3.1.4. Training of the ANN

The introduced network in this study is an MLP network with back propagation error. The selected training function for the network was the Levenberg–Marquardt function due to its ability to converge fast. The transfer function was selected by trial and error, until the MSE reached the lowest value in both the training set and testing set. The data set was randomly divided into three groups. Seventy percent of the data was used for acquisition of the network, fifteen percent was used for testing

3.1.4. Training of the ANN

the data, and fifteen percent was used for validation. The settings of the training ANN in MATLAB are demonstrated in Figure 4. The number of epochs was selected as 1000. As a result, the network reached its lowest acquisition error after 15 epochs. The network's gradient function performance, MSE graph and regression graphs are shown in Figures 5–7, respectively. groups. Seventy percent of the data was used for acquisition of the network, fifteen percent was used for testing the data, and fifteen percent was used for validation. The settings of the training ANN in MATLAB are demonstrated in Figure 4. The number of epochs was selected as 1000. As a result, the network reached its lowest acquisition error after 15 epochs. The network's gradient function performance, MSE graph and regression graphs are shown in Figures 5–7, respectively.

lowest value in both the training set and testing set. The data set was randomly divided into three

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 8 of 17

The introduced network in this study is an MLP network with back propagation error. The selected training function for the network was the Levenberg–Marquardt function due to its ability


**Figure 4.** Settings of the training ANN in MATLAB. **Figure 4.** Settings of the training ANN in MATLAB. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 9 of 17

**Figure 5.** ANN's gradient function performance**. Figure 5.** ANN's gradient function performance.

**Figure 6.** Mean Squared Error (MSE) graph of the trained ANN.

respectively.

model.

**Figure 5.** ANN's gradient function performance**.** 

**Figure 6.** Mean Squared Error (MSE) graph of the trained ANN. **Figure 6.** Mean Squared Error (MSE) graph of the trained ANN. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 10 of 17

**Figure 7.** ANN's regression graphs. **Figure 7.** ANN's regression graphs.

**Figure 8.** Sample project's S-Curve according to the traditional Earned Value Management (EVM)

As a sample, one of the studied project's Status Curve (S-Curve) was drawn using the trained ANN and was compared with the traditional EVM's S-Curve. Improvement of the S-Curve is clearly seen in the figures below. Figures 8 and 9 illustrate the traditional model and ANN's S-Curves, respectively. As a sample, one of the studied project's Status Curve (S-Curve) was drawn using the trained ANN and was compared with the traditional EVM's S-Curve. Improvement of the S-Curve is clearly seen in the figures below. Figures 8 and 9 illustrate the traditional model and ANN's S-Curves, respectively.

**Figure 7.** ANN's regression graphs.

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**Figure 8.** Sample project's S-Curve according to the traditional Earned Value Management (EVM) **Figure 8.** Sample project's S-Curve according to the traditional Earned Value Management (EVM) model. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 11 of 17

**Figure 9.** Sample project's S-Curve according to the ANN model. **Figure 9.** Sample project's S-Curve according to the ANN model.

#### *3.2. Determination and Prioritization of Factors Affecting Earned Value in the ANN 3.2. Determination and Prioritization of Factors A*ff*ecting Earned Value in the ANN*

After training of the ANN in MATLAB, each variable is given a unique coefficient. Coefficients for the identified factors are illustrated in Table 3. After training of the ANN in MATLAB, each variable is given a unique coefficient. Coefficients for the identified factors are illustrated in Table 3.

**Table 3.** Prioritization and importance coefficients of the study factors using ANN.

According to the factors' coefficients, the ANN's function to predict the aim is obtained as follows:

$$\begin{array}{l} n = (0.81)\text{F1} & + (0.65)\text{F2} - (0.58)\text{F3} + (0.42)\text{F4} + (0.4)\text{F5} + (0.38)\text{F6} - (0.33)\text{F7} \\ & + (0.24)\text{F8} + (0.21)\text{F9} + (0.2)\text{F10} + (0.14)\text{F11} + (0.12)\text{F12} \\ & + (0.1)\text{F13} - (0.017)\text{F14} \end{array} \tag{5}$$

3 F3 Inflation rate −0.58 4 F4 Fortuitous events 0.42 Then, the final equation is obtained as follows:

follows:

$$\text{CPI} = \tan \text{sig}(n) = \frac{2}{1 + \exp(-2n)} \tag{6}$$

1 + (−2) (6)

(5)

+ (0.24)8 + (0.21)9 + (0.2)10 + (0.14)11 + (0.12)12

= (0.81)1 + (0.65)2 − (0.58)3 + (0.42)4 + (0.4)5 + (0.38)6 − (0.33)7

= () <sup>=</sup> <sup>2</sup>

+ (0.1)13 − (0.017)14

Then, the final equation is obtained as follows:

According to the factors' coefficients, the ANN's function to predict the aim is obtained as

 F8 Climate 0.24 F9 Minor contractors 0.21 F10 Plans 0.20 F11 Relationship among project's parties 0.14 F12 Risk management 0.12 F13 Accessibility of materials and appliances 0.1



*3.3. Determination and Prioritization of Factors A*ff*ecting Earned Value Using Multiple Regression Method and Comparison with the ANN Model for Data Validation*

3.3.1. Investigating the Condition of Using Multiple Regression Analysis

*and Comparison with the ANN Model for Data Validation* 

In this stage, SPSS software was exploited. The first condition if using linear regression is having normal data of earned value. Thus, a Kolmogorov–Smirnov test was conducted on the data in order to determine whether they were normal. The results illustrated that the data were not normal. Table 4 and Figure 10 illustrate the information regarding the abovementioned test. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 12 of 17

*3.3. Determination and Prioritization of Factors Affecting Earned Value Using Multiple Regression Method* 


**Figure 10.** Normalization test histogram**. Figure 10.** Normalization test histogram.

CPI 0.519 51 0.000

3.3.2. Analysis of Multiple Regression Model

Tables 5 and 6, respectively.

**Kolmogorov–Smirnov**  Statistic df Sig.

Data analysis was conducted in order to validate the ANN results by comparing them with the multiple regression results. The correlation coefficient and determination coefficient of this study's fitted multiple regression were 0.864 and 0.747, respectively. This means that about 74% of the dependent variable's variance is determined according to the model's independent variables. Information regarding the mentioned coefficients and the model analysis results is illustrated in

> **Table 5.** Determination and correlation coefficients of the multiple regression model. **Model R R Square Adjusted R Square**  1 0.864 0.747 0.646
