Predicting freeway pavement construction cost using a back-propagation neural network: a case study in Henan, China/Greitkelio dangos irengimo sanaudu prognozavimas naudojant atgalinio sklidimo neuronini tinkla: Kinijos Henano provincijos pavyzdys/Automagistralu segas konstrukciju buvniecibas izmaksu prognozesana ar pagatne versto macisanas algoritma neiralo tiklu: Henanas piemers Kina ...
He, Jie ; Qi, Zhiguo ; Hang, Wen 等
Kiirtee katendiehituse maksumuse prognoos kasutades tagurpidi
narvivorke: juhtumiuuring Henanis, Hiinas
1. Introduction
Henan Province is located in the centre of China. Its area is 167
000 km2, it has a population of 99 mln and contains 18 cities ranging in
size from 1.5 mln to 11 mln people. In 1994, Henan's first freeway
was built from Zhengzhou to Kaifeng. In 2007, the total length of the
freeways in Henan Province was 4556 km, and by 2020, it is expected that
the total length will reach 6280 km.
In the past 10 years, the freeway network in China has developed
very quickly and the total investment has been huge. However, in some
freeway projects, the final construction cost is higher than the
estimated cost at the detailed design stage, which in turn is higher
than the conceptual cost at the preliminary design stage. In the context
of government financial accountability practices in China this presents
challenges; any deviation is likely to be queried, and the Secretary of
the Provincial Transportation Dept or a senior official in the
department will often have to defend the increased costs publicly or in
the state legislature. As a result, the legislature and the public will
have perceptions of incompetence and erosion. A more accurate cost
estimation process for freeways would therefore contribute to greater
public and government confidence in the operation of infrastructure
planning and development agencies, as well as contributing to more
efficient budget processes.
Researches have indicated that project definition in the early
planning process is an important factor leading to project success (Le
et al. 2010; Scott-Young, Samson 2008; Thomas, Fernandez 2008). To
prepare reliable budgets for freeway construction programs, road
authorities must have accurate estimates of future funding allocations
they are likely to receive, and future project costs for long term
infrastructure programs. While future funding is obviously never known
with a great deal of certainty, it is more often the inaccurate
estimation of project costs that causes greater disruption to the
execution of construction programs.
Various critical factors must be identified to estimate
construction costs effectively. Several studies have set out to identify
relevant factors, ranging from generic management and financial factors
through to those that are specific to the industry under consideration.
Stoy et al. (2008) identified quantitative cost factors such as absolute
size, construction duration, and compactness as influence factors for
good bidding information. Liu et al. (2011) found uncertain factors such
as meteorological factor has a great uncertainty in the construction
schedule of hydropower construction.
Pinto and Mantel (1990) identified the ten critical factors such as
project scope, management goals, time planning and management,
communication with owner, etc. In a study conducted in Newfoundland,
Hegazy and Ayed (1998) found that season, location, type of project,
contract duration, and contract size had a significant impact on an
individual contract cost. Wilmot and Cheng (2003) described future
construction cost in terms of predicted index values based on forecasts
of the price of construction labour, materials, and equipment and the
expected contract characteristics and contract environments. In a
building construction study conducted by Cheng et al. (2009b), ten key
quantitative factors were identified in the planning stage of projects.
Six were quantitative: floors underground, total floor area, floors
aboveground, site area, the number of households and households in
adjacent buildings; and four were qualitative: soil condition, seismic
zone, interior decoration and electromechanical infrastructure,. Thus,
examination of the literature shows that a wide variety of factors have
been found to influence construction costs.
Factors such as those described above have been used in models of
construction costs, but the models rarely attempt to use a comprehensive
set of factors. In part, this is a consequence of the methods used for
estimation. Shi, Li (2008) integrated rough sets (RS) theory and
Artificial Neural Network (ANN) to forecast construction project cost.
To overcome cost overruns in projects, some methods such as
Probabilistic Simulation (Chou et al. 2009) and Support Vector Machine
(Cheng et al. 2010; Chou 2011) have been used to develop appropriate
cost models for predicting the expected project cos.
On the contrary, regression analysis represents a traditional
approach (Khosrowshahi, Kaka 1996), an inherent disadvantage of which is
its requirement of a defined mathematical form for cost functions, i.e.
the nature of the relationships between variables must be assumed at the
outset. In addition, such traditional methods of estimating project
costs are hampered by the large number of important variables and the
interactions between them. In addition, some of the variables that
influence construction costs, such as the cost of labour, equipment, and
materials, are usually highly correlated with each other, resulting in
multicollinearity in the model when more than one of them is included.
Thus, traditional methods are limited in their potential applicability
to the estimation of construction costs.
As a comparatively new method, Neural Network (NN) models have no
implicit functional form and therefore have greater freedom to fit the
data than do regression models. It is therefore possible that the
greater flexibility in the relationship between input and output
variables in NN might translate into a better model than that achieved
with regression analysis. One purpose of the research reported in this
paper is to use NN to identify a better model.
