## 2 Materials and Methods
### Artificial Neural Networks  
ANN can be defined as a computer-based program which uses special tools for simulation tasks. A very widespread and popular type of ANN is known as multilayer perceptions (MLPs), which satisfactorily received a good reputation and acceptance in major engineering investigations and development areas such as: petroleum engineering, classification and speech recognition, pattern recognition and identification, control systems as well as computer vision applications. These networks utilize input layer with an output layer. Moreover, for processing units, it uses one or more layers, known as hidden layers. These networks can be trained into carrying a precise type of work by re-adjusting the ideal forms of the nodal connections among several parts. The MLPs are trained in a professional manner such that any kind of individual input parameter leads to a target/result value. For this kind of model, all the nodal connections (weights) are changed uninterruptedly for accomplishing the targeted value. Normally, several trials are required for training of network before reaching an acceptable difference (error) between actual and target value. In addition to MLPs, radial basis function neural networks (RBFNNs) were also used in this study. Both these types have been frequently used in prediction problems in various studies including the following: [PERSON] and [PERSON] [31], [PERSON] and [PERSON] [32], and [PERSON] et al. [33]. Some of these studies also presented a comparison between the performances of these models. [PERSON] and [PERSON] [32] showed higher performance of RBFNN, while it was the opposite for [PERSON] et al. [33]. However, it was observed that the difference in performance of these models was not substantial in both cases for validation of the dataset. The basic structure of ANN and the difference in the processing units of both types of ANNs were given by [PERSON] and [PERSON] [32] as shown in Figure 2 along with Equations (1) and (2). \[f(x)=f\{\sum((W)X),b\} \tag{1}\]  
\[f(x)=f\{(X-\mu),W\} \tag{2}\]  
where: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variables** & **Sample Size** & **Mean** & **Standard Deviation** & \(p\)**-Value** &
\begin{tabular}{c} **Statistical** \\ **Significance** \\ \end{tabular} \\ \hline CNT 0.5\% & 135 & 2.2020 & 0.20468 & & \\ \hline CNT 1.0\% & 135 & 2.2185 & 0.19242 & 0.586 & Not Significant \\ \hline CNT 1.5\% & 135 & 2.2258 & 0.18412 & & \\ \hline Base Case & 45 & 2.2585 & 0.18749 & & \\ \hline SB 4\% & 90 & 2.2062 & 0.15290 & & \\ \hline SB 5\% & 90 & 2.2003 & 0.17912 & 0.182 & Not Significant \\ \hline SBS 4\% & 90 & 2.1909 & 0.21714 & & \\ \hline SBS 5\% & 90 & 2.2429 & 0.21839 & & \\ \hline SWNT & 225 & 2.2183 & 0.19404 & & \\ \hline MWNT & 180 & 2.2119 & 0.19376 & 0.745 & Not Significant \\ \hline Si\({}_{3}\)N\({}_{4}\) & 81 & 2.1442 & 0.13702 & & \\ \hline NH\({}_{3}\) & 81 & 2.4040 & 0.16257 & & \\ \hline OH & 81 & 2.0385 & 0.11166 & 0.00 & Significant \\ \hline CH\({}_{3}\) & 81 & 2.1755 & 0.13600 & & \\ \hline COOH & 81 & 2.3151 & 0.16967 & & \\ \hline Fresh & 135 & 2.1970 & 0.17861 & & \\ \hline Aged & 135 & 2.2965 & 0.17533 & 0.00 & Significant \\ \hline Moisture damaged & 135 & 2.1528 & 0.19893 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of One-Way ANOVA tests. A Gaussian function is applied to the processing unit for RBFNN, while MLP adopts a generalized regression function. Hence, the applicability of each type of model depends upon the nature of problem to be addressed and it cannot be generalized for all cases. Hence, comparison of these types for prediction of modified asphalt adhesion force is justified. Three performance measures were used in this study to evaluate the accuracy of ANN models, namely root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (CC). These measures focus on different aspects of accuracy.