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 Frayyeh

2, Gafel kareem aswed

3

1Associate Professor, College of Engineering, Alnahrian University, Baghdad, Iraq

2Associate Professor, Department of Building and Construction Engineering, UOT, Baghdad, Iraq 3Post 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,

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ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 5, Issue 7, July (2014), pp. 42-54

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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.



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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 MonitoringHeadquarters, Department of School finished primary schools of the same design, number of classes, area, number of storiesin same manner (competitive biddingconsist of (12) classes, one principal, teachers, andservice 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 modelresult, nine out of eleven parameters based on questionnaire respondents. Thestimated cost(I3), contractor ranknumber 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 determineresulted value of K which is (3) is used in Kplot 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 storiesding) 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 that intended to be used in the model were collected from the literature review of previous studies.

Fifty questionnaires were directed to expert engineers from the relatedcompletely answered forms are collected, showing a response rate

(64%) of the total number. The respondents were asked to select the parameters that they believe mathematical model for predicting the final cost of school projectsparameters 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 throughscaling, 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 that intended to be used in the model were collected from the literature review of previous studies.

related public sector a response rate of

(64%) of the total number. The respondents were asked to select the parameters that they believe 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

minn 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).



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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(0.8e1

1FC

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 θj i=10 i=11 i=12 - - -

j=13 5.6525 3.6123 -4.493 -0.8497



49

SV=TFmin+�TFmax-TFmin�* 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:

851.02668.1

0781.1range

i*)01(0WI1

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

rangeFC

321

+−++−

+

=

(7)

3342.20)xtanh49.4xtanh61.3xtanh65.55(0.8

e1

0202.1FC

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 withwas ranked third in Olatunji study importance of (13.068%). This reasonable result indicatescompetition 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 Ahiagaresults are also presented in fig. (3).

Figure (3):



50

in table (5) indicate that the natural log of estimated cost (Iwith 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:

�� /�� 100

Where: A = actual value, E = estimated or predicted value, n = total number of cases (6 for validation).

2. Root Mean Squared Error:

RMSE � �∑ �E � �A ! �"#�� n

3. Mean Absolute Percentage Error:

MAPE � ��|A � E|A"

#�� 100� /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 nodelearning rate while very sensitive to the type of thetransformed 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 doneestimated duration must be set out by the owner and must not be one of competitive conditions.

9. REFERENCES

[1] Elhag, T M S and Boussabaine, A. H., “Tender Price Estimation: Neural networks VS. Regression analysis”, Proceedings of Construction and Building Research (COBRA) Conference, 1-2 September 1999, University of Salford, UK.RICS Foundation.



52

generalization ability, which means that, once they have been properly trained, they are able to 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

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

based on questionnaire respondents' recommendations. The ANN model study the impact of the internal network parameters on the model performance. It indicatesperformance 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

he expected cost deviation which is the difference between 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.

alysis indicated (I3) (estimated cost) has the most significant effect on the (number of bidders) with a relative importance of (23.49%) and

results of a numerical example carried out in this work showed the robust

ttention must be paid to the tendering evaluation process taking into account the ccurate estimate must be done to avoid cost overrun

be set out by the owner and must not be one of competitive conditions.

Elhag, T M S and Boussabaine, A. H., “Tender Price Estimation: Neural networks VS. Proceedings of Construction and Building Research (COBRA)

2 September 1999, University of Salford, UK.RICS Foundation.


generalization ability, which means that, once they have been properly trained, they are able to 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

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

. The ANN model is developed to indicates that ANN

s, momentum terms, and the The ANN model could be

transformed into a simple and practical formula from which final cost of school projects can be expected cost deviation which is the difference between

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.

) (estimated cost) has the most significant effect on the (number of bidders) with a relative importance of (23.49%) and

work showed the robust

ttention must be paid to the tendering evaluation process taking into account the estimated to avoid cost overrun. A reasonable

be set out by the owner and must not be one of competitive conditions.

Elhag, T M S and Boussabaine, A. H., “Tender Price Estimation: Neural networks VS. Proceedings of Construction and Building Research (COBRA)

2 September 1999, University of Salford, UK.RICS Foundation.



53

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modeling final costs of iraqi public school projects

Engineering

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cost modelling

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cost control

magnitude of final cost

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detailed cost estimating