Some researchers have employed NN models to estimate the
construction costs of individual projects (Ji et al. 2009). By combining
NN and fuzzy logic, Boussabaine (1999), Boussebaine and Elhag (1999)
developed neurofuzzy systems to estimate the construction cost and
project duration of individual building projects. Wilmot and Mei (2005)
developed a NN model to estimate highway construction cost escalation
over time. Cheng et al. (2009b) developed an evolutionary fuzzy neural
inference model to estimate costs at the concept stage. Ma et al. (2012)
propose to modify the existing model (a single cost for cost-sensitive
neural networks), the traditional back-propagation neural networks
(TNN), by extending the back-propagation error equation for multiple
cost decisions. Yip et al. (2014) presents a comparative study on the
applications of general regression neural network (GRNN) models and
conventional Box--Jenkins time series models to predict the maintenance
cost of construction equipment.
Furthermore, hybrid models (combining NN and other approaches) have
also been developed to estimate construction costs. Hegazy and Ayed
(1998) used NN to develop a parametric cost estimating model for highway
projects, with optimal NN weightings optimized by genetic algorithms.
Kim et al. (2005) applied hybrid models of NN and genetic algorithms to
residential building cost estimation in order to predict preliminary
cost estimates.
These studies indicate that NN and NN hybrid models have been used
instead of traditional methods to estimate the cost, duration, and other
features of construction project costs, including highway construction
projects. However, it is also clear from the limited literature that NN
models have usually been used only for individual construction projects,
rather than investigating the overall cost of construction across a
range of projects, and examining how their cost alters over time. This
approach has an inherent limitation, i.e. that the models developed are
relevant only to the case studied, and will therefore not be readily
generalizable to other projects. And the models discussed also lack
relevance to similar projects undertaken some time later, as the model
is specific to a particular time as well, whereas some of the important
variables are changing over time in ways which they are modelled. The
objective of this paper is to address these issues by developing a NN
model based on a range of freeway pavement construction projects and
taking temporal factors into consideration. In particular, this research
will apply a back-propagation (BP) NN model to predict design cost
estimates for freeway pavement construction projects, using historical
data on freeway construction projects in Henan Province as a case study
of the application of the approach.
2. Influential factors analysis
The first step in developing the model is to identify which factors
influence the costs of freeway pavement construction, so that they are
considered for inclusion in the model. These factors have been
categorized below as location, resource or time factors, though they
also incorporate other variables, e.g. location is related to altitude
and topography, both of which influence pavement construction costs in
Henan. While the list of potential influencing factors is quite lengthy,
a balance needs to be found, such that the number of factors is
sufficient to provide adequate forecasts of costs, but not too large for
practical application in a management setting. There is no clear
guideline as to what the ideal number of factors should be. In this
study, it was judged that the nine factors described below (two
location, four resource and three time-related factors) should provide a
more comprehensive basis for modelling and forecasting than has
previously been the case, without creating disproportionate information
needs.
2.1. Location factors
The freeway construction projects were located across Henan, which
is characterized by differences in climate, geology, and topography that
might be expected to have an influence on the cost of the projects.
These characteristics tended to vary together, so that it was possible
to define just three regions based on climate, geology and topography.
The region factor is given in Table 1.
An important practical issue for highway construction is the amount
of variation in altitude along the road, as greater variation increases
costs. This is related to topography, which is taken into account in a
broad sense in the regional categories above, but the degree of
variation between individual projects pointed to a need to develop
categories at the project level. Variation in altitude was therefore
divided into five categories from "very small", which
described roads that were essentially flat, to variations of between 450
m and 800 m. The variation in altitude factor categories (B1 to B5) are
listed in Table 2, along with an indication of where the projects for
each category took place, the range of absolute altitudes which applied
there, and the freeway contracts which fell into these categories.
2.2. Resource factors
Labour, material and equipment are the main resources for a
construction project. For simplicity, this study randomly selected five
cases as an example to illustrate pavement construction cost components
as shown in Table 3. Material costs constituted nearly 85% of pavement
construction costs and the equipment costs constituted nearly 12%.
A construction project usually requires more than 100 types of
material. The components of pavement material costs of the five cases
are shown in Table 4, with the largest four components listed
separately. Taken together, the two largest components (concrete and
asphalt costs and stone costs) accounted for approximately 76% of
material costs.
For simplicity, the authors proposed to use the costs of crushed
stone (diameter 4 cm) as a proxy for stone costs. The quantity of stone
category material is written in the following form:
[N.sub.stone] = [n.summation over (i=1)][N.sub.i] x
[[P.sub.io]/[P.sub.Crushed Stone(4 cm)o]], (1)
where [N.sub.stone]--the quantity of stone category material;
[N.sub.i]--the quantity of material i; [P.sub.io]--the bid price of
material i at time o; [P.sub.Crushed Stone(4 cm)o]--the crushed stone
price at time o. This equation provides equivalence between all other
stone materials and crushed stone. This allows the quantity of other
stone materials to be included in the evaluation by linking it to an
equivalent amount of additional crushed stone.
