Modeling final costs of iraqi public school projects

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 7, July (2014), pp. 42-54 © IAEME
42
MODELING FINAL COSTS OF IRAQI PUBLIC SCHOOL PROJECTS
USING NEURAL NETWORKS
Dr. Zeyad S. M. Khaled1
, Dr. Qais Jawad Frayyeh2
, Gafel kareem aswed3
1
Associate Professor, College of Engineering, Alnahrian University, Baghdad, Iraq
2
Associate Professor, Department of Building and Construction Engineering, UOT, Baghdad, Iraq
3
Post graduate student, Building and Construction Engineering, UOT, Baghdad, Iraq
ABSTRACT
The final cost of public school building projects, like other construction projects, is unknown
to the owner till the account closure. Artificial Neural Networks (ANN) is used in an attempt to
predict the final cost of two story (12 classes) school projects under lowest bid system of award
before work starts. A database of (65) school projects records completed in (2007-2012) are used to
develop and verify the ANN model. Based on expert opinions, nine out of eleven parameters are
considered to have the most significant impact on the magnitude of final cost. Hence they are used as
model inputs while the output of the model is going to be the final cost (FC). These parameters are;
accepted bid price, average bid price, estimated cost, contractor rank, supervising engineer
experience, project location, number of bidders, year of contracting, and contractual duration. It was
found that ANN has the ability to predict the final cost for school projects with very good degree of
accuracy having a coefficient of correlation (R) of (91%), and an average accuracy percentage of
(99.98%).
Keywords: Cost Estimation, Cost Modelling, Neural Network, Schools Projects.
1. INTRODUCTION
At the early stage of any project, a budget is to be decided, while no detailed information is
available. Therefore some parametric cost estimating techniques are used. Once the project scope is
well defined, detailed cost estimating can be carried out for bidding and cost control. The objective
of those parametric costs estimating techniques is to use some historical cost data and try to find a
functional relationship between changes in cost and factors influencing these changes. A major
drawback of statistical techniques is that a general mathematical form of the relationship has to be
defined before any analysis can be applied to best fit historical cost data. To avoid this drawback,
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING
AND TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 7, July (2014), pp. 42-54
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43
stochastic tools such as Artificial Neural Network (ANN), through their learn-by example process,
have been used for the modeling of the final cost.
2. RESEARCH OBJECTIVES
The research objectives are:
1. To explore factors that can be used to predict the final cost of school projects before starting
works.
2. To increase estimating efficiency of initial costs according to past data of already constructed
projects.
3. To build a mathematical model using (ANN) to predict construction cost deviation in school
projects before starting works.
3. RESEARCH JUSTIFICATION
The reasons for adopting this research are:
1. The high number of under construction school projects accompanied with continual cost
overrun.
2. The ever growing demand on schools buildings.
3. The need of successful completion of projects within contracted costs.
4. The need of knowing the final cost of the project before starting works.
4. RESEARCH HYPOTHESES
At awarding stage, it can be said that the estimated cost, accepted bid price, average bidding
price, contractor rank, supervising engineer experience, number of bidders, contractor estimated
time, project location, year of contracting, owner's estimated duration and the second lowest bid are
good predictors to the final cost of public school building projects before starting works.
5. RESEARCH METHODOLOGY
The following methodology is adopted in this research:
5.1. Literature review
Cost estimate, cost control, cost management, bidding strategy, and cost overrun related
literature are reviewed to identify the main topics to be handled in this research. The types of
Artificial Neural Networks (ANN), their structure, and uses in construction management are
outlined. Capabilities of some useful software such as: Neuframe, MS Excel, and Statistical Package
for the Social Sciences SPSS are also explored in this essence.
5.2. Data collection
Historical data is collected from (65) completed schools projects in Karbala province .The
projects were awarded under the lowest bid tendering system having the same design and number of
classrooms. Questionnaires have been directed to fifty experts in this field. These experts are asked
to pinpoint the most significant factors influencing the final cost of school projects. Thirty two
respondents’ answers are analyzed and the model input data are screed according to the results.

