37.89 21 37.89 37.89
7 37.89 37.89 22 37.89 37.89
8 37.89 37.89 23 37.89 37.89
9 37.89 37.89 24 37.89 37.89
10 37.89 37.89 25 37.89 37.89
11 37.89 37.89 26 37.89 37.89
12 37.89 37.89 27 37.89 37.89
13 37.89 37.89 28 37.89 37.89
14 37.89 37.89 29 37.89 37.89
15 37.89 37.89 30 37.89 37.89

According to Table 7, we can see that the design plans for the cost-based design
and energy-design are different in locations 2 and 3. In the case of the cost-based design,
the same pipe was used in locations 2 and 3 to minimize cost, and in the case of the
energy-based design, different pipes were used in locations 2 and 3 to minimize energy.
Table 8 presents the results of the cost- and energy-based optimal designs using the
MHVCA based on the WDS in the study area.

Table 8. Cost- and energy-based optimal design results using MHVCA.

Cost-Based Optimal Design Energy-Based Optimal Design

Total energy expenditure * (GJ) 805.549 494.769
Total energy expenditure per year
33.565 20.615
(GJ/year)
Life cycle (year) 24 24
E f ab (GJ) 173.730 174.560
Ereh (GJ) 418.806 426.196
Erpi (GJ) 24.623 0.000
Erep (GJ) 173.730 174.560
Edis (GJ) 23.195 23.310
Erec (GJ) 8.535 303.858
Cost per year (USD/year) 7375.432 7377.704
Cost (USD) 177,010.359 177,064.903


Note(s): * Total energy expenditure is sum of all consumed energies (Eall = E f ab + Ereh + Erep + Erpi − Erec + Edis ).
 Water 2024, 16, 3300 14 of 20

According to Table 8, the energy-based optimal design achieves approximately 39%

more energy savings compared to the cost-based design, with a total energy expenditure
difference of about 310.779 GJ. On an annual basis, the energy-based design leads to
savings of approximately 24.949 GJ compared to the cost-based design throughout the life
cycle. While the cost-based design exhibits lower fabrication, rehabilitation, repair, and
disposal energies, the energy-based design excels in repair energy efficiency. Focused on
minimizing energy consumption, the energy-based design results in lower repair energies
during the maintenance stage. Moreover, the energy-based design outperforms in recycled
energy during maintenance, with around 303.858 GJ compared to the cost-based design’s
approximately 8.535 GJ. The E f ab of the energy-based optimal design is 0.48% higher than
x FOR PEER REVIEW that of the cost-based optimal design, and in the case of Edis , it is about 0.49% higher.
15 of 22 Unlike
the cost-based optimal design, the energy-based optimal design is a design method for
reducing CO2 emissions. The energy-based optimal design considers the amount of carbon
generated during maintenance stages such as rehabilitation and repair during the life cycle.
energy-based optimal design
Therefore, thehas a lower 𝐸optimal
energy-based than the cost-based
design optimaldesign
derives an optimal design. byBased
selecting a pipe
𝐸 ,aitrelatively
on the results of with largethat
can be seen diameter. This is because
the energy-based pipes with
optimal a large
design candiameter
use WDSs decrease less
without replacement because it uses pipes with a relatively large diameter. In addition, optimal
in aging over time than pipes with a small diameter. However, the energy-based
design has a lower E than the cost-based optimal design. Based on the results of Erep ,
the 𝐸 of the energy-based optimalrepdesign is about 35 times higher than that of the cost-
it can be seen that the energy-based optimal design can use WDSs without replacement
based optimal design. It can be seen that the optimal design of the energy-based optimal
because it uses pipes with a relatively large diameter. In addition, the Erec of the energy-
design recovers more
based energy
optimal than
design the optimal
is about design
35 times of the
higher thancost-based
that of theoptimalcost-based design,
optimal design.
and in terms of energy, the energy-based optimal design is better than the
It can be seen that the optimal design of the energy-based optimal design recovers cost-based op- more
timal design. 𝐸 energy
is lower
thaninthethe energy-based
optimal design ofoptimal designoptimal
the cost-based than indesign,
the cost-based op- of energy,
and in terms
timal design. Thethe energy-based
probability optimal
of pipe design
failure is iscalculated
better thanaccording
the cost-based to theoptimal design.The
diameter. Erpi is lower
energy-based optimal design uses larger pipes than the cost-based optimal design, andprobability
in the energy-based optimal design than in the cost-based optimal design. The
of energy-based
this shows that the pipe failure is calculated according
optimal design hastoa the diameter.
lower The energy-based
probability of pipe failure optimal
in design
uses larger pipes than the cost-based optimal design, and this shows that the energy-based
areas where failure mainly occurs. 𝐸 is the same as 𝐸 for each design method. Erep
optimal design has a lower probability of pipe failure in areas where failure mainly occurs.
is the energy generated when replacing a pipe. Therefore,
Erep is the same as E f ab for each design method. if allErep
individual pipes generated
is the energy in the when
WDS reach the pipe replacement
replacing point, all if
a pipe. Therefore, pipes are replaced.
all individual pipesSince
in thethe WDS lifereach
cycle is pipe
the longerreplacement
than the pipe replacement point,
point, all pipes areallreplaced.
pipes are replaced,
Since the life producing
cycle is longerthethansame the result as 𝐸 .
pipe replacement point,
Figure 7 shows the results
all pipes areof the cost-
replaced, and energy-based
producing the same result optimal
as E f ab designs
. Figure 7basedshows on the the
results of the
consumed energy. cost- and energy-based optimal designs based on the consumed energy.