A similar process is used to quantify an equivalent amount of Calx
(calcium oxide) as a proxy for concrete and asphalt material costs. The
quantity of concrete and asphalt category material is written in the
following form:
[N.sub.Concrete And Asphalt] = [n.summation over (j=1)][N.sub.i] x
[[P.sub.jo]/[P.sub.calxo]], (2)
where [N.sub.Conctere And Asphalt]--the quantity of concrete and
asphalt category material; [N.sub.j]--the quantity of material j;
[p.sub.jo]--the bid price of material j at time o; [P.sub.calxo]--the
calx price at time o.
2.3. Time-related factors
Freeway construction costs change over time because the Index
Number of Prices (INP) always changes (Levinson, Gillen 1997; Wilmot,
Cheng 2003; Wilmot, Mei 2005; Tawfek et al. 2012). Three indices were
developed to reflect how construction costs change as a result of
changes in the INP. They were Index Number of Labour Prices (INLP),
Index Number of Material Prices (INMP), and Index Number of Equipment
Prices (INEP).
First, INLP is written in the following form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)
where [INLP.sup.L.sub.K]--the INLP at time k based on the INLP at
time o; [W.sup.L.sub.ik]--the proportion of labour item i at time k, and
for each time k, [n.summation over (i=1)] [W.sup.L.sub.ik] = 1;
[M.sup.L.sub.ik]--the quantity of labour item i at time k; n--the number
of main labour items;--the price of labour item i at time k;
[p.sup.L.sub.io]--the price of labour item i at time o.
Similarly, INMP is written as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)
where [INMP.sup.M.sub.K]--the INMP at time k based on the INMP at
time o; [W.sup.M.sub.ik]--the proportion of material item i at time k,
and for each time k, [n.summation over (i=1)] [W.sup.M.sub.ik] = 1;
[M.sup.M.sub.ik]--the quantity of material item i at time k; n--the
number of material items; [p.sup.M.sub.ik]--the price of material item i
at time k; [p.sup.M.sub.io]--the price of material item i at time o. In
practice, this study did not base INMP calculations on all material
items, selecting only major items which together accounted for more than
76% of all construction material costs.
The INEP has the same form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
where [INEP.sup.E.sub.K]--the INEP at time k based on the INEP at
time o; [W.sup.E.sub.ik]--the proportion of equipment item i at time k,
and for each time k, [n.summation over (i=1)] [W.sup.E.sub.ik] = 1;
[M.sup.E.sub.ik]--the quantity of equipment item i at time k; n--the
number of equipment items; [p.sup.E.sub.ik]--the price of using
equipment item i at time k; [p.sup.E.sub.io]--the price of using
equipment item i at time o. As with the materials costs, this study did
not base INEP calculations on all equipment items, selecting only major
items which together accounted for more than 80% of all equipment costs.
3. Data for model development
Data were obtained for freeway construction projects contracted by
the Henan Transportation Department during the period 1994-2007. Some
nonstandard design and construction projects were removed from the data
base. The effective data consisted of contractual information on 88
projects, all of which were four lane divided carriageway freeways with
120 km/h speed limits. Pavement construction cost factors for a sample
of the projects are shown in Table 5.
Eighty one of the 88 projects in the data set were used as a
training data set, which was designed to comply with the following
criteria for minimum size and proportion of total data set.
The minimum training set for the NN is written as follows:
N = [n.sub.1] x [n.sub.2] x ..... x [n.sub.m], (6)
where m--the number of the factors of a BP NN; n--the possible
value of each factor (Shi 1995); N--the number of combinations of all
possible values of the m parameters. The training sample set is
considered incomplete in terms of solving the problem without a sample
equal to or greater than N.
The problem in this paper has 9 factors. The location factor has
three possible values; the altitude factor has five possible values; the
labour cost per km is simple and does not involve categories, so it has
only one possible value; the two largest components of the cost of
materials are "concrete and asphalt" and "stone", so
it has two possible values; and the cost of equipment is simple and
therefore has one possible value. The influence of "other
costs" on the overall cost of pavement construction is not
significant compared with other resource costs; it is assigned a value
of 1 in our calculation. The possible values of the Index Number of
Labour Prices (INLP) and Index Number of Equipment Prices (INEP), which
correspond with the labour and equipment resource factors, are both 1.
As the possible value of different types of materials has been taken
into account in the materials resource costs, the value of the Index
Number of Material Prices (INMP) is set at 1 to avoid recalculation.
From the discussion above, it can safely be concluded that the
minimum size of the training set for the BP NN used in this paper was
30. In theory, the more training samples, the better, but in practice
there are limitations on the number of road segments available. 88
samples are gathered; most researchers will select 90% of them as
training samples and use the remainder for testing. This research
selected 81 of the 88 samples as training samples and used the remaining
7 for testing.