44
5.3. Model formulation
Previous studies showed different methods used to interpret the relation between the
construction cost and factors believed to influence the final project cost. Most of them are parametric
cost estimating approaches that use statistical analysis techniques ranging from simple graphical
curve fitting to multiple correlation analysis. In this research the Artificial Neural Network technique
is adopted. (ANN) have a great potential in dealing with historical cost data effectively for the sake
of developing budgeting and cost estimating models. NEUFRAME program is used to develop the
desired model.
5.4. Model evaluation
The developed model is evaluated using a data set that is not used in constructing the
model.Resultsvs. Observed data are plotted to explore the model efficiency. This validation is carried
out to ensure that the model is applicable within the limits set by the training data. The coefficient of
correlation r, the root mean squared error RMSE, and the mean absolute error MAE as the main
criteria that are often used to evaluate the prediction performance of ANN models are checked.
Therefore the final model can estimate new project costs with no changes needed in the structure of
the ANN model.
6. APPLICATION OF ANN IN COST ESTIMATION
Neural networks models have been proposed in recent years for cost modeling using different
prediction parameters by many researchers (Elhag and Boussabaine [1]; Al-Tabtabai et al. [2]; Bode
[3]; Margaret et al. [4]; Elhag [5]; Steven and Garold [6]; Kim et al. [7]; Sodikov [8]; Wilmot and
Mei [9]; Pewdum et al. [10]; Cheng et al. [11]; Wang and Gibson [12]; Xin-Zheng et al. [13];
Attal[14]; Murtala [15];Arafa and Alqedra [16]; Sonmez[17]; Wang et al. [18]; Ahiaga-Dagbui and
Smith [19]; Feylizadeh et al. [20]; Bouabaz et al. [21]; Amusan et al. [22]; Alqahtani and Whyte
[23]). Literature review showed the variety of ways that are used to predict the project cost and its
deviation. Different variables were used as predictors in these studies. This research adopted all the
factors stated in literatures at first. Then factors are screened according to experts' opinions and used
to build a neural network capable to forecast the final cost of Iraqi school projects before work starts.
7. DESIGN OF THE ANN MODEL
Artificial Neural Networks are "computational models that attempt to imitate the function of
the human brain and the biological neural system in a simple way"[24]. They are very sophisticated
modeling techniques, capable of modeling extremely complex functions.
The most common structure of an artificial neural network consists of three layers (groups of
units): a layer of "input" units, a layer of "hidden" units, and a layer of "output" units, each layer is
connected to the adjacent ones through neurons forming a parallel distributed processing system
[25]. Different types of neural networks can be distinguished on the basis of their structure and
directions of signal flow.
In this study, a three-layered Multilayer Perceptron (MLP) feed-forward neural network
architecture is used and trained with the error back propagation algorithm. The back propagation
training with generalized delta learning rule is an iterative gradient algorithm designed to minimize
the root mean square error between the actual output of a multilayered feed-forward neural network
and a desired output [26].

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue
7.1. Data Collection
The required data for developing a school final
collected from many governmental
Directorate of Planning and Monitoring
Headquarters, Department of School
finished primary schools of the same design, number of classes, area, number of stories
in same manner (competitive bidding
consist of (12) classes, one principal, teachers, and
service staff rooms, water closets, paved
projects executed during (2007-2012)
that intended to be used in the model were collected from the literature review of previous studies.
7.2. Deciding Parameters
Fifty questionnaires were
supervisory staff. Thirty two completely answered forms are collected
(64%) of the total number. The respondents were asked to select the parameters that they believe
important in developing a mathematical model
result, nine out of eleven parameters
based on questionnaire respondents. Th
estimated cost(I3), contractor rank
number of bidders(I7), year of contracting
7.3. Data division and processing
Data processing is very important in using
information is presented to create the model during the training phase. It can be
scaling, normalization and transformation.
model. The best division is made using default parameters of PC
(version 20) to perform Ward’s methods hierarchical cluster to determine
resulted value of K which is (3) is used in K
plot of fig. (1) for the three clusters (groups) showed that the record
(2), so it will be excluded from the data processing.
