an approach to track maintenance prioritization for urban rail transit - r1

7/25/2019 An Approach to Track Maintenance Prioritization for Urban Rail Transit - r1

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AN APPROACH TO TRACK MAINTENANCE PRIORITIZATION FOR URBAN RAIL

TRANSIT

ABSTRACT

Track infrastructure is the most fundamental among various elements of Urban Rail Transit

(URT) systems, and thus ensuring the optimal allocation of resources between track segments for

inspection and maintenance is a vital objective of rail transit agencies. This paper proposes an

integrated approach, combing Analytical Hierarchy Process (AHP) and improved Fuzzy

Synthetic Evaluation (FSE), to evaluate the potential risks in track systems and prioritize the

inspection and maintenance of various track segments of urban rail systems. Three major steps

are determining evaluation indicators, calculate relative importance among indicators, and

deciding potential risk levels and crisp values (quantitative actionable results). A case study on a

track segment of Beijing URT is conducted to illustrate the evaluation process. The result shows

that the risk levels and crisp values obtained from this method are very promising and helpful in

evaluating and ranking risk levels for maintenance prioritization.

Key Words:Track Maintenance Prioritization; Urban Rail Transit; Analytical Hierarchy Process

(AHP); Fuzzy Synthetic Evaluation (FSE); Risk Reporting Matrix

Ma, Jiaqi, Xiaohua Ma, and Fang Zhou. (2014) An Approach to Track Maintenance

Prioritization for Urban Rail Transit. Public Works Management and Policy, 19 (3).


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INTRODUCTION

With the fast development of urban rail transit (URT) systems, it is very critical to maintain high

level of operational safety. Track infrastructure is the most fundamental among various elements

of the URT system and thus, ensuring the optimal allocation of resources between various

segments of track systems for inspection and maintenance is a vital objective of rail transit

agencies, particularly when available resources, specifically funding, to address maintenance and

improvement needs are limited. Additionally, there is an ever increasing demand on URT

systems in megacities around the world, imposing heavier burdens to track systems and leading

to more safety concerns.

Most of the literature in the past many years focuses on mechanisms on how the track

system damages occur (Rama & Andrews, 2013; Priest et al,2013; Andrews,2013) and the

techniques to preserve and maintain various track elements (Zarembski,2013; Nunez,2013; Volpe

National Transportation Systems Center,2013). Also, great attention is given to the track state

monitoring with various methods. Usually, track geometry recording vehicles and on-track

inspectors could be used to monitor track condition and ensure prompt maintenance. For instance,

Wanel-Libman (2012) proposed an automated process using machine vision technology for tie

inspection. However, these machines are usually very expensive and it is impossible to assign

enough of them to cover the entire network. Stevens (2013) introduced an onboard autonomous

track monitoring system which aims to facilitate track monitoring with low cost. Yet, these data

are subject to many other factors and usually not of high enough quality.

While the literature has been discussing how to detect and fix track problems, much less

literature is found addressing how to assign limited resources for maintenance and preservation.


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While one of the few examples is that Guler (2013) analyzed the rich database and proposed a

decision support system for track maintenance and renewal, they usually require large amount of

historical data. Some research tends to use mathematical modeling to optimize the maintenance

plan (Andrews,2013; Nystrom,2010). But these models are usually based on certain

simplification of the problem, making these methods less practical and usable in the real world.

While these analyses are mostly for conventional freight or passenger rail, it is also

pointed out by the literature that no work has been found on the maintenance framework for the

URT system (Parasram et al,2013), which is a big gap in research and real needs.

Also, in terms of analysis methodology, multiple methods have been applied in the

literature for identification of risks and prioritization in infrastructure management. Most of the

studies adopt data-driven statistical methods (e.g., regression models [Rahim,2013], neural

network [Kargah-Ostadi,2010]). Very few studies mentioned the solution when there is a lack of

enough data. Ma (2013) proposed a integrated method for evaluating URT facility risks under

advers whether conditions under inadequate data conditions.