4. Artificial neural network models for construction cost
estimation
Artificial Neural Networks (NNs) were selected to model the
pavement construction cost. ANNs are versatile because of their highly
distributed parallel structures and adaptive learning processes (Cheng
et al. 2009b; Raab et al. 2013; Sliupas, Bazaras 2013; Wilmot, Mei
2005). Of the many structures available for NNs, the multilayer
feed-forward network was chosen for this study because such networks
have the ability to deal with complex systems and yet are relatively
easy to construct (Hegazy, Ayed 1998; Hunter et al. 2012; Ji et al.
2009). To train the model, the back-propagation (BP) learning algorithm
was used because it has strong classification and generalization
capabilities (Cheng et al. 2009a; Li, Chen 2012; Xiaokang, Mei 2010).
The form of neural network used in this study is common in civil
engineering applications.
In theory, a three layer BP network consisting of an input layer, n
input variables are mapped to m target output variables in a hidden
layer and an output layer. Therefore, the general form of the neural
network models used in this study is represented as the simple three
layers shown in Fig. 1.
The number of neurons in the hidden layer is difficult to ascertain
and is normally found by experiment and experience.
The number of neurons in the hidden layer is directly related to
the requirements of the problem and the number of neurons in the input
or output layer. If the number is too small, there will be insufficient
information acquired by the network to resolve the question; if there
are too many neurons, it will increase the number of iterations of the
network, thus extending the training time and reducing network
generalization, thus decreasing predictive power.
First, the number of neurons in the hidden layer is determined
using empirical formulae during the design of the network. Second, the
network is trained using different neuron numbers. Finally, the optimal
number of neurons is obtained by comparing the operating results. The
general empirical formula used to determine the number of neurons in the
hidden layer (Hirose et al. 1991; Sheela, Deepa 2013) is:
i = [square root of n + m] + a, (7)
where i--the number of hidden neurons; n--the number of input
neurons; m--the number of output neurons; a--a constant and 1 < a
< 10.
[FIGURE 1 OMITTED]
According to Kolmogorov's theorem, if the number of neurons in
the input layer was n, then the number of neurons in the hidden layer is
2n + 1. i is written as:
i = 2n + 1. (8)
And i is written as:
i = [log.sup.n.sub.], (9)
where n--the number of input neurons; i--the number of hidden
neurons.
In this study, the max and min number of hidden neurons (i_max,
i_min) was determined by (7), (8) and (9), while training the network
from the min to max increased the number of neurons by one. The optimal
number of hidden neurons was selected by convergence data and training
error using the operating results of different neurons number.
4.1. Pavement construction cost model development
Nine neurons were used in the input layer. These arose from the
construction cost factors identified earlier and shown in Table 5
(region, variation in altitude, labour costs, stone costs, concrete and
asphalt costs, and equipment costs, INLP, INMP and INEP).
The min and max determined by (7), (8) and (9) were 4 and 19. The
training error and testing error that varied through different numbers
of neurons are listed in Table 6. According to the changes of training
step and training error listed in Table 6, the training error gradually
decreased with the increase of the number of hidden layer neurons, but
it rebounds when the number was 17 to 19. In summary, the optimal hidden
neurons number was 16.
Only one neuron appeared in the output layer, representing pavement
construction cost.
4.2. MATLAB program
The MATLAB software package was used to estimate the neural network
models. The MATLAB training function for BP network has training
functions traingd, trainrp, traincgf, trainscg, trainlm, trainbr and so
on. Each has its own characteristics but no single function is adapted
to the training process in all cases (Adeli, Wu 1998; Minli, Shanshan
2012). There are also many improved BP algorithms such as the algorithm
with adaptive study velocity and the additive momentum which is
implemented using Matlab function 'traingdx, the gradient descent
with momentum function that is implemented using 'traingdm',
and the gradient descent adaptive function which is implemented by
'traingda' etc.
The training data set was used to map the input variable pattern to
the target output pattern and minimize the error by adjusting the
weights of the network links in an iterative process. Training was set
to stop after 7000 iterations or until convergence of the root mean
square error (RMSE) to a value less than 0.01.
Observing the changes of training step and training error obtained
by different training functions determined the number of neurons in each
layer of the network. The result showed that 'trainbr' was the
best function, as its testing error was the minimum; even
'trainlm' and 'trainrp' had a small training step,
but their testing error was relatively large; 'trainscg',
'traincgf' and 'traingd' showed much worse results;
'traingdm' and 'traingd' showed the worst results.
In short, 'trainbr' is chosen as the training function for the
network.
4.3. Model testing
A random selection of 81 freeway cases were used as a training data
set for the neural network model and the remaining 7 freeway cases were
used as a testing set on which the performance of the NN model was
evaluated. The testing set projects were Shang-Zhou 4, Shang-Zhou(SQ)02,
YongBo A4, An-Nan, Daguang-Xin 8, Ji-Jin and Feng-Nan 08.