Figure 7. Energy
Figure 7. Energy consumption consumption
by optimal by methods.
design optimal design methods.

It is evident that the energy-based design results in higher values for 𝐸 , 𝐸 , 𝐸 ,

and 𝐸 compared to the cost-based design. However, the energy-based design exhibits
a considerably lower 𝐸 value than that of the cost-based design. The 𝐸 plot (repre-
sented by the diagonal lines) in Figure 6 indicates that higher recycled energy values lead
to improvements in energy efficiency gains. The energy-based design exhibits considera-
Water 2024, 16, 3300 15 of 20

It is evident that the energy-based design results in higher values for E f ab , Ereh , Erpi ,
and Edis compared to the cost-based design. However, the energy-based design exhibits
a considerably lower Erep value than that of the cost-based design. The Erec plot (repre-
sented by the diagonal lines) in Figure 6 indicates that higher recycled energy values lead
to improvements in energy efficiency gains. The energy-based design exhibits consider-
ably higher Erec values than those of the cost-based design. Moreover, Figure 7 shows
that the energy-based design performs optimization based on various energy consump-
tion values and, overall, is more effective in achieving energy savings compared to the
cost-based design.
In this study, the proposed LCEA model was used to analyze the results of energy- and
cost-based optimal designs for the Goyang network. The analysis revealed that the energy-
based optimal design showed lower total energy expenditure and total energy expenditure
per year than the cost-based optimal design. To conduct additional analysis, the benefits of
reducing energy consumption were converted into costs. To convert energy savings into
costs, all fuels used during the Goyang network’s life cycle were assumed to be petroleum-
based. A method of converting energy into kWh and subsequently into costs was employed,
as suggested by the Korea Energy Economics Institute (KEEI), and the settlement unit prices
for each fuel type provided by the Korean Statistical Information Service (KOSIS) were
used [42,43]. According to the KEEI, 1 GJ is equivalent to 277.8236 kWh, and according to
the KOSIS, the cost per 1 kWh is KRW 299.78. Additionally, recent exchange rates were used
to convert KRW to USD. By applying this conversion method, the energy consumption
results shown in Table 5 were analyzed based on the energy- and cost-based optimal
designs. When implementing the energy-based optimal design for the Goyang network,
approximately USD 20,526.22 was saved compared to the cost-based optimal design, with
an annual saving of USD 855.26. However, the direct application of the results, obtained
by converting energy into costs using the current exchange rate, was not entirely accurate,
owing to potential fluctuations in the exchange rate.
Based on the energy-based and cost-based optimal designs, the new resilience and pipe
failure scenarios proposed were established and applied to compare the performance of
each design. In the failure simulation of the WDS, various failure scenarios, such as single-
pipe failure and multiple-pipe failure, can be established [24]. According to Beker and
Kansal, it was mentioned that when natural disasters such as earthquakes and landslides
occur, multiple pipe failures rarely occur [44]. Jung et al. (2014) simulated single-pipe
failure conditions after optimization, and Pagano et al. (2019) evaluated the impact of
single-pipe failure in the water pipe network [45,46]. Therefore, in this study, resilience
according to failure was calculated using failure scenarios for all pipes of the energy-based
and cost-based optimal designs for the Goyang pipe network. Based on each design plan,
PDA was performed using EPANET 2.2. To simulate PDA using EPANET 2.2, the minimum
pressure was set to 0, required pressure was set to 15, which is the minimum required water
pressure of the Goyang pipe network, and the pressure component was set to 0.5 [47,48].
Since the Goyang network used in this study is a network with no reservoir within
the network, R2 was assumed to be 1. In the case of water quality, R3 was assumed to
be 1, assuming that all factors subject to water quality testing are maintained above the
standards set by the law [23]. Additionally, in the case of the population affected by a
water outage, it was assumed that the same population lives at all nodes. The pipe failure
scenario was constructed as a single-pipe failure scenario for the pipes existing in the WDS
from the first pipe to the final pipe. Table 9 is a table presenting the resilience calculated
according to the scenario based on each optimal design.
According to Table 9, the energy-based optimal design yielded high or equal resilience
results in all but three scenarios. Upon calculating the average of resilience indices, it was
determined to be approximately 0.8377 for the cost-based optimal design and around 0.8512
for the energy-based optimal design. The energy-based design showed a maximum increase
of approximately 9.2176% in the resilience index compared to the cost-based design and an
average increase of approximately 1.95%. Both the overall and average results indicate that
Water 2024, 16, 3300 16 of 20

