An integrated tool for optimizing rehabilitation programs of highways pavement.
Marzouk, Mohamed ; Awad, Ehab ; Said, Moheeb El- 等
Kompleksine priemone automobiliu keliu dangu atnaujinimo programoms
optimizuoti
Integrejosa cela segu atjaunosanas programmas optimizacijas metode
Teekatete remondiprogrammide optimeerimise integreeritud vahend
1. Introduction
The total length of the road network in Egypt exceeds 65 000 km.
According to the statistics of General Authority for Roads, Bridges and
Land Transport, the total length of arterial road networks increased
from 12 500 km in year 1972 to 47 500 km in year 2008. In Egypt, road
networks are characterized by two aspects: i) they are aging and in some
parts they are not functioning well, and ii) they are expanding rapidly
to meet the economic growth. The share of freight transport in the road
network is 95%. Keeping road networks in good condition is not possible
without optimizing available limited resources. Therefore, the need to
optimize maintenance planning is inevitable. The deterioration of road
network assets is noticeable due to commercial and industrial
activities. Keeping the workability of road networks in good condition
is considered a cumbersome task which needs to be addressed on strategic
level (Vanier 2001). The maintenance of such road network
infrastructures requires the use of comprehensive Pavement Management
Systems (PMS). The environment for running such system is characterized
by the uncertainty of road condition in the future and the inaccuracy of
the gathered data. A lot of efforts have been made to develop Pavement
Management Systems and bridges (Abu Dabous, Alkass 2011; Amador-Jimenez,
Mrawira 2011; Sobanjo 2011; Tsai, Lai 2002; Yang et al. 2009). In this
paper, a framework for pavement performance prediction is developed
utilizing Markov chain. The input for this model is Pavement Condition
Index (PCI) which is adopted by General Authority for Roads, Bridges and
Land Transport for measuring the performance of the Egyptian roads.
Output from performance model is input for optimization process to
provide decision makers with several alternatives for min budgeted cost
with considering max quality of work performed and max percentage of
area coverage. Further, the framework helps to achieve three goals: 1)
minimizing budgeted cost to meet the need of strategic planners, 2)
maximizing the quality of performing maintenance and rehabilitation
programs, and 3) maximizing the total percentage of the network area
that will be under maintenance and rehabilitation. A case study is
presented to illustrate the main features of the model.
2. Pavement management systems
PMS is defined by AASHTO as "A systematic process that
collects and analyzes pavement information with rational procedures that
provide optimum pavement strategies based on predicted pavement
attributes incorporating feedback regarding various attributes, criteria
and constraints involved". In general, typical structure of a PMS
consists of six main components as follows (Fig. 1):
i) Data Input Module: it collects and standardizes data to meet the
validations requirements of the database.
ii) Database Module: it acts as a repository for all historical
field information. This organized information is considered the base for
performing any analysis or decision, pertaining to the current or future
road maintenance plans. In the proposed model, the essential database
attribute is the PCI for each segment which is retrieved at each
inspection. This technique classifies and rates different segments of
the network based on visual inspection.
iii) Performance Prediction Module: role of this module is to
predict future network condition based on the available information. The
prediction module is either based on deterministic or probabilistic
approach. In the proposed model, the focus of research is the
probabilistic approach which represents the real life situation and
provides a better accuracy with respect to the future condition of the
network.
iv) Optimization and Analysis Module: the output obtained from the
performance prediction module is fed to this module to calculate the
different options for future maintenance programs. The cost is estimated
based on different scenarios. Different outputs are based on the
selection of different resource options.
v) Planning and Implementation Module: it tracks and reports the
programs for maintenance plans including the budgets and resources. All
cost components are detailed and reported via this module.
vi) Reporting and Feedback Module: this module plays a major role
in developing and upgrading the system. In addition, it communicates
with all network stakeholders regarding any reporting requests.