Establishing an approach that optimally allocates resources, inspection personnel or

machines, for the maintenance and preservation of URT track systems is of critical importance.

Also, an approach that relies less on historical data is needed because of the usual unavailability

of enough such data for decision making, not to mention for the entire URT network. This paper

aims to propose an approach to prioritizing the use of available resources for track maintenance

by analyzing the potential risks of the track system, including all its elements.


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The remaining of this paper is organized as follows. First, we state the research objective.

Then, the methodology is detailed and applied to a case study of a URT track segment in Beijing.

Last, we discuss the results based on our analysis and make a conclusion for the study.

RESEARCH OBJECTIVE

Urban rail agencies need an approach to evaluating current track system state and prioritizing the

track maintenance in a cost effective manner. Therefore, we aim to propose a methodology to

understand the URT track system state by analyzing potential risks of various elements, ensuring

the optimal allocation of limited resources between various segments of track systems in a URT

network. This approach is designed to be applicable for all URT systems, especially where no

reliable and adequate historical data are available.

METHODOLOGY

We develop an integrated approach for track system risk ranking and maintenance prioritization.

Considering the reality that many URT systems around the world lack historical data that are

detailed enough for prioritization, we attempt to combine objective mathematical modeling with

subjective evaluation of engineering judgment from experts and technicians, who are usually

very familiar with or responsible for the daily inspection and maintenance work. As shown in

Figure 1, the proposed integrated approach includes three steps: develop evaluation index system,

calculate index relative importance, and decide potential risk levels.

Step 1 Determine Evaluation Indicators


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The evaluation index is the basis for the integrated approach used in this paper. It is very critical

to have a set of well-selected indicators to effectively carry out the evaluation. Several criteria

are identified to be essential in the indicator selection for evaluating track system state.

Brain Storming Group Discussion

On-site Survey Consultation w/ Experts

Expert Judgment

AHP Application

Consistency

Check

Develop Evaluation Index System

Calculate Index Relative Importance

Decide Potential Risk Levels

Fuzzy Synthetic

EvaluationRisk Reporting Matrix

Risk Crisp Value

Yes

No

Matrix

Adjustment

FIGURE 1 Framework for proposed three step integrated approach

1. The indicators need to be comprehensive to be able to describe major types of damage to

various elements of the track system, including rail, switch, tie, connecting parts and

track bed.


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2. The index system could be a three-layer system, with the first level as overall track

system, second level as various elements of the track system and third level as different

damages to the corresponding track elements.

3. The establishment of the index system should go through iterations with brain-storming,

group discussion, on-site survey, consultation with experts and technicians, etc.

4. The indicator system should be accompanied with a document explaining the meaning of

each indicator to maintain consistency when experts are asked to give their judgments.

Step 2 Identify Relative Importance between Indicators

Analytic Hierarchy Process (AHP) is a decision-making tool that incorporates both qualitative

and quantitative factors. AHP has increased in use and popularity because of its ability to reflect

the way people think and make decisions by simplifying a complex decision into a series of one-

on-one comparisons. It is used to calculate the weights among different track elements and

among the indicators of each element in this paper (Drake,1998;Saaty,2010).

First, experts are invited to make the preference judgment pairwise by assigning value 1

if the elements are of equal importance, value 3 to a weakly more importantelement, value 5

to a strongly more important element, value 7 to a very strongly important element, and value

9 to an absolutely more important element. The values 2, 4, 6 and 8 are not necessary

in this study and too many scale levels might cause confusion to the experts. If the first indicator

is less important than the second indicator in comparison, value "1/3", "1/5", "1/7" and "1/9"

could be given to describe "weakly less important", " strongly less important ", " very strongly

less important " and "absolutely less important". Multiple experts are usually invited and the

final comparison score can be obtained by different ways, such as taking average, median and


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mode, etc., each with its own advantages and disadvantages (Satty,2010). The effect of using

different method to aggregate expert judgments is out of the scope of this paper, we simply

choose one of the methods, using the mode in this study.