the energy-based optimal design outperforms the cost-based optimal design in terms of
disaster recovery. This suggests that the energy-based optimal design possesses a superior
ability to restore the system to its original state in the event of a disaster compared to the
cost-based optimal design.

Table 9. Comparison of resilience between cost-based and energy-based optimal designs by scenario.

Cost-Based Energy-Based Cost-Based Energy-Based

Pipe Failure Optimal Optimal Difference Pipe Failure Optimal Optimal Difference
Scenario Design Design (%) Scenario Design Design (%)
(A) (B) (A) (B)
1 0.0000 0.0000 0 16 1.0000 1.0000 0.0000
2 0.1490 0.1548 3.7628 17 1.0000 1.0000 0.0000
3 0.4975 0.5001 0.5263 18 1.0000 1.0000 0.0000
4 0.4807 0.4831 0.4893 19 0.9544 1.0000 4.5599
5 0.8055 0.8526 5.5220 20 0.9079 0.9543 4.8716
6 0.7996 0.8050 0.6776 21 1.0000 1.0000 0.0000
7 0.8941 0.8953 0.1262 22 0.8062 0.8083 0.2669
8 0.9041 0.9048 0.0852 23 0.8054 0.8116 0.7576
9 0.9078 1.0000 9.2176 24 0.9023 0.9063 0.4498
10 0.9543 1.0000 4.5744 25 0.9541 1.0000 4.5888
11 1.0000 1.0000 0.0000 26 0.8096 0.8118 0.2779
12 1.0000 1.0000 0.0000 27 0.8479 0.8496 0.1972
13 0.9077 0.9545 4.9062 28 1.0000 1.0000 0.0000
14 1.0000 1.0000 0.0000 29 0.8936 0.8947 0.1170
15 1.0000 1.0000 0.0000 30 0.9494 0.9500 0.0639

4. Discussion
In this study, sensitivity analysis was performed on each parameter of the MHVCA
used. A total of six parameters were subjected to sensitivity analysis. Sensitivity analysis
was conducted by setting initial values for CG, CGSR, DR1 , DR2 , CF, and AF based on
previous studies and then applying various values to analyze the results and select values.
Sensitivity analysis was performed 10 times in total with the goal of cost minimization, and
the maximum cost, minimum cost, mean cost, and standard deviation were compared and
analyzed to set the values. Tables 10–15 show the results of sensitivity analysis and selected
values for each parameter.

Table 10. CG sensitivity analysis results and parameter value selection.