[FIGURE 1 OMITTED]
3. Markov chain
Markov chain is a stochastic process that handles the uncertainty
condition of road system performance through time. Applying Markov chain
models for asset management systems has proved to be reliable in
different applications (Adedimila et. al. 2009; Black et. al. 2005;
Orcesi, Cremona 2010; Puz, Radic 2008; Yang et. al. 2005). Several
efforts have been made utilizing Markov chain to optimize maintenance
and replacement decisions of bridges' components (Golabi, Shepard
1997; Jiang et al. 2000; Madanat 1993). Markov chain has been adopted
for developing performance deterioration model for bridge deck, taking
into consideration the history of deterioration and maintenance
(Madanat, Robelin 2007). This stochastic process is an indexed
collection of random variables |Xt| for t runs through a given set of
non-negative integers (T) (Hillier 2000). The Markov process is
considered to have Markovian property if conditional probability of any
future event is independent of the past and depends only upon the
present state; for any matrix to be considered a Markov Matrix or
Transition Matrix the following two properties should be valid (Janssen,
Manca 2006).
[P.sub.ij] [greater than or equal to] 0 for all i, j [member of] T,
(1)
[SIGMA] [P.sub.ij] = 1 for all i, [member of] T, (2)
where p--the probability of transition from one state i to another
state j. Fig. 2 shows the graphical representation of the transition
between two states.
[FIGURE 2 OMITTED]
Using Markov model, the transition matrix represents the
probability of change from state i to state j over time period; the one
step transition matrix P is a two dimensional matrix of size 4x4 to
represent states of the road condition which are Excellent, Good, Fair,
and Bad as per Eq (3). The Transition Matrix after some time n is
calculated using Eq (4) as per Janssen and Manca (2006).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[P.sub.n] = [P.sup.n] (4)
The transition states, i.e., the values of the matrix, are
classified into three types as follows:
--Transient; if upon entering this state, the process may never
return to this state again.
--Recurrent; if upon entering this state the process will
definitely return to this state again.
--Absorbing; if upon entering this state, the process will never
leave the state again.
As such, it is possible to predict the deterioration of the
pavement through a fixed period of time which is the period between two
consecutive inspections (Black et. al. 2005). The adaptation of this
method requires large amount of data to decrease errors and to gain
reliable results.
4. Model development
The methodology that has been followed in the proposed research
includes three major stages (Awad 2010). These are: 1) data collection,
2) developing performance prediction module, and 3) optimization module.
The details of these stages are described hereinafter.
4.1. Data collection
Road network consists of several roads. The road comprises smaller
units that are called road segments. In this research, the length of
road segment is considered two kilometres long with adopting the actual
data that are collected by GARBLT to capture the characteristics of road
segments. The data represents the PCI for each segment for two
consecutive periods without applying any maintenance. The inspection of
the network is performed every three years. The data of road segments
are collected manually (via visual inspection). The main target of data
collection stage is to track the PCI values for each road segment within
the overall road network including record keeping of new inventory.
4.2. Performance predication module
The processing of information includes the classification of road
network conditions based on the segments data. A lot of efforts have
been made to set standard for the assessment of pavement conditions. In
this research, a scale has been introduced for the PCI index. The road
network conditions are grouped into four classes; Excellent, Good, Fair,
and Bad. Table 1 lists the PCI values of the different classes of the
network conditions along with the corresponding type of maintenance that
should be performed. To get the Vector Matrix in future or after a
certain number of inspections (n), Eq (5) is applied:
[V.sub.n] = [V.sub.0] [P.sub.n], (5)
where [V.sub.0]--the initial Vector Matrix of the network based on
the current road inspection; [P.sub.n]--the transition matrix after n
inspections.
The elements of the transition matrix, which are calculated based
on the proposed four classes, constitute Markov mode to capture
probabilistic transition process model. The elements of the matrix are
calculated taking into account the following assumptions:
--no improvement in any state to the upper state to maintain the
integrity of the matrix. As such, the upper triangle elements are used;
the elements of lower triangle elements are all zero.
--maintenance is not applied within two consecutive condition
records.
The elements of the probability matrix is calculated using Eq (6),
proposed by Jiang et al. (1988). The matrix is formed while rendering
the validity of Eq (7) for the four classes, considered in the proposed
model.
P = [n.sub.ij]/[n.sub.i], (6)
[SIGMA] [p.sub.ij] = 1 for 1 [less than or equal to] i [less than
or equal to] 4 (7)
where [n.sub.ij]--the number of transitions from state i to state j
within a given period, [n.sub.i]--the total number of segments in state
i before the transition; [p.sub.ij]--the probability of transition from
state i to state j between two successive inspections without any
maintenance.
