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DEVELOPMENT OF THE ARTIFICIAL
NEURAL NETWORK MODEL FOR
PREDICTION OF IRAQI EXPRESS WAYS
CONSTRUCTION COST
Dr. Tareq Abdul Majeed KhaleelBuilding and Construction Engineering Department University of Technology, Iraq
ABSTRACT
The main objective of this research is to introduce a new and alternative approach of using a neural network for cost estimation of the expressway project at the early stage.
A preliminary literature survey and data collection have identified the problem and led to the formulation of the research hypothesis that there is a weakness in estimating the cost of the expressway construction projects because the current available techniques are poor and suffer some disadvantages such as being traditional, aged, slow and uncertain. Besides, the need for a modern efficient construction cost estimation techniques that have more advantages such as being modern, fast, accurate, flexible and easy to use is of value. Also, the application of Artificial Neural Networks, as a modern technique, in Iraqi construction industry is necessary to ensure successful management, and many of the construction companies feel the need of such system in project management
One model was built for the prediction the cost of expressway project. The data used in this model was collected from Stat Commission for Roads and Bridges in Iraq. It was found that ANNs have the ability to predict the Total Cost for expressway project with a good degree of accuracy of the coefficient of correlation (R) was 90.0%, and average accuracy percentage 89%.The ANNs model developed to study the impact of the internal network parameters on model performance indicated that ANNs performance was relatively insensitive to the number of hidden layer nodes, momentum term, and learning rate.
Key word: Cost Estimate, Expressway Project, Average Accuracy and Artificial Neural Network
Cite this Article: Dr. Tareq Abdul Majeed Khaleel. Development of The Artificial Neural Network Model For Prediction of Iraqi Expressways Construction Cost. International Journal of Civil Engineering and Technology, 6(10), 2015, pp. 62-76.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=10
1. INTRODUCTION
Expressways were an expressway especially planned for high-speed traffic, usually having few if any intersections, limited points of access or exit, and a divider between lanes for traffic moving in opposite directions.
Conceptual cost estimate is one of the most important activities to be performed during the project planning phase. It includes the determination of the project’s total costs based only on general early concepts of the project (Kan, 2002). Like all other planning activities, conceptual cost estimating is a challenging task. This is due to the availability of limited information at the early stages of a project where many factors affecting the project costs are still unknown
Major difficulties which arise while conducting cost estimation during the conceptual phase are lack of preliminary information, lack of database of road works costs, and lack of up to date cost estimation methods. Additional difficulties arise due to larger uncertainties as result of engineering solutions, socio-economical, and environmental issues. Parametric cost estimation or estimation based on historic database during the conceptual estimate phase is widely used in developed countries. However, developing countries face difficulties related to the creation of a road work costs database, which may be used for cost estimation in either the conceptual stage or the feasibility study of a project cycle.
One of the earliest papers to introduce the benefits and the implementation of ANN in the civil engineering community is published by (Flood and Kartam,1994). This research has opened the door for many proposals that suggest ML as the preferred method to tackle various challenges in the construction industry. Wilmot and Mei,(2005) introduced an ANN model for expressway construction costs. This research used the following factors as a base for cost estimation: price of labour, price of material, price of equipment, pay item quantity, contract duration, contract location, quarter in which the contract was let, annual bid volume, bid volume variance, number of plan changes, and changes in standards or specifications. The main contribution of this work was that it covered all required factors. Nevertheless, the validation of the proposed method and the data collection process used for training and testing the results were not fully presented. Furthermore, (Hola and Schabowicz, 2010) developed an ANN model for determining earthworks’ execution times and costs. Basically, this model was developed on the basis of a database created from several studies that were carried out during large-scale earthwork operations on the construction site of one of the largest chemical plants in Central Europe. However, the validation of the presented results is not mentioned. Petroutsatou et al.,(2012) introduced the ANN as a technique for early cost estimation of road tunnel construction. The data collection strategy of this research was based on structured questionnaires from different tunnel construction sites. The main drawback of this research was the ignoring of some of the construction cost factors. Jafarzadeh et al.,(2014) proposed the ANN method for predicting seismic retrofit construction costs. This study selected data from 158 earthquake-prone schools. The validation of this method is not clear. Recently, (Al-Zwainy.,2008) used the multi-layer
perceptron trainings using the back-propagation algorithm neural network is formulated and presented for estimation of the total cost of highway construction projects. twenty influencing factors are utilized for productivity forecasting by ANN model. four model was built for the prediction the productivity of marble finishing works for floors. It was found that ANNs have the ability to predict the total cost of highway construction projects with a very good degree of accuracy of the coefficient of correlation (R), and average accuracy percentage .