The outcome of each set of final pairwise comparison values can be expressed in a

judgment matrix, after which eigenvector method is often used to derive the final weight

vectors for each of the factors and indices. The calculation process is expressed as follows from

Equation 1 to 6.

a) Normalization for every column

n

1

b , , 1,2, ,ij

ij

kj

k

bi j n

b

(Eq. 1)

where bijis the element of judgment matrix B.ijb

is the element of normalized judgment matrix

B .

b) Add all the elements in the rows of normalized judgment matrix

b to obtain vector

w

1

w b , 1,2, ,n

i ij

j

i n

(Eq. 2)

c) Normalize i

w to obtain nwwwww ,,, 321 as the Eigenvector

1

, 1, 2, ,ii n

j

j

ww i n

w

(Eq. 3)


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d) Calculate the largest eigenvalue max

n

i i

i

wn

wB

1

max

)(

(Eq. 4)

where

iwB refers to the ith element of vector obtained by multiplying judgment matrix B by

weight vector w.

e) Check for consistency

To check for consistency in the judgments of decision makers, Saaty (2010) defined the

consistency ratio (CR), which is a comparison of the consistency index (CI) with the random

consistency index (RI), as follows:

CICR=

RI (Eq. 5)

where CI is given by

maxCI1

n

n

(Eq. 6)

where n is the size of the matrix. RI is usually given in a table and readers could refer to the

literature (Saaty,2010). A matrix is considered consistent only if CR is 0.1.

Step 3 Decide Potential Risk Levels

Fuzzy Synthetic Evaluation (FSE) is used in this paper to evaluate the risk levels of track

segments and their elements. The use of a fuzzy method is for the reasons that the factors are

hard to be quantified and detailed historical data are not available. Fuzzy methods are usually


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adopted in this case to achieve a balance between objectivity and subjectivity.

(Klir&Yuan,1995;Lu et al,1999).

(1) Decide Indicator Set U

Set U= {u1, u2, , un} as different elements of track system. The evaluation indicators of each

element is expressed as ui= {ui1, ui2,,uil}, where uijis the jth indicator of the ith track element.

(2) Decide Evaluation Set V

The evaluation set is the set of all the possible judgments an expert might give, expressed as V=

{v1, v2,,vm}. The Evaluation Set could be given to experts directly and ask for their selection

for each element or indicator. Otherwise, we could let experts evaluate on different aspects of the

system and then convert their results to a Evaluation Set, such as risk matrix method, which is

used this paper.

This paper defines eight levels for the risks: Very Low, Relatively Low, Low, Medium,

High, Relatively High, Very High and Extreme, expressed as V= {v1, v2, v3, v4, v5, v6, v7, v8} =

{1, 2, 3, 4, 5, 6, 7, 8} respectively. Extreme and Very High refers to the level that are not

allowed at any time and the risk should be eliminated immediately; Relatively High, High,

and Medium refers to the undesired level and it is only acceptable after measures are taken to

reduce the risk. Low, Relatively Lowand Very Low refer to the ignorable risks. Note that

the evaluation set is unbalanced and has more elements for the side of higher risk since we are

interested in segments and track elements of high risks and distinguishing between stations of

low risks with too many levels will make no sense.

(3) Obtain indicator relative importance: Weight Vectors W


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Use AHP as in Step 2 to obtain the relative weights of various indicators, W = {w1, w2,, wn}.

(4) Decide Membership Matrix R

Risk Matrix method is used to assist experts judgmentsand reduce the uncertainty caused by

experts subjectivity in the evaluation process. In this study, instead of asking the experts to give

judgments based on the Evaluation Set directly, we ask them to evaluate from two aspects:

occurrence probability and consequence. Occurrence probability indicates the possibility that

damage of a certain indicator will happen. Consequence reflects the harm severity of the

occurrence. We define five different levels for each, as in Table 1. Experts are asked to give their

judgments on both the Probability and Consequence and then we convert their judgments with

Table 1 to the elements in the Evaluation Set V(USDOD,2006).