The performance prediction module encompasses two main elements:
Transition Matrix (P) and Initial Vector Matrix ([V.sub.0])). These two
elements are deemed essential to provide the status of the network
condition after any number of inspections. The Initial Vector Matrix is
essentially the initial condition vector that represents the current
status of the road (Morcous 2005). It is built by calculating the
percentage of each state to the total number of road segments for the
data of the initial year as per Eqs (8) and (9):
[V.sub.0] =[[V.sub.1] [V.sub.2] [V.sub.3] [V.sub.4]], (8)
[V.sub.i] = [[summation][v.sub.i]]/N for 1 [less than or equal to]
i [less than or equal to] 4, (9)
where N--the number of all segments in the network; [V.sub.1],
[V.sub.2], [V.sub.3], [V.sub.4]--the percentage of road segments that
are in Excellent, Good, Fair and Bad conditions, respectively.
As such, the vector matrix or the future condition of the network
over time is obtained. To plot the performance of the road, a scale from
1 to 4 is used to quantify the vector matrix into one single value that
is used as an index to draw the curve. This performance index (I) is
calculated by applying Eq (10):
I = 4[V.sub.1] + 3[V.sub.2] + 2[V.sub.3] + 1[V.sub.4], (10)
where the value [V.sub.i]--used to represent the percentage of each
state to the total area of the network. The performance index (I) varies
from 1 to 4. For example, Excellent road network has a performance index
close to 4 (Fig. 3), whereas, Bad road network has a performance index
close to 1. The result should provide an input to predict the future
requirements of road network including the allocation of resources by
using these values as the upper limit of each state that requires
maintenance.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
5. Optimization module
Optimization module works to achieve three goals: 1) minimizing
budgeted cost to meet the need of strategic planners, 2) maximizing the
quality of performing maintenance and rehabilitation programs, and 3)
maximizing the total percentage of the network area that will be under
maintenance and rehabilitation. Minimizing budgeted cost is major demand
by strategic planners and different proposals should be made available
to empower the decision making process. The main goal is to optimize
budgeted cost to receive endorsement of network stakeholders
(government, legislatures, etc.) on one of these proposals. But this
item is not the only objective and it is not evaluated without setting
two other major factors, the quality of performance and the percentage
of area covered to the total area of the network. Maximizing quality
ensures that final output from M&R programs should be made according
to acceptable standard. Maximizing area percentage that is targeted by
M&R programs ensures high road serviceability and safety and
decreases the deferred backlog. In order to achieve these goals, the
framework of the M&R includes six types of programs as per Table 2.
It is assumed that these programs are selected concurrently and that
none of them is to be eliminated. Achieving these objectives requires
the formulation of an optimization problem that is modeled via genetic
algorithms chromosome. The chromosome handles the presence of the six
programs together and is capable to provide different scenarios for
planning of M&R programs. The chromosomes consist of eighteen genes.
The first six genes (1-6) represent the resources required to apply
these programs, whereas, the second six genes (7-12) are the quality of
each option. The quality is defined as the quality of performing these
programs upon each resource selection. percentage of each type of
project to the total pavement area of the network; The last six genes
(13-18) represent the percentage of each sub area that is to be selected
for M&R to the total proposed area for M&R (Fig. 4).
Subsequently, the first objective function is formulated to
minimize the cost of maintenance and rehabilitation programs as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
where T--total area of the network, [m.sup.2]; %A, %B, %C, %D, %E
& %F: percentage of the area that requires program type A, B, C, D,
E & F, respectively; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] cost of square
meter in program A, B, C, D, E & F using resource R with option i.
The second objective function is formulated to maximize quality of
performed maintenance and rehabilitation works as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]--quality
of program i with budgeted cost c for option j which is one of three
budgeted cost options for each program.
The third objective function is formulated to maximize the total
percentage of area selected for maintenance.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII]--percentage of area a of program i with budgeted cost c for
option j which is one of three budgeted cost options for each program.
These three functions are optimized using Non-dominated Sorting
Genetic Algorithm (Deb 2001). The main objective of the optimization
module is to optimize the total budgeted cost of the program considering
the quality of each maintenance program and the area of each program.
The advantage of this module is its ability to expand, to include
further parameters of the road and to customize the list of programs to
meet agencies requirements. Finally, this module ensures that
maintenance of road network is adjusted to the limits of budgeted cost
with maintaining standard quality of performance. Detail description of
optimization module is found elsewhere (Awad 2010). In addition to its
simplicity, the model is capable of being dynamically modified to
include further parameters like user cost.