They concluded that neural networks performed the best prediction accuracy but case – based reasoning indicated better results in long run. Accurate cost estimation at the early stages of project development is not only a problem for developed countries but also developing countries. Therefore, there is need for better cost estimation techniques at the conceptual phase to be developed. The application of ANN systems is growing rapidly in the financial and manufacturing sectors. Neural network systems offer several advantages over traditional methods for the prediction of construction projects' cost and duration. . (Boussabaine,1996).
ARTIFICIAL NEURAL NETWORK: BACKGROUND
According to Rumelhart et al. (1986), there are eight components of a parallel distributed processing model such as the neural network. These eight components are the processing units or neurons, the activation function, the output function, the connectivity pattern, the propagation rule, the activation rule, the learning rule and the environment in which the system operates. Neural networks are a series of interconnected artificial neurons which are trained using available data to understand the underlying pattern. They consist of a series of layers with a number of processing elements within each layer. The layers can be divided into input layer, hidden layer and output layer. Information is provided to the network through the input layer, the hidden layer processes the information by applying and adjusting the weights and biases and the output layer gives the output (Karna and Breen 1989). Each layer may have a number of processing units called neurons. The inputs are weighted to determine the amount of influence it has on the output (Karna and Breen 1989), input signals with larger weights influence the neurons to a higher extend. An activation function is then applied to the weighted inputs, to produce an output signal by transforming the input. The input can be a single node or it may be multiple nodes depicting different parameters where each of the input nodes acts as an input to the hidden layer. The hidden layer consists of a number of neurons/nodes which calculate the weighted sum of the input data.
Figure (1) shows how neural network adjusts the weights and biases by comparing the output with the target. The weights are not fixed but they change over time by gaining experience after several iterations (Rumelhart et al. 1986). Artificial neural networks are used in pattern classification, clustering/categorizing, function approximation, predicting, optimization, control and content-addressable memory
Figure 1 Correction of error using target data (Demuth, 2006)
Back-propagation algorithm is simple and effective in solving large and difficult problems (Alavala, 2008). Thus, it is used in learning process of the model. It consists of two phases: forward pass and backward pass (Beale and Jackson, 1990). In forward pass, the parameters of the input variables pass though the functions of the network and an output data is produced, in the end. In backward pass, firstly the error is calculated by subtracting the actual output from desired output. Then, it is propagated backward through the network. The weights are adjusted during the backward pass (Ayed, 1997). This process optimizes the weight parameters of the model, decrease the error value and increase the prediction power of the ANN model.
There are methods that significantly improve the back-propagation algorithm’s performance (Haykin, 1999):
Sequential versus batch update: When the training data set is large and highly redundant, sequential mode of back propagation learning could be preferred than the batch mode of the algorithm.
Maximizing information content: The training data should be strong enough to maximize the learning rate or the model. There are two ways to form such strong training information; using data that is having the largest training error, and using data that is oppositely different the other data used before.
Activation function: Using sigmoid activation function increases the learning ability of the model. Applying hyperbolic tangent, a nonlinear sigmoid antisymmetric activation function of sigmoid nonlinearity, is popular in this way. Learning from hints: Learning from a set of training examples deals with an
unknown input-output mapping function.