Figure (1): Box-
6316(Online), Volume 5, Issue 7, July (2014), pp. 42-54 © IAEME
45
The required data for developing a school final construction cost predicting model is
agencies in Kerbela province namely: Department of
Directorate of Planning and Monitoring, and Division of Governmental Contracts at the Governorate
, Department of School Buildings and Committee of Regions Development.
schools of the same design, number of classes, area, number of stories
ding) are selected as a case study. They are two story
principal, teachers, and administration rooms, auditorium
, paved playing yard, and external fence. Complete records
2012) are used for developing the final model. The initial parameters
Fifty questionnaires were directed to expert engineers from the related
completely answered forms are collected, showing a response rate
mathematical model for predicting the final cost of school projects
parameters are adopted as independent variables of the ANN equations
based on questionnaire respondents. These variables are: accepted bid price(I1), average bid price
, contractor rank(I4), supervising engineer experience(I5), project
, year of contracting(I8), and contractor duration (I9).
Data processing is very important in using neural networks successfully. It determines what
information is presented to create the model during the training phase. It can be done through
scaling, normalization and transformation. Sixty school projects are selected to develop the ANN
best division is made using default parameters of PC-based software package SPSS
(version 20) to perform Ward’s methods hierarchical cluster to determine number of cluster
resulted value of K which is (3) is used in K-means clustering in SPSS instead of assuming it.
for the three clusters (groups) showed that the record no. (40) is an outlier from cluster
data processing.
-plot of Case Distance From its Cluster Center
predicting model is
Department of Projects,
at the Governorate
of Regions Development. Completely
schools of the same design, number of classes, area, number of stories, and awarded
two story buildings
auditorium, studio, two
Complete records of (65)
. The initial parameters
related public sector
a response rate of
the final cost of school projects. As a
as independent variables of the ANN equations
, average bid price(I2),
project location(I6),
s successfully. It determines what
done through data
o develop the ANN
based software package SPSS
number of cluster (K). The
tead of assuming it. Box
is an outlier from cluster

46
From each cluster, three samples are selected; one for training, one for testing and one for
validation. In the instance when a cluster contains two records, one record is then chosen for training
set and the other one is chosen for testing set. If a cluster contains only one record, this record is
chosen in the training set [27].
Transforming input data into some well-known forms like log., exponential, and alike, may
be helpful to improve ANN performance. Therefore natural log is used to transform accepted bid
price (I1), average bid price(I2), and estimated cost (I3) parameters only. Many rounds of trial and
error are generated to reach the best data division according to the lowest testing error and the
highest coefficient of correlation (R). The best performance is obtained when the data divided
into(75%) for training set, (5%) for testing set, and (20%) for validation set. As a result, a total of
(44) records are used for training, (3) for testing and (12) for validation.
In order to ensure that all variables receive equal attention during training; input and output
variables are pre-processed by scaling them (eliminate their dimension). Scaling is proportionated
with the limits of the transfer functions used in the hidden and the output layers within (–1.0 to 1.0)
for tanh transfer function and (0.0 to 1.0) for sigmoid transfer function. As part of this method, for
each variable (x) with minimum and maximum values of (xmin) and (xmax) respectively, the scaled
value (xn) is calculated as follows:
minmax
min
n
xx
xxx
−
−
= (1)
7.4. Training the ANN model
The number of hidden nodes affect the ANN performance, nevertheless a number of studies
have found that the forecasting performance of neural networks is not very sensitive to this
parameter [8]. Therefore the general strategy adopted in this study to find the optimal network
architecture and its internal parameters that control the training process starts with initial trials using
default parameters of the Neuframe software with one hidden layer and one hidden node then
slightly increasing the number of nodes until no significant improvement in the model performance
is gained. The network that shows the best performance with respect to the lowest testing error and
high correlation coefficient of validation is retrained with different combinations of momentum
terms, learning rates, and transfer functions in an attempt to improve the model performance.
Consequently, the model that has the optimum momentum term, learning rate, and transfer function
is retrained many times with different initial weights until no further improvement occurs.
Using the default parameters of the Neuframe software in which the learning rate is (0.2), the
momentum term is(0.8), and the transfer functions in the hidden and output layers nodes are sigmoid,
many networks with different numbers of hidden nodes are developed. It is found that a network
with three hidden nodes has the lowest prediction error for the testing set which is (2.894) with a
high coefficient of correlation (R) of (95.35). Therefore, three hidden nodes approach is chosen in
this model.