6. Model implementation
The proposed model was implemented using Microsoft Access 2000 and
VB.net for facilitating data entry, processing of the gathered
information, and generating reports. First, the user inputs the gathered
data from field which contains the identification of the road segment
(RoadSegment), PCI for that segment (PCI), and inspection year (Year).
The database of the model is designed to perform several queries that
calculate the elements of the Transition Matrix at initial state
([P.sub.0]) and Initial Vector Matrix ([V.sub.0]). These results are
automatically populated in a user interface, depicted in Fig. 5. Running
the model provides the Transition Matrix after any number of inspections
and the corresponding Vector Matrix. Finally, the information of the
deterioration model is generated and is represented in a graphical
format. Output from performance model is used as input for optimization
model. Fig. 6 shows the dataflow in the proposed pavement management
system.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
7. Case study
7.1. Case description
This section describes a hypothetical case to clarify the use of
optimization module. The final results from this example are
near-optimum solutions for the optimized budgeted cost, percentage of
quality of work performed, and selected area percentage of total area
covered. Table 3 lists the data that are obtained from Helwan/El-Saf
rural road from years 1999 to 2005. The input data of the case are
listed in Tables 4 to 6 for budgeted cost, percentage quality of work
performed, and percentage area for each maintenance program. As shown,
there are six maintenance and rehabilitation programs with three options
for each one. Each option provides different scenario. The purpose of
this optimization is to minimize budgeted cost and to maximize
percentage quality and percentage covered area for road segments that
have a total area of 120 000 [m.sup.2].
7.2. Case analysis
The optimization module is triggered to evaluate its performance in
searching large space of possible solutions. A number of optimization
parameters are defined including; number of generations (G = 200),
population size (S = 20), crossover (C = 0.6), and mutation (M = 0.02)
values as described hereinafter. The results shown in Figs 7 to 9 are
obtained, indicating Pareto set. The final Pareto set of chromosomes and
the corresponding Budgeted Cost (LE), Quality (%), and Area (%) are
listed in Table 6 and depicted in Fig. 10.
8. Conclusions
This paper presented the development of pavement prediction model
and optimization model within the frame of pavement management system.
As a stochastic approach, Markov chain is applied to provide valuable
information about the state of the pavement in the future. The process
is applicable on the network level geared towards furnishing
decision-makers with a tool for assessing road conditions. Therefore,
reasonable maintenance budgets for analyzed network(s) are allocated.
Road maintenance should be based on strategic decision that adopts PMS.
The paper presented the methodology that was followed in the proposed
research including; 1) data collection, and 2) developing performance
prediction module 3) optimization module. Furthermore, the optimization
model is dynamically modified to include further pavement related
parameters to enable better selection of programs by decision makers.
The road network conditions are classified into four classes; Excellent,
Good, Fair and Bad. The model was implemented using Microsoft Access
2000 and VB.net.
The paper presented an optimization framework that helps to achieve
three goals: 1) minimizing budgeted cost to meet the need of strategic
planners, 2) maximizing the quality of performing maintenance and
rehabilitation programs, and 3) maximizing the total percentage of the
network area that will be under maintenance and rehabilitation
(M&R). In order to achieve these goals, the framework of the M&R
includes six types of programs. Achieving these goals requires the
formulation of an optimization problem that is modeled via genetic
algorithms chromosome. The chromosome handles the presence of the six
programs together and is capable to provide different scenarios for
planning of M&R programs. A case study was presented to demonstrate
the capabilities of the proposed model and its ability in identiying
near-optimum Pareto solutions. The case was obtained from Helwan/El-Saf
rural road from years 1999 to 2005 for a total area of 120 000
[m.sup.2]. The Pareto fronts have been plotted in 2D and 3D to
demonstrate the near-optimum feasible M&R programs. This research is
extendable for future integration of user cost as a major factor in the
optimization model. Additional efforts are recommended for optimizing
the program with considering other deterioration models of different
infrastructure in the same location of the road network.