Learning rates: Learning rate values are important for the network in learning process. Neurons with many inputs should have smaller learning rate parameter, or vice versa.
2. BACKGROUND OF EXPRESSWAYS COST PREDICTION
The variations of several parameters that influence a construction project costs create complexities for developing an accurate model of future Expressways construction costs determination. However, there have been numerous publications describing methods and techniques that approximate the future projects‟ costs. Thus, the aim of this research is to develop a sufficient and accurate method of forecasting the costs of the future Expressways ‟ construction. The compiled data have been initially analyzed based on Artificial Neural Networks (ANN).Input
Neural network computes weights
Compare with target
Adjust weights computes weights
3. IDENTIFICATION OF ANN MODEL VARIABLES
One of the most important tasks of this objective is to determine which variables are important indicators. Once the appropriate variables have been determined, the cost estimation can be performed either using a neural network or any other tool, such as regression analysis.
This research describes the development of neural network models of total cost structure work of Expressways project based on recent historical projects data. The initial impetus for the research was the paucity of data available that can provide reliable information about the costs. The data used to develop the neural network model of estimation of the cost were past expressway contract data from Iraq from 2010 to 2014.
The model input variables for this model were consisting of six variables (i.e. V1, V2, V3, V4, and V5and V6). There are two types of variables that might affect the estimation of expressway project construction cost objective variables and subjective variables
Objective variables: This type comprised eleven variables, as the following V1 Length of the Pavement in (km)
V2 Capacity –the number of standard Width lanes V3 Interchanges- number of expressway interchanges V4 Number of Stream Crossing
b) Subjective variables: This type comprised nine variables, as the following
V5 Material- this classifies pavement as flexible and rigid. And assigns the values of 1 and 2 respectively to them
V6 Furnishing- Expressway furnishing level; without (1), normal (2), high standards (3).
3. DEVELOPMENT OF ANN MODEL
In an effort to develop a more realistic cost model, this study attempts to overcome some of Neural Network drawbacks , and presents it as a simple and transparent approach for use in construction. Accordingly, a three-layer Neural Network has been simulated on a (NEUFRAME, Version 4) program that is easy to use, transparent, and customary to many practitioners in construction. The simulation of Neural Networks on a NEUFRAME program presents its underlying mathematical formulas in a simple and fully controllable form. . Figure (2) shows the scheme of the NEUFRAME 4 program which is built to determine the relationship between the independent variables (inputs) and the dependent variable (output).
Artificial neural network models need to be in a systematic manner to improve its performance. Such Method needs to address major factors such as, development of model inputs, data division and pre-processing, development of model architecture, model optimization (training), stopping criteria, and model validation, (Shahin et al, 2002) . These factors are explained and discussed below.
Figure 2 Graphing Component of NEUFRAM 4 Program
4. MODEL INPUTS AND OUTPUTS
The selection of model input variables that have the most significant impact on the model performance is an important step in developing ANN models. Presenting as large a number of input variables as possible to ANN models usually increases network size, resulting in a decrease in processing speed and a reduction in the efficiency of the network, (Shahin, 2003)
It is generally accepted that eleven parameters have the most significant impact on the cost estimation of Expressways projects, and are thus used as the ANN model inputs. These include Objective variables and Subjective variables
The output of the model is the cost of Expressways project. A code is used in this research to identify the names of the different models developed. The code consists of two parts separated by a hyphen. The first part represents an abbreviation of the current output (i.e. Total Cost Expressways, ID). The second part denotes the model number. Hence, for example “TCE –1” represents Total Cost model number one.
5. PRE-PROCESSING AND DATA DIVISION
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 in the form of data scaling, normalization and transformation. Transforming the output data into some known forms (e.g. log., exponential, etc.) may be helpful to improve ANN performance. Thus, the logarithm of total cost Expressways is taken before introducing forward in the next steps.