TABLE 1 Risk Level Definition based on Occurrence Probability and Consequence.

Risk Level Consequence

Negligible Marginal Serious Critical Catastrophic

Probability

Impossible Very Low Relatively

Low

Low Medium High

Remote Very Low RelativelyLow Medium High RelativelyHigh

Occasional Relatively Low Low High Relatively

High

Very High

Probable Low Medium Relatively

High

Very High Extreme

Frequent Medium High Relatively

High

Very High Extreme

Then we count the number times that each element of Evaluation Set, vi, is given by all

the experts for each indicator. A Membership Matrix R from U to V is decided based on this

value, as in Equation 7. For example, if we find that, through conversion with Table 1, five

experts consider the risk level as Medium for a certain indicator, the value corresponding to v4

in matrix R for this indicator is 5.


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11 12 ... 1

21 22 2

1 2

...

... ... ... ...

...

ij m n

n

n

m m mn

r r r

r r r

r r

R

r

r

i=1, 2, , m; j=1,2,, n (Eq. 7)

where rijof matrix R refers to frequency of which uiis evaluated as vj. Generally it will be

normalized so that. .(5) Calculate Fuzzy Synthetic Evaluation Set Q

The effect of different indicators uijof one track element can be calculated with Equation 8. This

is called Level 1 Synthetic Evaluation since it evaluates a single element based on its indicators.

11 12 ..

1 2 1 2

. 1

21 22 2

1 2

...

..., , , ,

... ... ...

...

, ,

n

n

m m mn

n m

r r r

r r r

r r

Q w R w w w q q

r

q

(Eq. 8)

where qiis the membership degree corresponding to the ith element of the evaluation set element

vi. The value indicates to what extent the evaluation target has the risk of v i.

Level 1 Synthetic Evaluation is going to be the basis for Level 2 Synthetic Evaluation,

where we need to evaluate the overall risk of a track segment. The Level 1 Fuzzy Synthetic

Evaluation Set Q for various elements will need to be combined to make Level 2 Membership

Matrix, each row of which corresponds to the Level 1 Fuzzy Synthetic Evaluation Set Q of a

track element. Then the same method of Equation 8 is used to obtain the Level 2 Fuzzy Synthetic

Evaluation Set.

(6) Calculate risk level and crisp value


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Weighted average method can be adopted to reach the evaluation conclusion form the

membership degree matrix Q: take weighted average of qifor every vias the weights as Equation

9, to obtain the risk crisp value, an actionable result more accurately describing potential risks

with a quantified value.

m

j

jjave vqV1

(Eq. 9)

CASE STUDY

This paper takes one segment of Beijing Urban Rail Transit Line 1 as an example and we aim to

evaluate the potential risk levels for the track segment as a whole and its different elements. The

evaluation track segment is defined as a portion of track infrastructure between two adjacent

stations and tracks in between. Sometimes several track segments can be combined if they share

similar attributes such as surrounding geological environment, passenger volumes and train

dispatch frequency, etc. The segment studied in the case study is a single segment. The names of

stations are not introduced here due to other concerns but the information we give is adequate for

explaining the proposed approach.

Step 1 Determine Evaluation Indicators

To achieve this objective, the research team conducted in-depth literature review, on-site survey

and consultation with experts and technicians of URT Operations Company. We then proposed

an index system from the perspective of various elements of the URT track system: rail, switch,

tie, connecting parts and track bed.


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Then we sent a survey along with a background description about the research to selected

experts and technicians. In the survey, we asked the experts to comment on the indicators we

proposed on a two-point scale basis (agreeand disagree). They were also asked to give

suggestions on either proposing new or replacing existing indicators if necessary. The survey

was sent through email to 15 experts and 12 of them responded to the survey.

