Optimal Rehabilitation Model for Water Pipeline Systems with Genetic Algorithm Academic research paper on "Economics and business"

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Procedía Engineering 154 (2016) 384 - 390

Procedía Engineering

www.elsevier.com/locate/procedia

12th International Conference on Hydroinformatics, HIC 2016

Optimal Rehabilitation Model for Water Pipeline Systems with

Genetic Algorithm

Hwisu Shina, Choongnam Joob, Jayong Kooa*

aDepartment of Environmental Engineering, University of Seoul, Seoulsiripdaero 163, Dongdaeun-gu, Seoul 130-743 Korea, bDepartment of Water Supply Waterworks team. Korea Environment Corporation, 664 Wondang-daero, Seo-gu, Incheon, 22689, Korea

Abstract

In a pipeline system, aging of the pipeline due to a variety of internal and external factors reduces its functionality as a water supply system and increases the risk of pipe failure. Failure of aging pipelines leads to greater social and economic damage. Thus, through proper rehabilitation and replacement, the pipeline systems must be managed to ensure safe water quality and structural performance. This paper shows the use of the genetic algorithm technique to find a near optimal rehabilitation schedule of water pipeline systems. The goal is to minimize the present value of pipe replacement, renovation and repairs costs over a defined analysis period while requirements for water standards are fulfilled. A case study shows that the rehabilitation model proposed in this study can be a powerful tool to assist in planning the asset management strategies for water pipeline systems.

© 2016Published byElsevierLtd. Thisis anopenaccess article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of HIC 2016

Keywords: Asset management; Genetic algorithm; optimal rehabilitation schedule; pipe failure; water pipeline systems; water standards

1. Introduction

Nowadays, many countries face the task of maintenance or rehabilitation of the deteriorated water pipeline systems. To maintain these systems, a huge budget is necessary annually. Rehabilitation of aging pipe components demands huge sums of money from annual budgets of water utilities worldwide and yet the funds available for rehabilitation of these assets are limited. It is important therefore that the available funds are used in the most

* Corresponding author. Tel.: 02.6490.5460; fax: 02.6490.5465. E-mail address: jykoo@uos.ac.kr

1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of HIC 2016

doi:10.1016/j.proeng.2016.07.497

effective manner. In Korea, in the meantime, in spite of efforts for the rehabilitation of aging pipelines, the proportion of aging pipe is still high by 23%. So, asset management of water pipeline systems gain force for economical maintenance. But, until today, maintenance of aging water pipeline systems has been carried out by replacing them by new pipes according to fixed pipe age without considering deterioration. It is an ineffective manner in restricted budget. So it is required that the water pipeline systems are managed economically while keeping the physical functions by appropriate rehabilitation strategies in restricted budget.

This research shows how to adjust the whole life costing optimization model to the pipeline system to regulate rehabilitation of water pipeline networks. The whole life costing approach for the network management is aimed to achieve optimal network maintenance cost when all costs are considered to meet regulatory standards. The approach is applied to the S city water pipeline systems to facilitate decision-making process in the management of pipe network. For the case study, data requirement and pipe failure rate models are developed, followed by the whole life cost rehabilitation model that is optimized by the genetic algorithm.

2. Case study

The proposed optimal rehabilitation model will be demonstrated for an actual system. The study area, C water distribution area is located in north of S city which is large scale city in Korea. The study area included the system's being sufficiently large enough so that a realistic level of funds can be assigned to the rehabilitation of pipes, and the area's having failure history data so that a failure prediction model can be obtained.

C water distribution area accounted for 1.7% of the total area of S city encompasses an area of about 2.34 km! and approximately 30,000 people are living in the area. The area has 16,374m of water distributing pipes with a size and material distribution. In case of pipe material, because of the insufficient data, all the pipes in the study area were assumed by ductile cast iron pipe(DCIP). (According to 2011 national census data, DCIP accounted for approximately 94% of the total distributing pipes in S city.)

Tablel. Current situation of study area

Area(km2) 2.43

Population(person) 29,300

Number of service connection(No.) 2,196

Ratio of water supply(%) 100

Water Supplied(m3/day) 2,380

Distributing pipe length(m) 13,383

Average age of pipe(year) l9

Distribution networks data in the study area were collected using GIS. And distributing Pipes which have 80mm or more diameter were selected for the study because of the critical risk caused by pipe breaking. And the study period was set by 40years, known as a DCIP life time. The study area could be isolated from the entire network then from the GIS data, we established hydraulic model for networks analysis through EPANET. It ensures that the hydraulic performance of the system can be predicted fairly accurately. The Existing dimensions for C water distribution systems are indicated in Appendix A and the network layout of the study area is shown in the figure 1.

Fig. 1. Water distribution map of the study area by EPANET 2.0

3. Model development

3.1. Pipe failure rate

In order to estimate future failure costs for the different pipes in the network, it is necessary to predict pipe failure rates basing on available data(Dandy and Engelhardt, 2001). For pipe failure rate, recorded failure historical data which is total 1064 breaks from 32,851(1078.3km) distributing Pipes, 80mm or more diameter, during 5year(2004~2008) of S-city were used.