The NN model was programmed in MATLAB, with each run producing a
slightly different result. The results of 10 runs on the testing set are
listed in the Table 8. The statistical measure mean absolute percentage
error (MAPE) was used to measure the performance of the models. The MAPE
of the seven test cases varied from 0.048% to 2.24%, and the mean MAPE
was 0.67%. The implications of this value for the accuracy of cost
estimates are discussed below.
5. Forecasting future costs
5.1. Predicting
The model was used to forecast the change in future freeway
pavement construction costs based on predictions of input values.
Input variables such as labour, [N.sub.stone], [N.sub.Concrete and
Asphalt], and equipment costs utilized average values observed between
1994 and 2007. The next two variables, variation in altitude and region,
were taken from Tables 1 and 2 based on the specific location and
characteristics of each contract. The other three variables
[INMP.sup.M.sub.K], [INEP.sup.E.sub.K], [INLP.sup.L.sub.K] and were
calculated using (3), (4), and (5) and were based on forecasts of future
GDP. The resulting values are listed in Table 9.
Using these values, the freeway pavement construction costs
predicted by the model for 2010 are shown in Table 10.
5.2. Accuracy of predicted costs
As noted above, the MAPE is around 0.67%, which needs to be taken
into account in the predictions made by the model. The MAPE is used to
calculate an expected range within which the actual future cost is
expected to fall.
MAPE is written in the following form:
MAPE = [absolute value of [C.sub.Forcast] -
[C.sub.Reality]]/[C.sub.Reality]. (10)
Hence, [C.sub.Reality] is expressed as
[C.sub.Reality] = [C.sub.Forcast]/[MAPE + 1] = 1/[MAPE + 1].
[C.sub.Forcast]([C.sub.Forcast] [greater than or equal to]
[C.sub.Reality]), (11)
[C.sub.Reality] = [C.sub.Forcast]/[MAPE - 1] = 1/1 -[MAPE].
[C.sub.Forcast]([C.sub.Forcast] < [C.sub.Reality]), (12)
where 1/[MAPE + 1] and 1/[1 - MAPE] are the correction
coefficients.
Therefore, the range of future freeway pavement construction costs
is written in the following form:
[[[C.sub.Forcast]/1+0.0067]], [[C.sub.Forcast]/1-0.0067]]. (13)
Using (13), the range of future freeway pavement construction costs
in 2010 is shown in Table 11.
6. Discussion
The paper presents prediction of the construction cost of freeway
pavement in Henan, China using an Artificial Neural Network. It seems to
be informative and to provide accurate forecasts. However, the following
issues need to be taken into account:
--there are more than 9 factors that influence the costs of freeway
pavement construction--increasing the number of factors would give a
more accurate model, but a greater sample size might also be needed;
--for NN, in theory, the more training samples the better, but in
practice there are limits to numbers of road segments available;
--the price of product is changed suddenly due to the international
economic situation;
--the model will need to be tested using actual data.
In short, there is still some distance to go in order to pursue
this approach as an engineering application, but in the meantime it is
useful for the Secretary of the Provincial Transportation Department or
a senior official in the department to adopt as a reference.
7. Conclusion
1. This paper has explored a new approach to the estimation of
future freeway pavement construction costs by using a Neural Network
trained with real data from 81 construction projects and incorporating a
more comprehensive set of factors than is typically employed. Data were
obtained from freeway construction projects let by the Henan
Transportation Department during the period 1994-2007. The data
consisted of information on 88 freeway contracts. Data from a random
selection of 81 freeway cases were used to train a neural network model
and the remaining data were used to test the performance of the Neural
Network model. Finally, the likely range of pavement construction cost
of three freeways in 2010 was predicted.
2. The factors used in the Neural Network model in this study
reflect the characteristics of location (region--which incorporates
differences in climate, geology and topography --and variation in
altitude along the constructed road), resources costs (labour costs, and
proxy costs for stone, concrete and asphalt, and equipment), and
time-related changes dependent on indexation costs of labour, materials
and equipment (Index Number of Prices, Index Number of Labour Prices and
Index Number of Equipment Prices, respectively). Neural Network models
have usually been used only for individual construction projects, rather
than investigating the overall cost of construction across a range of
projects, and examining how their cost alters over time, so that this
approach represents a new way of addressing the problem of predicting
future pavement construction costs.
3. A question which arises is the generalizability of the results,
however this is relevant to the specific model derived rather than the
process described. While the Neural Network was developed using data
from Henan Province, the principal factors and the applicability of the
Neural Network process are transferable to other locations. The nine
factors used in this study will not all be applicable in another
location, and this would need to be determined at the outset through
consultation with the relevant agencies and experts.
4. The general form of the neural network model used in this study
was three layers and for training, the Back-Propagation learning
algorithm was used. In addition, the MATLAB[R] software package was used
to estimate the neural network models, utilizing the training function
'trainbr' with characteristics of adaptive study velocity and
the additive momentum method. Again, alternative approaches are tested
and other software packages used.