The survey result confirmed our original index system and no indicators were removed

by the experts. Also, based on experts suggestion, two indicators, B5 and D4 were added to the

system. The final index system is shown in Table 2. Note that the segment under investigation in

the case study has ballastless track bed and thus all the indicators in Table 2 are used.

TABLE 2 Track Risk Evaluation Index System

Track Elements Indicators

Rail Damage (A) Fracture (A1)

Corrugation (A2)

Fatigue Crack (A3)

Shelling(A4)

Corrosion (A5)

Engine Burn (A6)

Welding Defects (A7)

Bolt Hole Crack (A8)

Oval flaw (A9)

Switch Damage (B) Switch Point Damage (B1)

Connection Parts (B2)

Frog (B3)

Switch Parts (B4)

Bad Switch Geometry (B5)

Tie Damage (C) Cracks (C1)

Shelling (C2)

Shoulder Damage (C3)

Connecting Parts Damage (D) Fracture (D1)

Corrosion (D2)

Loose Parts (D3)

Worn Parts (D4)Track Bed Damage (E) Mud-pumping (E1)

loose tie (E2)

Cracks (Ballastless) (E3)

Deformation (Ballastless) (E4)

Subsidence (Ballastless) (E5)

Longitudinal/traverse Deviation (Ballastless) (E6)


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Step 2 Identify Relative Importance between Indicators

AHP method is then utilized to identify the relative importance between indicators. We also

asked the 12 experts who responded the survey to give their judgments. Also, a separate

document is also given to the experts to explain the meaning of each indicator to ensure

consistency among experts understanding. For example, an expert is asked to give their

judgment on the relative importance of Fracture (A1) and corrugation (A2). He/she is also given

explanations of what the two terms refer to in this study. All of the processes are realized using

spreadsheets via email. All 12 experts replied the email request.

Due to space constraints, we give an example of calculation for indicator relative

importance for the "Tie" sub-system. We asked experts to compare relative importance between

indicator pairs of C1-C2, C1-C3and C2-C3. As a result, for C1-C2, eight experts give score "3",

two experts give score "1" and two experts give score "5"; for C1-C3, nine experts give score

"1/3" and three give score "1"; and for C2-C3, eleven experts give score "1/3", and one give score

"1". Then we take the mode of all scores as the final score. The final judgment matrix is show as

the first matrix of the following calculation process, based on Equation 1 to 3.

Using Equation 4, we obtained max=3.047.

Using Equation 5 and 6 to check the consistency:


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The consistency requirement is met. The results of all calculation are shown in Table 3.

TABLE 3 Relative Importance between Indicators

Rail Damage (0.457) Switch Damage

(0.191)

Tie Damage (0.061) Connecting Parts

Damage (0.191)

Track Bed Damage

(0.099)Indicator Weight Indicator Weight Indicator Weight Indicator Weight Indicator Weight

A1 0.337 B1 0.271 C1 0.334 D1 0.501 E1 0.273

A2 0.060 B2 0.066 C2 0.141 D2 0.077 E2 0.196

A3 0.062 B3 0.463 C3 0.525 D3 0.159 E3 0.046

A4 0.150 B4 0.090 - - D4 0.263 E4 0.088

A5 0.029 B5 0.109 - - - - E5 0.303

A6 0.052 - - - - - - E6 0.094

A7 0.110 - - - - - - - -

A8 0.035 - - - - - - - -

A9 0.166 - - - - - - - -

We also checked the consistency ratio using Equation 5 and 6 to ensure judgments as

being consistent. The respective consistency ratios for indicators under five elements are 0.0338,

0.0818, 0.0405, 0.0746 and 0.0443. The ratio for judgments between five elements is 0.0451.

The results indicate that the consistency requirement is met.

Step 3 Decide Potential Risk Levels

Due to the space constraints, we illustrate the calculation process only for the element of Switch

Damage (B).