Pipe failure rate equation was established by non-linear regression analysis using SPSS18 and the input model suggested by Dandy and Engelhardt (2001) explained relationship between failure rate and pipe age and diameter was applied.

Fr = 0.109 • exp(—0.0064 • DJ • yj11 (1)

Where, f = failure rate(breaks/km/year); y age = pipe age(year); Di = pipe diameter(mm)

3.2. Costs of system

This analysis considers the rehabilitation plan of next 40years and at each year, the decision variables represent different types of rehabilitation strategies that are applicable to each pipe segment. In this study three rehabilitation options are considered ; replacement , renovation(lining) and no action.

Pipe failure cost

Pipe failure cost includes repair cost and indirect cost according to Traffic jams and damage to third parties through burst cost factor. In this study, BCF is assumed by 3 because of the land use type of study area mixed commercial and residential area. Expected repair costs of pipes over analysis period are determined by when it is replace.

fn t fr d, OX Peparr (di ) X BCF X l.

failure cost =-——---(2)

(1 + r)t

Where, fr(dt,t)=failure rate for diameter d: at time t (bursts/km/year); p (dt)=: unit cost of repair(won/burst); BCF =burst cost factor; =length of the pipe(km); r =discount rate(2.74%)

Renovation cost

Epoxy lining method, The most commonly used in Korea, was applied for renovation option. The present value of the renovation cost of a pipe with diameter di at time t is given by;

renovation cost = Prenovation (di) x li (3)

(1 + r)'

Where, PrenmicÉmn (d, ) = unit cost of epoxy lining (won/km)

After applying the epoxy lining process, 30% of the lifetime was assumed to be recovered. Replacement cost

The present value of the replacement cost of a pipe with diameter di at time t is given by;

replacement cost = repla:e ( ' )—- (4)

(1+ r)t

Where, Prp>lace ( dt ) = unit cost of replacement(won/km)

Objective function

Costs according to maintenance options are calculated as the equations presented blow(6~8).

No-Action option ( C1) = Failure costs (5)

Renovation option (C2) = Failure costs + Renovation costs (6)

Replacement option (C3) = Replacement costs (7)

In case of No-action option, only failure cost were considered. Renovation option, failure costs and Renovation costs were considered. Because, after renovation, pipe still has pipe failure rate. In case of replacement option, only replacement cost were considered. Objective function is minimize whole life system rehabilitation costs through out all the pipes in the study area during study period.

min .CTotal = min ^ system(costt) (8)

Where, system(cost t ) = ^ costy (dj ); cost y (dj ) = C 1 + C 2 + C 3 ; N is the number of pipes in the network .

3.3. Hydraulic analysis : Pipe roughness(C-factor)

Pipe roughness changes slowly over the life of the pipe and knowledge of pipe roughness of in-place pipeline is important for network hydraulic performance and pipe sizing calculations (Walski et. al, 1998).

In this study, the formulation of C-factor proposed by Kim(1996) as shown below was used to check hydraulic performance by EPANET.

C = 0.052Y2 -3.669Y + 0. 015D +119.086 (9)

Where; Y= pipe age(year); D= pipe diameter(mm)

There is no effect when no-action was applied. And if renovation and replacement option were appiled, it is assumed to return to value of new pipe.

4. Optimization : Genetic Algorithm

A genetic algorithm is a procedure used to find optimal solutions to search problems through application of the principles of evolutionary biology. Genetic algorithms use biologically inspired techniques such as genetic inheritance, natural selection, mutation, and sexual crossover. Genetic algorithm has shown to find better solution when applied to pipe network problems(Savic and Walters 1997) than other optimization techniques.

4.1. GA representation of solution

In order to solve the given problem, we should represent the solution as a string of numbers or chromosomes. GAs can easily handle integer decision variables that represent discrete pipe sizes.

This is not easily accommodated by other optimization techniques. Table 2 gives the GA representation for the

nd pipe diameter.

Table 2. Genetic algorithm representation of solution

GA representation Rehabilitation option GA representation pipe diameter

0 No-Action 1 80

1 Renovation 2 100

2 Replacement 3 150

- - 4 200

- - 5 250

- - 6 300

- - 7 350

- - 8 400

4.2. GA optimization procedure

Figure 2 is flow chart of GA optimization procedure of this study.

Fig. 2. Procedure of optimization using genetic algorithm

At first, genetic parameters were set and initial population was generated. Genetic parameters used this problem are shown below as table 3.

Table 3. GA parameters applied for this study

Population size Number of generation Crossover probability Mutation rate

200 30,000 0.85 0.01

For a given problem, 200 of feasible solutions were generated and it organized the initial population. Each individuals represent rehabilitation schedule of whole pipe in the network during study period by real number 0 to 2. And also represent pipe diameters of whole pipe in the network during study period by real number 1~8.