doi: 10.3846/bjrbe.2012.39
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Received 21 October 2010; accepted 16 March 2011
Mohamed Marzouk (1), ([mail]), Ehab Awad (2), Moheeb El-Said (3)
(1,3) Dept of Structural Engineering, Cairo University, 12613 Giza,
Egypt
(2) Orascom Construction Industries, Nile City Towers,
Corniche El Nil, 11221 Cairo, Egypt
E-mails: (1) mmarzouk@nileuniversity.edu.eg; (2)
Ehab.Awad@orascomci.com; (3) elsaid1204@yahoo.com
Table 1. Road network conditions vs. maintenance types
PCI Road Condition Maintenance
Type
100 [greater than or equal to] PCI Excellent Routine
[greater than or equal to] 85
84 [greater than or equal to] PCI Good Preventive
[greater than or equal to] 70
69 [greater than or equal to] PCI Fair Rehabilitation
[greater than or equal to] 40
39 [greater than or equal to] PCI Bad Complete
[greater than or equal to] 0 reconstruction
Table 2. Description of maintenance and rehabilitation programs
Program Program Description Before After
Program Program
Status Status
A Complete reconstruction Bad Excellent
B Major rehabilitation Fair Excellent
C Minor rehabilitation Fair Good
D Major maintenance Good Excellent
E Minor maintenance Good Good
F Routine Excellent Excellent
Table 3. Helwan/El-Saf rural road data
Segment From, km To, km Year
ID
1999 2000 2002 2005
1 0 2 74 79 94 43
2 2 4 79 46 100 65
3 4 6 82 77 96 28
4 6 8 77 59 96 63
5 8 10 85 91 96 42
6 10 12 87 82 81 55
7 12 14 69 88 81 77
8 14 16 80 72 55 71
9 16 18 81 72 84 80
10 18 20 85 82 50 100
11 20 22 87 100 100 87
Table 4. Budgeted cost of resources' options
Program Cost of option Cost of option Cost of option
1 (LE/[m.sup.2]) 2 (LE/[m.sup.2]) 3 (LE/[m.sup.2])
A 30 35 37
B 20 24 28
C 14 16 18
D 9 12 14
E 6 7 8
F 2 3 5
Table 5. Thresholds for quality options vs. budgeted cost
Program Quality, %
Option (1) Option (2) Option (3)
A 80 85 88
B 80 88 92
C 80 85 88
D 80 85 88
E 80 85 90
F 80 85 90
Table 6. Thresholds for percentage area options
vs. budgeted cost
Gene Name Area percentage
Option (1) Option (2) Option (3)
A 31 28 30
B 22 20 20
C 10 14 12
D 10 8 10
E 16 12 15
F 8 6 4
Table 7. Estimated objective functions
of Pareto solutions
Pareto Program option
front
A B C G E F
QB 2 2 3 3 3 3
1 1 2 3 3 3
1 1 2 2 3 3
1 1 2 2 3 2
1 1 2 2 2 2
1 1 2 1 2 2
1 1 1 1 1 3
1 1 1 1 1 2
1 1 1 1 1 1
AB 1 1 2 1 1 1
1 1 1 1 1 1
AQ 2 2 3 3 3 3
3 3 2 3 3 2
1 1 2 3 3 3
1 1 2 2 3 1
1 1 2 3 1 1
Pareto Program area, %
front
A B C G E F
QB 28 20 12 10 15 4
31 22 14 10 15 4
31 22 14 8 15 4
31 22 14 8 15 6
31 22 14 8 12 6
31 22 14 10 12 6
31 22 10 10 16 4
31 22 10 10 16 6
31 22 10 10 16 8
AB 31 22 14 10 16 8
31 22 10 10 16 6
AQ 28 20 12 10 15 4
30 20 14 10 15 6
31 22 14 10 15 4
31 22 14 8 15 8
31 22 14 10 16 8
Pareto Objective functions
front
Quality, Area, Budgeted cost
% % (LE *)
QB 88.2 89 24 492000
85.5 96 21 444000
85.5 94 21 204000
84.2 96 21 036000
83.3 93 20 856000
82.5 95 20 496000
81.7 93 20 196000
80.8 95 20 028000
80.0 97 19 944000
AB 80.8 100 20 232000
80.0 97 19 944000
AQ 88.2 89 24 492000
88.0 95 25 716000
85.5 96 21 444000
83.3 98 20 952000
82.2 100 20 832000
* 8 LE = 1 EUR