5. One limitation which requires further testing relates to the
success of the model's predictions in practice. This study has
shown how to develop and train the model, and has tested how consistent
its predictions were when applied to a different set of cases, but no
attempt was made to test the accuracy of the predictions in practice.
This requires a longer term study with greater amounts of data.
Caption: Fig. 1. Structure of three-layer NN BP network
doi:10.3846/bjrbe.2014.09
Received 20 December 2011; accepted 1 February 2012
Acknowledgments
The authors would like to thank National Natural Science Foundation
of China for its financial support (Project No. 51078087), Education
Department of Jiangsu Province(sponsored by Qing Lan Project), Henan
Province Transportation Department for its financial support (project
"Analysis of Freeway Construction Costs") and for providing
essential data and support, and Professor Rod Troutbeck (Centre for
Accident Research and Road Safety--Queensland (CARRS-Q), Queensland
University of Technology) for grammar edit. Their assistance is
gratefully acknowledged.
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Jie He (1) ([mail]), Zhiguo Qi (2), Wen Hang (3), Chihang Zhao (4),
Mark King (5)
(1,2,3,4) Transportation College, Southeast University, Sipailou
2#, Nanjing, Jiangsu Province, 210018 P.R. China
(1,5) Centre for Accident Research and Road Safety, Queensland
University of Technology, 130 Victoria Park Road, Kelvin Grove, QLD,
4059 Australia
E-mails: (1) hejie@seu.edu.cn; 2176761442@qq.com; (3)
czghw@126.com; (4) chihangzhao@seu.edu.cn; (5) mark.king@qut.edu.au
Table 1. Region factor
Region list Corresponding city Average pavement
cost, $/km
A1 West Henan Sanmenxia, Luoyang, Jiyuan, 692 998
Jiaozuo
A2 South Henan Xinyang, Nanyang, Zhumadian 956 815
A3 East Henan and Anyang, Puyang, Hebi, 980 169
North Henan Xinxiang, Zhengzhou, Kaifeng
Xuchang, Shangqiu, Luohe,
Zhoukou, Pingdingshan
Table 2. Altitude factor
Location Altitude, Variation in
m altitude
B1 East Henan Plain 0~50 Very small
B2 East Henan Plain 0~100 [less than or
equal to] 50 m
B3 Nanyang Basin 100~200 [less than or
equal to] 100 m
Plain 0~100 [less than or
equal to] 100 m
West Henan Plain 50~100 [less than or
equal to] 100 m
B4 Plain and Mountain 50~500 [less than or
equal to] 450 m
B5 Mountain 200~1000 [less than or
equal to] 800 m
Location Corresponding freeways and contracts
B1 East Henan Plain 15 contracts from Shang-Zhou Freeway,
Kai-Tong Freeway
B2 East Henan Plain 2 contracts from Shang-Ze Freeway, 6
contracts from Yong-Bo Freeway, 4
contracts from Xu-Bo Freeway, Xin-
Chang Freeway, Chang-Feng Freeway, Xi-
Zhou Freeway, Zhou-Jia Freeway, Hu-Xin
Freeway, Pu-Fan Freeway
B3 Nanyang Basin 2 contracts from Nan-Deng Freeway, 11
contracts from Da-Guang
Plain Freeway, 13 contracts from Feng-Nan
Freeway, 2 contracts from Luo-Ping
Freeway, Mi-Nan Freeway, An-Nan
West Henan Plain Freeway, Ping-Zheng Freeway,
Xin-Zhu Freeway, Ji-Jiao Freeway, Jiao-
Xiu Freeway, Zhu-Mi Freeway
B4 Plain and Mountain 8 contracts from Da-Xin Freeway, Xing-
Mi Freeway, Ji-Jin Freeway, Yu-Deng
Freeway, Mi-Tong Freeway
B5 Mountain Ji-Feng Freeway, Zheng-Shi Freeway, 15
contracts from Feng-Nan Freeway
Table 3. Components of pavement cost of five cases
Cost Shang-Zhou 11 Xu-Bo (Fugou) Da-Guang 6
category %