Next, pipe failure rate and C-factor of each pipe during the study period were calculated from each solution generated from step.1. Pipe failure rate was used to calculate rehabilitation cost and pipe roughness was used to analysis distribution network. Network analysis was performed by EPANET2.0 integrated into Genetic algorithm. Then according to result of hydraulic analysis, penalty costs were added to fitness function when each pressure and velocity did not meet the criterion. In case of the annual maintenance costs were not to exceed the available budget, the penalty costs were also added. And fitness of each individuals in the population were evaluated by adding total maintenance cost and penalty cost from two constraint. After evaluating fitness, genetic operator is performed and new generation is produced. Tournament selection, Arithmetical crossover and simple mutation were used by genetic operator. And elitism function was used to avoid that the best solution disappear by substituting with others. Next, it was repeated until to meet the terminating condition. Optimization was terminated when the number of generation was reached to 30,000 of generation which was set initially.

5. Results

Optimal rehabilitation schedules of total 124 pipes in the study area during next 40year determined by using GA. The analysis carried out by 2 case, minimum cost scheduling and budget constraint scheduling.

5.1. Minimum cost scheduling

Total maintenance cost during analysis period is 8,787 million won. And annual maintenance costs are shown in figure 3. It is needed lots of rehabilitation costs in the early part because the proportion of aging pipes in the target area is high.

RifJiKfflWA!

H'. ji. :

Fig. 3. Expected annual maintenance cost

*mtîi 'piksi

Fig. 4. Rehabilitation schedules of pipe 33, 62 and 84

Change of failure rate and pipe roughness(C-factor) of each pipe in the network can be predicted according to rehabilitation schedule during study period. Figure 4 shows rehabilitation schedules of pipe 33, 62 and 84 over the study period. According to rehabilitation schedules, pipe failure rates of each pipes change as below figure 5.

130 120 110 -100 S 90

PIPE %1

PIPE«

■ PIPE S4

if \X II Nx/ \ v r v„

■s O

11 Z 'il 2 o 'I n n " S !v! ,7. ]-i! S OOOÖOOOOOOOOOO 1 3 1111

Year Year

Fig. 5. Change of pipe failure rate according to the Rehabilitation schedule in pipe 33, 62 and 84 Fig. 6. Change of C-factor according to the Rehabilitation schedule in pipe 33, 62 and 84

This figure shows that the change pattern of pipe 33 and 62 is similar but the change pattern of pipe 84 has big variation. It because that the pipe 33 and 62 have same diameter as 200mm but pipe 84 has smaller diameter as 100mm. It is easy to understand by pipe failure equation. According to rehabilitation schedules, pipe roughness of each pipes change as below Figure 6. This figure also shows similar change pattern like pipe failure rate.

5.2. Budget constraint scheduling

Annual available budget was assumed and set initially by 450 million won. As a result, total maintenance cost during analysis period is 8,913 million won. And annual maintenance costs are shown below as a figure 7. The rehabilitation targets which exceeding annual available budget in the initial part of Minimum cost scheduling analysis were deferred to the next time. Figure 8 shows diameter changes before and after analysis. The blue line is plotting of existing diameters and the red line is optimal diameters. Some pipes show gap between existing and optimal diameters, it means that the pipes were over-designed.

iilSSgiiilSiliiiiiiââilâSSSâSSSilISSSlSS

Fig. 7. Expected annual maintenance cost

-'-sasasiSssssssssssEssscjiaBssssssssaaaass

PipB NO

—*—CvslinBdiininet rU[L'n.Lr

Fig. 8. Diameter changes before and after analysis.

6. Conclusion

The purpose of this research is to develop an optimal rehabilitation and replacement scheduling model of pipe system which is satisfied with hydraulic criterion of in-place pipeline as well as economic during research period.

The optimal renovation and replacement scheduling model is developed while meeting that optimize the present value of pipe replacement, renovation and repair cost over a defined study period while requirements for water standards are fulfilled by using genetic algorithm. In addition, optimization model can determine appropriate diameter which meets defined performance standards for drinking water supply when pipes were replaced by integrating with EPANET..

In present maintenance of water distribution systems have been replaced by new pipe according to fixed pipe age without deterioration. It is an ineffective manner in restricted budget. Therefore, this research was expected that the optimal scheduling model is required for stable and good quality service by efficient management of pipe system.

Acknowledgements

This study was funded by the Korea Ministry of Environment(MOE) as "Public technology program based on Environmental Policy."

References

[1]. Constantine, G., and Darroch, J.(1995), "Predicting underground pipeline failure.", J. Australian Water Assn., 2(2), 9-10.

[2]. G.C.Dandy, M.Engelheardt(2001), "Optimal schedule of water pipe replacement using genetic algorithms", Journal of water resources planning and management

[3]. Mavin, K.,(1996), "Predicting the burst life of an individual main." Rep. No. 114, Urban Water Research Association of Australia, Melbourne, Australia.

[4]. Savic, D. A., and Walters, G.A.(1997), "Genetic algorithms for the least cost design of water distribution networks", J.Water Resour. Plng.and Mgmt., ASCE, 123(2), 67-77