The next step in the development of ANN models is the division of the available data into their subsets, training, testing and validation sets. trail–and-error process was used to select the best division, by using Neuframe software. The network that performs best with respect to testing error was used in this work (compared with other criteria to evaluate the prediction performance, training error and correlation of validation set). Using the default parameters of the software, a number of networks with different divisions were developed and the results are summarized in table (1) It can be seen that the best data subsets division is (80-10-10) % according to lowest testing and training error coupled with highest correlation coefficient of validation set (90.30%). Thus, this division was used in this model
Table 1 Effect of data division on performance of ANNs
Data Division training
error%
testing error%
coefficient correlation(r)% Training% Testing% Querying%
65 20 15 8.90 9.00 77.35 60 20 20 7.23 8.40 70.88 60 15 25 7.85 7.57 76.59 65 15 20 7.40 7.48 68.64 50 30 20 7.36 7.44 77.64 70 15 15 7.56 7.35 79.64 65 10 25 7.55 7.21 81.26 70 12 20 6.75 6.98 81.42 70 15 20 7.18 6.98 81.52 80 10 10 6.14 5.94 90.30
The effects of using different choices for divisions (i.e. striped, blocked, and random) were investigated and it was shown in table (2), it can be seen that the performance of ANNs model was relatively insensitive to the method of division. The better performance was obtained when the striped division was used, according to lowest testing (5.94%) and training error (6.14%) coupled with highest correlation coefficient of validation set (90.30%).
Table 2 Effects of method division on ANNs performance
Data Division% choices
of division training error% testing error% coefficient correlation(r)% Training Testing Querying
80 10 10 Striped 6.14 5.94 90.30
80 10 10 Blocked 9.99 8.98 77.90
80 10 10 Random 9.09 8.88 75.50
6. SCALING OF DATA
Once the available data have been divided into their subsets, the input and output variables are pre-processed by scaling them to eliminate their dimension and to ensure that all variables receive equal attention during training. Scaling has to be commensurate with the limits of the transfer functions used in the hidden and output layers (i.e. –1.0 to 1.0 for tanh transfer function and 0.0 to 1.0 for sigmoid transfer function). The simple linear mapping of the variables, extremes to the neural network’s practical extremes is adopted for scaling, as it is the most commonly used method, (Shahin, 2003). 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: min max min n
x
x
x
x
x
(1)7. MODEL ARCHITECTURE, OPTIMIZATION AND STOPPING
CRITERIA
One of the most important and difficult tasks in the development of ANN models is the determination of the model architecture. The network that performs best with respect to the lowest testing error followed by training error and high correlation coefficient of validation set was retrained with different combinations of momentum terms, learning rates and transfer functions in an attempt to improve model performance. Consequently, the model that has the optimum momentum term, learning rate and transfer function was retrained a number of times with different initial weights until no further improvement occurred.
The network of (Model 2) is set to one hidden layer with default parameters of software (learning rate equals to 0.2 and momentum term equals to 0.8). A number of trials were carried out with one hidden layer and 1, 2, 3…, 21 hidden layer nodes (2I+1) (where I the number of input nodes) and the results are graphically in figure. (3). It can be seen that the two hidden nodes have the lowest prediction error. Thus, it was chosen in this model.
Figure 3 Performance of ANNs model with different hidden nodes (Model 2) 6.0% 6.5% 7.0% 7.5% 8.0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 No. of Nodes Tra ini ng E rr or 6.0% 6.5% 7.0% 7.5% 8.0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 No. of Nodes T e s ti n g E rr o r 72.5% 77.5% 82.5% 87.5% 92.5% 97.5% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 No. of Nodes C orr e la ti on C oe ff .( r)
Figure (3) shows that the network with two hidden node has the lowest prediction error for the testing test (5.60%). Therefore, two hidden node was chosen in this model. It is believed that the network with two hidden node is considered optimal.
The effect of the momentum term on model performance was investigated for the model with two hidden nodes (learning rate = 0.20). The results are summarized in table (3). It can be seen that the optimum value for momentum term is 0.8, which has the lowest prediction error; hence it was used in this model.