(1) Decide Indicator Set U

As obtained in Step 1, the evaluation indicator set contains five indicators: U = {Switch Point

Damage (B1), Connection Parts (B2), Frog (B3), Switch Parts (B4), and Switch Geometry (B5)}.

(2) Decide Evaluation Set V

We adopt the evaluation set defined in the methodology part: V = {v1, v2, v3, v4, v5, v6, v7, v8} =

{1, 2, 3, 4, 5, 6, 7, 8}.


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(3) Obtain indicator relative importance, Weight Vectors W

As calculated by Step 2, the relative importance weights of the track switch is W = {0.271, 0.066,

0.463, 0.090, 0.109}.

(4) Decide Membership Matrix R

19 experts were invited to give their judgments on the segment we investigate. 8 of them were

interviewed on-site during a site visit and 11 of them were from the 12 experts who responded to

the first round email in Step 1 and 2. The experts are asked to evaluate the segment based on the

damage occurrence probability and consequence. Note that, this evaluation is specific to this

segment, while the two rounds of survey in Step 1 and 2 are for general cases. The example

survey table for "Switch Damage" is shown in Table 4. Experts are asked to check one of the five

cells in both "Probability" and "Consequence" for each of the elements from B1to B5. We then

converted all experts' judgments to the Evaluation Set V using Table 1. For example, for "Switch

Point Damage (B1)", expert "a" checked "Occasional" for "Probability" and "Critical" for

"Consequence", Table 1 would indicate "Relatively High". Then, the element of Membership

Matrix R corresponding to ""Relatively High" in Evaluation Set V increases by a value of 1 (i.e.,

R1,6=R1,6+1).

TABLE 4 Example survey table for risk reporting matrix

Switch DamageProbability

Impossible Remote Occasional Probable Frequent

Switch Point Damage (B1)bekgihos

adjflmn cpqr

Connection Parts (B2)pq

abilmnos cekghdr jf

Frog (B3) bekgios dhjf aclmnpqr

Switch Parts (B4) aeghk biflmnpqros cdj


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Bad Switch Geometry (B5) m fghdjklqo abceinprs

Switch Damage

Consequence

Negligible Marginal Serious Critical Catastrophic

Switch Point Damage (B1) bdjfpos acekghilmnqr

Connection Parts (B2) fj bdeghkios aclmnr pq

Frog (B3) abhlmno cdefgijkpqrs

Switch Parts (B4) bdijos cefghklmn apqr

Bad Switch Geometry (B5) bieos adfghjklnp cmqr

We use letters from a to s to indicate 19 experts in the table. Expert Letter in a box means the expert checked the

box during survey.

We then do the conversion and calculation for each expert's judgment and then come up

with the left matrix below. Normalizing the matrix could obtain the matrix in the right, which is

the Membership Matrix R.

R=

(5) Calculate Fuzzy Synthetic Evaluation Set Q

By multiplying the weight vector W with Membership Matrix R, we obtained the Level 1Fuzzy

Synthetic Evaluation Set for track element Switch.

(6) Calculate risk level and crisp value

With the Weighted Average Method, we take weighted average of qifor every vias the weights

as Equation 9 to obtain the risk crisp value of 5.3707, and risk level between of High and


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Relatively High,indicating undesirable level and requiring more resources for further

inspection and risk control.

DISCUSSION

The case study shows the effectiveness of proposed method and its application in evaluating risk

levels of track systems of urban rail transit. We now offer more discussions on the method and

case study.

First, the methodology proposed in this paper is practical and easy for implementation to

conduct network screening of track system state for maintenance prioritization. As illustrated by

the case study, since only expert judgment data are needed, the proposed method becomes very

useful in URT track evaluation, specially for places where database for historical inspection and

monitoring haven't been set up.