100 110 120 130 140 150

Mean Cost (USD) 177,071.823 177,015.813 177,021.255 177,064.903 177,015.636 177,031.778
Best Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359
Worst Cost (USD) 177,294.363 177,064.903 177,064.903 177,026.697 177,063.124 177,064.903
Standard Deviation 78.212 16.363 21.793 24.957 15.830 26.253
Selection
160 170 180 190 200 -
Mean Cost (USD) 177,026.521 177,026.685 177,031.600 177,015.427 177,026.158 -
Best Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 -
Worst Cost (USD) 177,064.903 177,064.779 177,064.903 177,061.038 177,064.903 -
Standard Deviation 24.692 24.938 26.033 15.204 24.149 -
Selection O -
Water 2024, 16, 3300 17 of 20

Table 11. CGSR sensitivity analysis results and parameter value selection.

0 0.1 0.2 0.3 0.4 0.5

Mean Cost (USD) 177,015.427 177,029.236 177,784.975 179,523.054 183,325.455 184,490.049
Best Cost (USD) 177,010.359 177,014.772 177,583.053 178,884.215 181,980.392 183,364.440
Worst Cost (USD) 177,061.038 177,064.903 178,028.545 180,156.294 184,345.112 185,891.822
Standard Deviation 15.204 22.111 134.937 396.245 707.003 877.799
Selection O
0.6 0.7 0.8 0.9 1.0 -
Mean Cost (USD) 184,521.035 192,010.403 191,279.585 194,634.407 198,455.637 -
Best Cost (USD) 182,186.073 188,093.943 182,095.278 190,812.490 195,333.524 -
Worst Cost (USD) 187,807.926 194,201.503 194,767.095 197,291.409 201,015.790 -
Standard Deviation 1532.913 1933.878 3502.999 1826.033 1872.217 -
Selection -

Table 12. DR1 sensitivity analysis results and parameter value selection.

0 0.1 0.2 0.3 0.4 0.5

Mean Cost (USD) 177,119.522 177,015.427 177,015.813 177,015.813 177,015.801 177,015.813
Best Cost (USD) 177,061.038 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359
Worst Cost (USD) 177,216.720 177,061.038 177,064.903 177,064.903 177,064.779 177,064.903
Standard Deviation 57.427 15.204 16.363 16.363 16.326 16.363
Selection O
0.6 0.7 0.8 0.9 1.0 -
Mean Cost (USD) 177,015.813 177,015.813 177,015.813 177,033.023 177,015.801 -
Best Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 -
Worst Cost (USD) 177,064.903 177,064.903 177,064.903 177,236.998 177,064.779 -
Standard Deviation 16.363 16.363 16.363 67.992 16.326 -
Selection -

Table 13. DR2 sensitivity analysis results and parameter value selection.

0 0.1 0.2 0.3 0.4 0.5

Mean Cost (USD) 177,199.296 177,039.121 177,043.797 177,042.471 177,036.864 177,031.753
Best Cost (USD) 177,014.772 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359
Worst Cost (USD) 177,828.255 177,085.639 177,072.511 177,064.779 177,064.779 177,064.779
Standard Deviation 222.011 29.482 27.392 26.242 26.523 26.222
Selection
0.6 0.7 0.8 0.9 1.0 -
Mean Cost (USD) 177,020.881 177,015.427 177,026.697 177,015.801 177,021.255 -
Best Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 -
Worst Cost (USD) 177,064.903 177,061.038 177,064.903 177,064.779 177,064.903 -
Standard Deviation 21.062 15.204 24.957 16.326 21.793 -
Selection O -

According to Tables 10–15, since the CGSR, DR1 , and DR2 of the parameters of the
MHVCA are probability parameters, sensitivity analysis was conducted in units of 0.1,
and CG, CF, and AF were analyzed by creating about 11 to 13 cases depending on the
range of parameters generally applied. When proceeding with the optimal design of the
Goyang pipeline using the MHVCA, it can be seen that the best result was shown when
CG = 190, CGSR = 0, DR1 = 0.1, DR2 = 0.7, CF = 30, and AF = 45. The MHVCA set with
the values of the corresponding parameters was mostly the same as the MHVCA applying
other parameters in terms of the minimum cost, but the maximum cost was lower, and it
could be confirmed that this led to the lowest standard deviation.
Water 2024, 16, 3300 18 of 20

Table 14. CF sensitivity analysis results and parameter value selection.