The effect of the internal parameters controlling the back-propagation algorithm (i.e.
momentum term and learning rate) on the performance of the latter model of three hidden layer
nodes is investigated. The optimum obtained value of the momentum term and learning rate are
found to be (0.9) and (0.7) with a testing error of (1.665%), training error of (5.728%), and
maximum correlation coefficient (R) of (91.13%).
The effect of using different transfer functions (i.e. sigmoid and tanh) is also investigated.
The better performance is obtained when the sigmoid transfer function is used for both hidden and
output layers. A neural network of nine input neurons, three hidden neurons and one output is found
to be the optimum architecture for the current problem as shown in fig. (2).

47
Input layer Hidden layer Output layer
Figure (2): Structure of the ANN Model for (FC)
7.5. Statistical tests
Estimation of statistical parameters is conducted to ensure that the data in the neuframe
training, testing, and validation sets represent the same statistical population. These parameters
include the mean, standard deviation, minimum and maximum values, and the range. The results
indicate that the training, testing, and validation sets are statistically consistent. Results are shown in
table(1).
To examine how representative the training, testing, and validation sets are with respect to
each other a t-test is exercised showing the results illustrated in table (2). The null hypothesis of no
difference in the means of each two data sets is checked by this t-test. The statistical tests are carried
out to examine the null hypothesis with a level of significance equal to (0.05). This means that there
is a confidence degree of (95%) that the training, testing, and validation sets are statistically
consistent.
Table (1): Input and Output Statistics for The ANN
Data Set
Statistical
parameters
Input Variables Output
Ln(I1) Ln(I2) Ln(I3) I4 I5 I6 I7 I8 I9 Ln(FC)
Training
n = 44
max 21.302 21.3495 21.3489 5 20 2 13 2012 487 21.3028
min 20.036 20.404 20.2691 1 8 1 8 2007 150 20.3342
mean 20.731 20.86643 20.83944 4.23 14.05 1.39 9.93 2009.39 321.68 20.76715
Std. 0.3280 0.303428 0.319757 0.831 3.457 0.493 1.246 1.715 82.227 0.319223
range 1.2668 0.9455 1.0798 4 12 1 5 5 337 1.0202
Testing
n = 3
max 20.637 20.8031 20.6804 5 30 2 9 2008 426 20.6029
min 20.427 20.5139 20.423 4 15 2 8 2008 270 20.475
mean 20.509 20.62027 20.54203 4.33 21.67 2 8.67 2008 338.67 20.55213
Std. 0.1120 0.159043 0.129785 0.577 7.638 0 0.577 0 79.658 0.067904
range 0.2096 0.2892 0.2574 1 15 0 1 0 156 0.1279
Valida-
tion
n = 12
max 21.183 21.2284 21.2101 5 20 2 10 2011 486 21.2921
min 20.037 20.4673 20.3887 3 7 1 8 2008 150 20.2934
mean 20.603 20.69795 20.68097 4 12.33 1.42 9.33 2008.83 352.42 20.69638
Std. 0.3135 0.267055 0.211935 0.853 3.676 0.515 0.888 1.193 104.213 0.293603
range 1.1456 0.7611 0.8214 2 13 1 2 3 336 0.9987

48
7.6. ANN Model Equation
The low number of connections weights obtained in the optimal ANN model enables the
network to be transformed into relatively simple hand-calculated formula. Connections weights and
threshold levels are summarized in table (3).
The predicted final cost can be expressed using the connections weights and the threshold
levels shown in table (3), as follows:
)xtanh49.4xtanh61.3xtanh65.55(0.8
e1
1
FC
321
−++−
+
=
(2)
Where:
99.1088.1077.1066.1055.1044.1033.1022.1011.10101 IwIwIwIwIwIwIwIwIwx +++++++++θ= (3)
99.1188.1177.1166.1155.1144.1133.11211211.11112 IwIwIwIwIwIwIwIwIwx +++++++++θ= (4)
99.1288.1277.1266.1255.1244.1233.1222.1211.12123 IwIwIwIwIwIwIwIwIwx +++++++++θ=
(5)
Where:
I1 = accepted bid price in Iraqi Dinars (IQD), I2 = average bid price in (IQD), I3 = estimated
cost in (IQD), I4 = contractor rank (from 1 to 5), I5 = supervising engineer years of experience,
I6 = project location (urban/ rural), I7 = number of bidders, I8 = year of contracting (2007 to 2012),
I9 = contractual duration (in days).