Labour costs 3.59 2.27 1.33
Material costs 81.87 85.30 86.54
Equipment costs 13.43 11.11 10.37
Other costs 1.11 1.33 1.76
Cost Ming-Tong Zhou-Jia Average
category
Labour costs 2.87 2.44 2.50
Material costs 85.90 83.83 84.69
Equipment costs 11.07 12.52 11.70
Other costs 0.15 1.21 1.11
Table 4. Components of pavement material costs for five cases
Cost Shang-Zhou 11 Xu-Bo (Fugou) Da-Guang 6
category %
Stone costs 38.21 23.1 24.84
Concrete and asphalt 41.71 52.73 43.86
costs
Water and power costs 1.38 0.59 0.42
Oil costs 6.09 5.35 2.52
Other costs 12.61 18.23 28.36
Cost Ming-Tong Zhou-Jia Average
category
Stone costs 32.21 21.86 28.04
Concrete and asphalt 45.98 54.45 47.75
costs
Water and power costs 2.43 1.79 1.32
Oil costs 3.47 4.97 4.48
Other costs 15.91 16.93 18.41
Table 5. Construction cost factors of the pavement construction
Location factors
The case
Region Altitude Labor,
$/km
1 Shang-Zhou 1 3 1 1436.332
2 Shang-Zhou 2 3 1 1399.976
3 Shang-Zhou 3 3 1 1409.092
4 Shang-Zhou 4 3 1 1161.524
5 Shang-Zhou 5 3 1 1471.174
6 Shang-Zhou 6 3 1 1362.988
7 Shang-Zhou 7 3 1 1820.468
8 Shang-Zhou 8 3 1 1551.688
9 Shang-Zhou 9 3 1 1327.206
10 Shang-Zhou 10 3 1 1443.558
11 Shang-Zhou 11 3 1 1146.895
12 Shang-Zhou 12 3 1 1054.623
Resources factors
The case
[N.sub.stone], [N.sub.Concrete Equipment,
$/km and asphalt] $/km
$/km
1 Shang-Zhou 1 6121.730 2227.225 174.2843
2 Shang-Zhou 2 6024.234 2256.014 170.0689
3 Shang-Zhou 3 6131.177 2235.037 159.245
4 Shang-Zhou 4 5039.263 1834.701 138.6546
5 Shang-Zhou 5 6236.763 2254.881 178.4577
6 Shang-Zhou 6 5944.144 2170.559 168.4096
7 Shang-Zhou 7 6135.445 2134.949 185.7811
8 Shang-Zhou 8 6132.593 2206.586 175.6292
9 Shang-Zhou 9 5696.227 2080.068 155.0239
10 Shang-Zhou 10 6174.912 2248.998 174.9466
11 Shang-Zhou 11 4467.522 3913.307 128.5997
12 Shang-Zhou 12 4208.745 1515.270 121.2685
Time-related factors
The case
[INMP.sup. [INEP.sup. [INLP.sup.
M.sub.K] E.sub.K] L.sub.K]
1 Shang-Zhou 1 342.028 121.670 105.119
2 Shang-Zhou 2 332.085 127.850 105.119
3 Shang-Zhou 3 323.589 128.547 105.119
4 Shang-Zhou 4 315.328 127.917 105.119
5 Shang-Zhou 5 316.268 127.463 105.119
6 Shang-Zhou 6 308.263 127.943 105.119
7 Shang-Zhou 7 303.403 125.389 105.119
8 Shang-Zhou 8 309.491 127.163 105.119
9 Shang-Zhou 9 311.207 128.052 105.119
10 Shang-Zhou 10 296.499 127.814 105.119
11 Shang-Zhou 11 290.243 127.066 105.119
12 Shang-Zhou 12 284.558 127.204 105.119
Table 6. Model testing using different numbers of hidden neurons
Hidden Training Training Testing error
neurons error step
number 1 2 3
4 0.00999766 732 -0.2380 0.0054 0.1989
5 0.00999745 699 -0.1205 -0.0011 0.1798
6 0.00999479 567 -0.1730 0.0715 0.4289
7 0.00999827 594 -0.2297 -0.0133 0.2288
8 0.00995648 623 -0.1163 0.1055 0.3286
9 0.00998786 698 -0.2908 -0.0597 -0.0133
10 0.00997415 597 -0.1937 0.0537 0.3125
11 0.00993162 729 -0.2009 0.0288 0.0824
12 0.00998699 704 -0.2675 -0.0858 0.1634
13 0.00998885 951 -0.1718 0.0482 0.2409
14 0.00999893 572 -0.1953 -0.0516 0.0472
15 0.00999976 560 -0.1872 -0.0571 0.0489
16 0.00998793 506 -0.1549 -0.0466 0.0747
17 0.00996809 706 -0.1929 0.0917 0.3651
18 0.00999765 562 -0.3058 -0.0344 0.0517
19 0.00997144 600 -0.2086 0.0086 0.1096
Hidden Testing error
neurons
number 4 5 6 7 Mean
absolute
4 0.0654 0.0843 0.1078 0.1302 0.83
5 0.0558 -0.0162 -0.0756 -0.1056 0.8336
6 0.1823 0.0850 0.1029 -0.1171 1.1607