0 10 20 30 40 50
Mean Cost (USD) 177,053.963 177,026.311 177,026.520 177,015.427 177,026.697 177,021.243
Best Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359
Worst Cost (USD) 177,286.754 177,064.779 177,064.779 177,061.038 177,064.903 177,064.779
Standard Deviation 81.170 24.386 24.689 15.204 24.957 21.768
Selection O
60 70 80 90 100 -
Mean Cost (USD) 177,026.311 177,021.243 177,021.225 177,015.813 177,015.813 -
Best Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 -
Worst Cost (USD) 177,064.779 177,064.779 177,068.339 177,064.903 177,064.903 -
Standard Deviation 24.386 21.768 21.793 16.363 16.363 -
Selection -

Table 15. AF sensitivity analysis results and parameter value selection.

0 15 30 45 60 75 90
Mean Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359
Best Cost (USD) 177,015.801 177,021.078 177,020.881 177,015.427 177,020.869 177,026.323 177,020.869
Worst Cost (USD) 177,064.779 177,064.779 177,064.903 177,061.038 177,064.779 177,064.903 177,064.779
Standard Deviation 16.326 21.440 21.062 15.204 21.036 24.406 21.036
Selection O
105 120 135 150 165 180 -
Mean Cost (USD) 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 177,010.359 -
Best Cost (USD) 177,042.110 177,031.778 177,015.801 177,026.336 177,025.937 177,026.311 -
Worst Cost (USD) 177,064.903 177,064.903 177,064.779 177,064.903 177,064.779 177,064.779 -
Standard Deviation 25.958 26.253 16.326 24.425 23.815 24.386 -
Selection -

5. Conclusions
In this study, an improved LCEA model was proposed to design an optimal WDS based
on cost and energy, and performance was compared through the developed new resilience
index. Using the specifications of the WDS under consideration and the regulations of the
target watershed, a criterion was established to determine the Hazen–Williams coefficient,
which serves as a basis for pipe renewal and replacement. The energy-based design has
several advantages in that it aims to minimize energy consumption at all stages, including
fabrication, maintenance, and disposal, due to the strength of the improved LCEA model.
The energy-based design showed better performance than the cost-based design, especially
in terms of energy recycling, which increased by approximately 36 times. Recycled energy,
pointing to the energy benefits gained from the pipe rehabilitation and replacement process,
had a positive impact on energy consumption. Additionally, the energy-based design
demonstrated zero energy consumption for pipe repairs. As a result, the energy-based
optimal design can consider a wide range of energy consumption aspects to achieve a more
efficient design over the entire WDS life cycle.
To compare the performance of the proposed WDS design using the improved LCEA,
an analysis was performed based on a new resilience index. As a result of analyzing
the resilience index according to the scenario, it was confirmed that in most pipe failure
scenarios, the energy-based optimal design showed better performance than the cost-based
optimal design when pipe failure occurred. Based on the resilience index analysis results, it
was found that the energy-based optimal design applied to a single-pipe failure scenario
can respond to disaster more effectively than the cost-based optimal design when a pipe
failure occurs.
The improved LCEA in this study relies on assumptions from prior research (e.g.,
energy consumption based on pipe diameter). To align better with real-world conditions,
Water 2024, 16, 3300 19 of 20

future studies should involve laboratory-scale experiments using the proposed equations.
Further and extensive research can facilitate the practical application of the life cycle-based
optimal design to actual drainage systems, allowing for the development of diverse optimal
design techniques for various networks and objectives beyond energy.

Author Contributions: Y.m.R. and E.H.L. carried out the literature survey and drafted the manuscript.
Y.m.R. worked on the subsequent draft of the manuscript. Y.m.R. performed the simulations. E.H.L.
conceived the original idea of the proposed method. All authors have read and agreed to the
published version of the manuscript.
Funding: This work was supported by Korea Environment Industry & Technology Institute (KEITI)
through Technology development project to optimize planning, operation, and maintenance of urban
flood control facilities Project, funded by Korea Ministry of Environment (MOE) (RS-2024-00398012).
Data Availability Statement: The data presented in this study are available on request from the
corresponding author.
Conflicts of Interest: The authors declare no conflicts of interest.

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