It should be noted that, before using equation (2), all input variables (I1 to I9) need to be
scaled between (0.0 and 1.0) using equation (1) and the ANN model training data shown in table(1).
This means that the predicted value of FC obtained from equation (2) is also scaled between (0.0)
and (1.0).In order to obtain the actual value of the final cost, the scaled value of FC has to be re-
scaled using equation (6) and the data shown in table (1). For linear scaling all observations are
linearly scaled between the minimum and maximum values according to the following formula [28]:
Table (2): Null Hypothesis Tests for the ANN Input and Output Variables
Statistical
Parameters
Input Variables Output
Ln(I1) Ln(I2) Ln(I3) I4 I5 I6 I7 I8 I9 Ln(FC)
Data sets Testing
t-value -1.005 -1.570 -1.815 -0.772 -1.646 -0.022 -1.626 -1.064 0.785 -0.538
Lower critical value -0.2902 -0.2907 -0.2456 -0.73 -4.08 -0.33 -0.98 -1.12 -42.60 -0.2321
Upper critical value 0.1082 0.0486 0.0236 0.35 0.59 0.32 0.15 0.39 89.83 0.1409
Sig.(2-tailed) 0.336 0.145 .097 0.457 0.128 0.983 0.132 0.310 0.449 0.601
Results Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept
Data sets Validation
t-value -1.005 -1.570 -1.815 -0.772 -1.646 -0.022 -1.626 -1.064 0.785 -0.538
Lower critical value -0.2902 -0.2907 -0.2456 -0.73 -4.08 -0.33 -0.98 -1.12 -42.60 -0.2321
Upper critical value 0.1082 0.0486 0.0236 0.35 0.59 0.32 0.15 0.39 89.83 0.1409
Sig.(2-tailed) 0.336 0.145 .097 0.457 0.128 0.983 0.132 0.310 0.449 0.601
Results Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept
Table (3): Weights and Threshold Levels for the ANN Model (FC)
Hidden
layer
nodes
wji(weight from node i in the input layer to node j in the hidden layer)
Hidden layer
threshold
i=1 i=2 i=3 i=4 i=5 i=6 i=7 i=8 i=9 θj
j=10 1.0781 0.9242 2.7347 -0.392 -0.873 -0.814 1.1534 -1.562 1.2841 -2.96178
j=11 -0.512 -0.353 1.5225 0.1001 0.2708 -0.543 -0.994 0.1261 0.3729 -1.33665
j=12 0.7865 0.5072 -0.751 0.0438 -0.633 -1.139 0.3986 -1.150 0.2923 0.41731
Output
layer
nodes
wji(weight from node i in the hidden layer to node j in the output layer)
Output layer
threshold θji=10 i=11 i=12 - - -
j=13 5.6525 3.6123 -4.493 -0.8497

49
SV=TFmin+൫TFmax-TFmin൯*
X-Xmin
Xmax-Xmin
(6)
Where:
SV is the scaled value, TFmin and TFmax are the respective minimum and maximum values of the
transfer function (0, 1), X is the value of the observation, and Xmin and Xmax are the respective
minimum and maximum values of all observations, for example:
851.0
2668.1
0781.1
range
i*)01(0W
I1
1
1.10 =−+= =
After scaling and substituting the weights and threshold levels of table (3), equations (2 t0 5)
can be rewritten as shown below:
min
)xtanh49.4xtanh61.3xtanh65.585(0.
e1
range
FC
321
+
−++−
+
=
(7)
3342.20
)xtanh49.4xtanh61.3xtanh65.55(0.8
e1
0202.1
FC
321
+
−++−
+
=
(8)
and:
X1=535.79 +10-3
[851I1+977 I2+ 2532I3- 98I4-72I5 -814I6 +230I7-312I8+3I9] (9)
X2=63.23-10-3
[404I1+374I2-1410I3 -25I4-22I5+544I6+198I7-25I8-I9] (10)
X3=458.95+10-3
[621I1+536I2- 696I3+11I4-53I5- 1139I6+79I7-230I8+0.8I9] (11)
A numerical example is also provided to better explain the implementation of FC formula.