7 0.1299 0.0648 0.1309 -0.1327 0.9301
8 0.2708 0.0796 0.1345 -0.1178 1.1531
9 0.0321 0.0891 0.0812 -0.1020 0.7682
10 0.0433 0.0623 0.0367 -0.1193 0.8215
11 0.0588 0.1092 0.1357 -0.1255 0.7413
12 -0.0681 0.1110 0.0849 -0.1086 0.8893
13 0.1448 0.0829 0.1091 -0.1380 0.8357
14 -0.0897 0.0834 0.0494 -0.0832 0.7198
15 -0.0033 0.1466 0.1387 -0.1021 0.6839
16 -0.0148 0.1716 0.1404 -0.0957 0.6938
17 0.1035 0.0971 0.0788 -0.1214 1.0956
18 -0.1001 0.1368 0.0906 -0.0939 0.8133
19 0.0094 0.0501 0.0618 -0.1136 1.0591
Table 7. Model testing using different training functions
Training Training Training Testing
function step error error
Trainlm 8 0.0088614 -0.1085
Trainscg 81 0.00999032 -0.0682
Traincgf 71 0.00989892 -0.0224
Trainbr 159 0.00999072 -2.5384e-4
Traingd 7000 0.032115 --
Trainrp 59 0.00995126 -0.0503
Traingda 506 0.00999976 -0.0549
Traingdm 7000 0.052164 --
Traingdx 716 0.00999408 -0.0715
Training Testing error
function
Trainlm 0.0077 0.0029 -0.0481
Trainscg -0.0782 0.1663 -0.0040
Traincgf 0.0962 0.3613 0.0891
Trainbr 4.1466e-5 4.9974e-4 -2.5216e-4
Traingd -- -- --
Trainrp 0.0596 0.0947 0.0144
Traingda -0.0466 0.0747 -0.0148
Traingdm -- -- --
Traingdx 0.0697 0.3900 0.1921
Training Testing error
function
Trainlm -0.0164 0.1486 -0.1292
Trainscg 0.0479 0.0161 -0.1156
Traincgf 0.1148 0.0338 -0.0878
Trainbr 6.8190e-4 1.3440e-4 0.0103
Traingd -- -- --
Trainrp 0.1017 0.0990 -0.1365
Traingda 0.1716 0.1404 -0.0957
Traingdm -- -- --
Traingdx 0.0883 0.1093 -0.1240
Table 8. Model testing using 10 runs of the trained NN
Run Shang- Shang-Zhou Yong-Bo An-Nan
number Zhou4 (SQ)02 A4
%
1 2.53 -0.012 -0.45 -0.069
2 -2.49 -0.13 -0.40 -0.0069
3 -1.82 -0.33 -0.56 -0.039
4 -1.07 -0.75 -0.19 -0.015
5 -2.37 -1.33 -0.27 -0.034
6 3.33 -0.50 -0.23 0.017
7 -2.72 -0.66 -0.045 -0.052
8 -1.93 0.28 0.091 -0.11
9 -2.25 -0.51 -0.66 -0.10
10 -1.87 -0.78 0.16 -0.043
MAPE 2.24 0.53 0.31 0.048
Run Daguang- Ji-Jin Feng-
number Xin8 Nan08
%
1 -0.12 -0.30 -0.44
2 -0.18 -0.0093 -0.52
3 0.19 -0.013 -2.66
4 0.69 -0.16 -0.86
5 0.57 -0.18 -0.82
6 -0.0051 -0.16 -2.87
7 -0.60 -0.027 -0.49
8 0.41 -0.22 -0.81
9 -0.077 -0.037 -0.60
10 0.68 -0.13 -0.86
MAPE 0.35 0.12 1.09
Table 9. Input values to predict freeway construction costs in 2010
Region Variation Labour,
in altitude $/km
Shang-Zhou (SQ)02 3 1 1573.58
Daguang-Xin8 2 4 839.29
Ji-Jin 1 4 1008.03
[N.sub.stone], [N.sub.Concrete Equipment,
$/km and Asphalt], $/km $/km
Shang-Zhou (SQ)02 6091.74 3331.30 195.09
Daguang-Xin8 4316.35 2804.54 186.33
Ji-Jin 4499.84 4568.21 159.78
[INMP.sup. [INEP.sup. [INLP.sup.
M.sub.K] E.sub.K] L.sub.K]
Shang-Zhou (SQ)02 291.65 140.70 105.119
Daguang-Xin8 336.65 129.24 105.119
Ji-Jin 194.47 145.55 105.119
Table 10. Predicted freeway pavement construction costs for 2010
(RMSE is 5.5%)
Run Shang-Zhou(SQ)02, Daguang-Xin8, Ji-Jin,
number $/km $/km $/km
1 1 235 363 976 003 716 929
2 1 315 463 968 878 489 248
3 1 260 963 1 055 278 488 152
4 1 352 458 836 262 494 183
5 1 140 996 886 604 540 177
6 1 265 787 1 017 648 540 542
7 1 160 771 812 265 730 435
8 1 236 395 913 139 706 566
9 1 347 458 873 621 749 226
10 1 322 176 1 000 095 486 502
Average 1 263 788 933 978 594 201
value
Table 11. Expected range of the construction costs, $/km
The range of cost Shang-Zhou(SQ)02 Daguang-Xin8 Ji-Jin
Forecast min cost 1 255 376 927 804 590 233
Forecast max cost 1 272 358 940 342 598 169