Table 3 Effects Momentum Term on ANNs performance (Model 2) Parameters Effect Momentum Term training error% testing error% coefficient correlation(r)% Model No. (TCSW-2) choices of division (Striped) Learning Rate (0.2) No. of Nodes (2) Transfer function in hidden layer (Sigmoid) Transfer function in output layer (Sigmoid) 0.1 7.69 5.74 85.44 0.2 7.59 5.74 85.66 0.3 7.49 5.73 86.55 0.4 7.48 5.73 86.85 0.5 7.48 5.74 86.95 0.6 7.38 5.75 86.77 0.7 7.29 5.77 87.99 0.8 7.20 5.60 90.55 0.9 7.54 5.82 88.44
In addition, the effect of the learning rate on the model performance was investigated (momentum term = 0.8) for Model 2. The results are summarized in table (4). the optimum value for learning rate is 0.2, which have lowest prediction error, hence it was used in this model.
Table 4 Effects Learning Rate on ANNs performance (Model 2) Parameters Effect Learning Rate training error% testing error% coefficient correlation(r)% Model No. (TCE-2) choices of division (Striped) Momentum Term (0.8) No. of Nodes (2) Transfer function in hidden layer (Sigmoid) Transfer function in output layer (Sigmoid) 0.1 6.98 6.83 87.97 0.2 7.20 5.60 90.55 0.3 7.42 5.86 88.78 0.4 7.44 5.87 88.76 0.5 7.45 5.91 89.22 0.6 7.49 5.94 89.76 0.7 7.46 6.99 89.57 0.8 7.46 6.99 89.12 0.9 7.65 7.00 89.20
The effects of using different transfer functions (i.e. sigmoid and tanh) were investigated and it was shown in table (5), it can be seen that the performance of ANNs model was relatively insensitive to the type of the transfer function. The better performance was obtained when the tanh transfer function was used for hidden and output layers, which have lowest prediction error coupled with highest correlation coefficient (r).
Table 5 Effects of transfer function on ANNs performance (Model 2)
Parameters Effect Transfer Function training error% testing error% coefficient correlation(r)% Hidden Layer Output Layer Model No. (TCE-2) choices of division (Striped) No. of Nodes (2) Momentum Term (0.8) Learning Rate (0.2) sigmoid sigmoid 7.20 5.60 90.55 tanh tanh 7.88 7.68 88.66 sigmoid tanh 7.84 7.74 85.53 tanh sigmoid 7.88 7.58 80.03
8. ANNS MODEL EQUATION (MODEL 2)
The small number of connection weights obtained by Neuframe for the optimal ANNs model (Model TCE-2) enables the network to be translated into relatively simple formula. The structure of the ANNs model is shown in figure. (7), while as connection weights and threshold levels (bias) are summarized in table (10).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Figure 7 Structure of the ANNs optimal model (TCE-2)
TCE-2 1 2 3 4 5 6 7 8 X1 X2 X3 X4 X5 X6 9
Table 10 Weights and threshold levels for the ANNs optimal model (Model TCSW-2)
Hidden layer nodes
wji (weight from node i in the input layer to node j in the hidden layer) Hidden
layer threshold θj
i=1 i=2 i=3 i=4 i=5
j=7 0.433 0.169 -0.300 -0.400 -0.500 0.11 i=6 -0.211 j=8
i=1 i=2 i=3 i=4 i=5
0.39 -0.800 -0.199 -0.500 -0.511 -0.200 i=6 0.333 Output layer nodes
wji (weight from node i in the hidden layer to node j in the output layer) Output
layer threshold θj
i=7 i=8
j=9 -0.10 -0.835 0.31
Using the connection weights and the threshold levels shown in Table (10), the predicted of total cost can be expressed as follows:
) tanh 0.835 tanh 10 . 0 31 . 0 ( 1 2
1
1
x xe
TCE
(2) Where: X1= {θ7+ (w7-1*V1)+(w7-2*V2)+(w7-3*V5)+(w7-4*V7)+(w7-5*V7)+(w7-6*V8) } (3) X2= {θ8+ (w8-1*V1)+(w8-2*V2)+(w8-3*V5)+(w8-4*V7)+(w8-5*V7)+(w8-6*V8) } (4) It should be noted that, before using Equation 3 and 4, all input variables (i.e. V1, V2, V3, V4, V5 and V6), need to be scaled between 0.0 and 1.0 using Equation (1) and the data ranges in the ANN model training (see Table 7). It should also be noted that the predicted value of total cost obtained from Equation 6.14 is scaled between 0.0 and 1.0 and in order to obtain the actual value this total cost has to be re-scaled using Equation (1) and the data ranges in Table (7) The procedure for scaling and substituting the values of the weights and threshold levels from Table (10), Equations (2) and (3) and (4) can be rewritten as follows:55
.