The equation is tested against data not used in ANN model training. These data are shown in
table (4).
Table (4): Data Record not Used in Training ANN
Ln(FC) Ln I1 Ln I2 Ln I3 I4 I5 I6 I7 I8 I9
21.19 21.18 21.31 21.27 5 18 1 12 2011 360
The results of equations (9, 10, and 11) are; X1= (1.653), X2= (125.4335), and
X3= (5.422).Therefor Ln (FC) is found to be (21.2125) using equation (8). By taking the inverse of
this natural log, the value of (FC) is found to be (IQD 1,631,066,610). This gives a very good
agreement with the measured values where (Ln FC=21.19 and FC = IQD 1,594,777,396).
7.7. Sensitivity Analysis of the ANN Model Inputs
Sensitivity analysis is carried out on the ANN model to identify which of the input variables
have the most significant impact on the final cost.
Simple and innovative technique proposed by Garson is used to interpret the relative
importance of the input variables by examining the connection weights of the trained network. For a
network with one hidden layer, the technique involves a process of partitioning the hidden output
connection weights into components associated with each input node (Garson, 1991: cited by [29]).

The results shown in table (5)
with a relative importance of (23.49%).
Table (5):
Ln(I1) Ln(I2)
Relative
importance (%)
11.41 7.83
Rank 5 8
It has the most significant effect on the predicted final cost model
the questionnaire results. This result consistent with
was ranked third in Olatunji study
importance of (13.068%). This reasonable result indicates
competition on the final project cost consistent with Mohd et al. regression model
also indicate that the location of the project (
(12.91%) in contradiction with Creedy et al. regression model [
ranked forth with relative importance (12.295%). The natural log of accepted bid price (
relative importance equals to (11.41%) and ranked fifths
(I2) has the eighth relative importance in the ANN mode
in Olatunji study [30]. The contractor classification (
low importance of contractor classification (
final cost model is consistent with Ewadh and Aswed study
seventh with relative importance (8.38%) consistent with Ahiaga
results are also presented in fig. (3).
Figure (3):
50
in table (5) indicate that the natural log of estimated cost (I
with a relative importance of (23.49%).
Table (5): Relative Importance of Each Input
2) Ln(I3) I4 I5 I6 I7 I
7.83 23.49 2.18 8.415 12.91 13.07 12.29
1 9 6 3 2
It has the most significant effect on the predicted final cost model whereas
the questionnaire results. This result consistent with Ahiaga- Dagbui and Smith study [
was ranked third in Olatunji study [30]. The number of bidders (I7) ranked second with a relative
This reasonable result indicates the significant impact of degree of
competition on the final project cost consistent with Mohd et al. regression model
also indicate that the location of the project (I6) (urban/rural) ranked third with relative importance
ntradiction with Creedy et al. regression model [31]. The year of contracting (
ranked forth with relative importance (12.295%). The natural log of accepted bid price (
relative importance equals to (11.41%) and ranked fifths while the natural log of average bid price
) has the eighth relative importance in the ANN mode whereas it is the most important parameter
]. The contractor classification (I4) comes ninth, same as in expert opinion.
classification (I4) and supervisor engineer experience (
final cost model is consistent with Ewadh and Aswed study [34].The contractor duration (
seventh with relative importance (8.38%) consistent with Ahiaga- Dagbui and Smith
: Relative Importance of Input Variables
indicate that the natural log of estimated cost (I3) ranked first
I8 I9
12.29 8.385
4 7
whereas ranked second in
Dagbui and Smith study [19] whereas it
) ranked second with a relative
the significant impact of degree of
competition on the final project cost consistent with Mohd et al. regression model [33]. The results
) (urban/rural) ranked third with relative importance
]. The year of contracting (I8)
ranked forth with relative importance (12.295%). The natural log of accepted bid price (I1) has a
log of average bid price
it is the most important parameter
) comes ninth, same as in expert opinion. The
) and supervisor engineer experience (I5) in the ANN
.The contractor duration (I9) ranked
Dagbui and Smith study [19]. The

51
It does not necessarily mean that low-value parameters should be excluded from the model.