Second, Although we only show the evaluation process of element Switch in the case

study, the method can be used to evaluate either the overall risk level of a track segment (Level 2

Synthetic Evaluation) or different elements of the segment (Level 1 Synthetic Evaluation), as

shown in Table 5. They are calculated using same method and higher level of the risk interval is

adopted as the evaluation result. In calculating risk level for a track segment as a whole,

Membership Matrix R can be obtained by taking Synthetic Evaluation Set Q for each track

element as row for matrix R. Then the evaluation can be completed by using Equation 8 and 9.

Also, evaluation should be conducted for each of the segments for a URT line or network. After

all segments are analyzed, we can then rank them based on risk crisp values and decision makers

would easily identify which segments are priorities in maintenance.


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TABLE 5 Final Risk Levels and Crisp Values of the Selected Track Segment

Evaluation Target Risk Level Risk Crisp Value

Track Segment High 4.825

Rail Relatively High 5.091

Switch Relatively High 5.371

Tie Medium 3.719

Connecting Parts High 4.256

Track Bed High 4.381

Third, One of the most significant advantages of this method is that it produces Risk

Crisp Values for the whole segment and various elements. Although the data drive the analysis

are subjective data, the method makes use of objective analysis techniques, AHP, FSE and Risk

Matrix, to produce risk crisp values, with which potential risk levels are quantified. These values

can then greatly facilitate decision making, far more accurate than the case where only vague

expert judgment is used.

Also, in real practice, an evaluation information system can be developed to facilitate the

process. A web based user end can be developed for the convenience of expert input and all the

expert judgment data will be sent back to the server and store in the database. A server

application can be developed to retrieve and analyze data, determine risk crisp values and

produce visualization charts. While using email for data collection as in this study is labor

intensive, the use of such an information system along with database technology can potentially

make data collection more convenient and time-saving for both study team and experts (thus

possibly increase response rate from expert), and would also be an important tool for

maintenance supervisor.

Further, The index system (Table 2) and the relative importance weights (Table 3) are

obtained for general cases, without specifying any URT segment. Therefore, these results could


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be borrowed for use in other studies, especially when the URT system is similar to Beijing's. The

results are also useful since they can be used directly to preliminarily decide which parts of the

track system and what problems need to be inspected when no resources for carry similar study

is available. For example, compared with Rail Damage, Tie Damage is much less important.

Therefore, the inspection or maintenance interval of ties could be generally longer than that of

the rail.

CONCLUSIONS

This paper proposes an integrated approach, combing Analytical Hierarchy Process (AHP) and

Fuzzy Synthetic Evaluation (FSE), to evaluate the potential risks in the track system and

prioritize the maintenance of various track segments of urban rail systems. Several important

conclusions are made.

First, the integrated approach, based on AHP and improved FSE is effective in evaluating

track system risk levels and rank track segments for maintenance prioritization, as shown in the

case study. The approach not only provides qualitative risk levels but also quantitative risk crisp

values that can greatly facilitate the decision-making process. The approach combines subjective

data with enhanced objective approach, AHP and improved FSE with risk matrix, to produce

reliable evaluation and it becomes especially useful where historical inspection and monitoring

data is not adequately available.

Second, the evaluation index system and relative importance weights, as shown in Table

2 and 3, are established for general cases and could be borrowed for the use in other locations.


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Also, these indicators are selected based on the four criteria proposed in the methodology part,

which have been proven helpful in improving the index system development.

Third, Risk Matrix method is successfully adopted in improving FSE in terms of

obtaining the Membership Matrix. This is very useful and effective in reducing subjective

uncertainty caused by vague judgment and in assisting experts judgments. This method is

recommended for future studies when FSE is adopted.

Although the proposed approach is applicable for most evaluation tasks, we admit that

the incorporation of reliable historical data can produce better evaluation results. The next step of

the research is to incorporate currently limited data, which are not enough for decision making,

into the integrated approach. One possible way is to validate various inferred results from expert

judgment and adjust them if inconsistency exists.


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