1
1
11
.
4
) tanh 0.835 tanh 10 . 0 31 . 0 ( 1 2
x xe
TCE
(5) And X1={17.088+(0.1*V1)+(0.03*V2)+(-0.01*V3)+(-0.005*V4)+(0.01*V5)+(-0.01*V6)} (6) X2={46.8954+(-0.13*V1)+(-0.016*V2)+(-0.11*V3)+(-0.012*V4)+(0.01*V5)+(-0.03*V6)} (7)9. VALIDITY OF THE ANN MODEL (MODEL TC-1)
The statistical measures used to measure the performance of the models included: Where:
Mean Absolute Percentage Error (MAPE),
n A E A MAPE n i
1 % 100 * (8) Average Accuracy Percentage (AA %)MAPE
AA%100% (9)
The Coefficient of Determination (R2); The Coefficient of Correlation (R);
The results of the comparative study are given in Table (11). The MAPE and Average Accuracy Percentage generated by ANN model (TCE-2) were found to be 11% and 89% respectively. Therefore it can be concluded that ANN model (Model 2) shows a good agreement with the actual measurements.
Table 11 Results of the Comparative Study Description ANN for Model TC-1
MAPE
11%
AA %
89%
R
90.0%
R2
81.0%
To assess the validity of the ANNs model for the total cost of expressways project (TCE), the logarithm of predicted values of TCE are plotted against the logarithm of measured (observed) values of TCE for validation data set, as shown in figure (8). It is clear from figure (8). The generalization capability of ANNs techniques using the validation data set. The coefficient of determination (R2) is (81.0%), therefore it can be concluded that ANNs model (Model 2) show very good agreement with the actual measurements.
Figure 8 Comparison of predicted and observed total cost structure work for validation data
10. CONCLUSION AND FUTURE RESEARCH
Through the development of expressways construction cost estimation model using neural network and the development of the proposed program, the following points are concluded:
a) Neural networks have demonstrated to be a promising tool for use in the conceptual stages of construction projects when typically only a limited or incomplete data set is available for cost analysis.
b) In this study, one hidden layer with two hidden node for model (TCE-2) is practically enough for the neural network analysis. The findings show that one ANN model is able to learn the cause-effect relationships between input and output, during the training stage, and obtained Average Accuracy percentage (AA) of 89% and the coefficient of correlation (R) was 90.0%
Finally, future research directions are suggested for cost estimation in order to overcome the gaps that have been discussed. These directions are as follows.
Providing cost estimation proposals that encourage the acquisition of human expertise: however, this releases the construction cost estimation from human dependability. Computerized expert systems are the better mechanism that might be used to replace human expertise.
Developing several ANN models to demonstrate the ways in which different types of civil engineering problems ensure the successful development and application of this technology to civil engine erring problems.
A research may be done on applying the same techniques to develop managements systems for production rates of any constructions operations such as: earthmoving, concreting etc. R2 = 0.8105 0 1 2 3 4 5 6 0 1 2 3 4 5 6
Logarithm of Observed Total Cost
Lo ga ri thm of P re di c te d To ta l C os t R2 =0.81
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