These parameters could enhance the learning ability of the model to achieve the best output
prediction. This argument is also supported by Arafa and Alqedra[16].
7.8. Validity of the ANN Model Equation
Additional statistical measures are used to measure the performance of the model include:
1. Mean Percentage Error:
‫ܧܲܯ‬ ൌ ቐ෍ ൤
‫ܣ‬ െ ‫ܧ‬
‫ܣ‬
൨ /݊
௡
௝ୀଵ
ቑ ‫כ‬ 100
Where: A = actual value, E = estimated or predicted value, n = total number of cases (6 for
validation).
2. Root Mean Squared Error:
RMSE ൌ ඨ
∑ ሺE െ Aሻଶ୬
୨ୀଵ
n
3. Mean Absolute Percentage Error:
MAPE ൌ ቐ෍
|A െ E|
A
୬
୨ୀଵ
‫כ‬ 100ቑ /n
4. Average accuracy percentage (AA %) [9]:
AA% = 100% -MAPE
5. The Coefficient of Determination (R2
)
6. The Coefficient of Correlation (R).
The results of these statistical parameters are shown in table (6).
Table (6): Statistical Measures Results
Description Statistical parameters
MPE 0.23%
RMSE 0.12
MAPE 0.014%
AA% 99.98%
R2
83 %
R 91%
To assess the validity of the derived equation of the ANN model in predicting the final cost
of a school project (FC), the natural logarithm (Ln) of predicted values of (FC) are plotted against the
natural logarithm (Ln) of measured (observed) values for validation data set as shown in fig. (4). It is
clear from this figure that the resulted ANN has a generalization capability for any data set used
within the range of data used in the training phase. It is a proven fact that neural nets have a strong

generalization ability, which means that, once they have been properly trained, they are able to
provide accurate results even for cases they have never seen before. The coefficient of determination
(R2
) is found to be (83.06%), therefore it can be concluded that this model shows a good agreement
with actual measurements.
Figure (4): Comparison of
8. CONCLUSIONS
A neural network model is developed to predict the final cost of school projects before the
work starts. Nine out of eleven variables were identified and analyzed as independent variables of the
ANN model based on questionnaire
study the impact of the internal network parameters on
performance is relatively insensitive to the number of hidden layer node
learning rate while very sensitive to the type of the
transformed into a simple and practical formula from which final cost of school projects
calculated by hand. Therefore the
contractual sums and predicted final cost obtained from the proposed ANN model can be easily
calculated. Future school budget could be estimated accurately using the proposed ANN model.
Sensitivity analysis indicated
predicted final cost followed by (I7)
(13.06%) respectively. The results of
of the ANN model.
Attention must be paid to the tendering evaluation process taking into account the
cost not the lowest bid. More accurate estimate must be done
estimated duration must be set out by the owner and must not be one of competitive conditions.
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52
accurate results even for cases they have never seen before. The coefficient of determination
%), therefore it can be concluded that this model shows a good agreement
Comparison of Predicted and Observed FC
based on questionnaire respondents' recommendations. The ANN model
study the impact of the internal network parameters on the model performance. It indicates
performance is relatively insensitive to the number of hidden layer nodes, momentum terms, and the
very sensitive to the type of the transfer function. The ANN model could be
transformed into a simple and practical formula from which final cost of school projects
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Proceedings of Construction and Building Research (COBRA)
2 September 1999, University of Salford, UK.RICS Foundation.
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%), therefore it can be concluded that this model shows a good agreement
. The ANN model is developed to
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s, momentum terms, and the
The ANN model could be
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expected cost deviation which is the difference between
) (estimated cost) has the most significant effect on the
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ttention must be paid to the tendering evaluation process taking into account the estimated
to avoid cost overrun. A reasonable
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53
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