ijciet 06 10_006

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 6, Issue 10, Oct 2015, pp. 62-76, Article ID: IJCIET_06_10_006

Available online at

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=10

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication

DEVELOPMENT OF THE ARTIFICIAL

NEURAL NETWORK MODEL FOR

PREDICTION OF IRAQI EXPRESS WAYS

CONSTRUCTION COST

Dr. Tareq Abdul Majeed Khaleel

Building 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

Development of The Artificial Neural Network Model For Prediction of Iraqi Expressways

Construction Cost


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

(Jain et al. 1996).


Construction Cost


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.


Construction Cost


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:

minmax

minn

xx

xxx

(1)


Construction Cost


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

inin

g E

rro

r

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

Testi

ng

Err

or

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

Co

rrela

tio

n C

oeff

.(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)


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)


hidden layer

(Sigmoid)


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


Construction Cost


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:

)tanh0.835tanh10.031.0( 211

1xxe

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:


Construction Cost


55.11

11.4)tanh0.835tanh10.031.0( 21

xxeTCE

(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),

nA

EAMAPE

n

i

1

%100*

(8)

Average Accuracy Percentage (AA %)

MAPEAA %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 (R 2 ) 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

gari

thm

of

Pre

dic

ted

To

tal

Co

st R2=0.81


Construction Cost


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