## 2 Materials and Methods  
### Case Study and Database  
In this study, the data of the road surface status were collected by the Vietnam Road Administration in coordination with the Japanese International Cooperation Agency (JICA) from April 2012 to March 2013 for each 100 m of lane for the entire national road network. This area is located in the north of Vietnam (Northwest region, Northeast region, Red River Delta Area) (Figure 1). The survey was conducted for two types of pavements including cement and asphalt concrete pavements. For the asphalt concrete pavement, it was implemented for the expressway and national highway (including newly operated and operated highways) named National Highway N1 (Figure 1). The content of survey consisted of scale, survey period, diagram of lane layout and survey direction, and survey parameters. The survey parameters contained a type of car survey, vehicle weight, air pressure of wheel, the surface temperature, testing apparatus, and testing method. This project was particularly important because of the need for surveying and collecting road surface status data, especially for expressways that ensure comprehensiveness, accuracy, speed, efficiency, economics, and the ability to not obstruct current traffic in Vietnam. Therefore, Hawkeye technology was a good method for road management, maintenance and operation units to meet new requirements on surveying and managing data at all levels ([[https://arrbsystems.com/hawkeye-1000-series/](https://arrbsystems.com/hawkeye-1000-series/)]([https://arrbsystems.com/hawkeye-1000-series/](https://arrbsystems.com/hawkeye-1000-series/))). Since then, there have been effective plans and solutions in road maintenance and operation. Data include three basic characteristics of the road surface namely the international roughness of IRI, the depth of the track and the depth of road surface cracking. In addition, the GPS coordinates of points on the road and the image of the road were automatically recorded continuously according to the recording step of 5 m. A total of 2811 samples were collected and tested to generate the datasets which includes road length (m), analysis area (m\({}^{2}\)), summed cracks, maximum depth of ruts (mm), average depth of ruts (mm), and IRI (mm/m) (Table 1). Table 2 describes the statistical measures of dataset features. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{X_{4}}\) & \(\mathbf{X_{5}}\) & \(\mathbf{Y}\) \\ \hline
90 & 340.2 & 0 & 31 & 9 & 10.25 \\
100 & 344 & 0 & 13 & 6 & 5.5 \\
100 & 327 & 0 & 10 & 6 & 2.93 \\
100 & 324 & 2.9 & 15 & 7 & 2.95 \\
100 & 328 & 0 & 11 & 8 & 2.3 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
25 & 91.5 & 0 & 9 & 6 & 4.3 \\
100 & 360 & 0 & 12 & 7 & 4.36 \\
100 & 349 & 0 & 17 & 9 & 5.78 \\
100 & 336 & 2 & 21 & 9 & 9.08 \\
100 & 344 & 0 & 25 & 12 & 7.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data presentation. Figure 1: Location and size of the Management Department I. In modeling, IRI was taken into account as the output variable (Y) while other parameters, which were road length, analysis area, summed cracks, maximum depth of rut, average depth of rut, were considered to be the independent variables X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), X\({}_{4}\), X\({}_{5}\), respectively. There were two parts generated from the original data. The first part data was a training dataset, which stood at 70% as opposite to that of the validating dataset (30%). The validating dataset was then used to test the models while training dataset was used to learn them. In the meantime, the principal component analysis method (PCA) [10] was used to reduce the dimensions data. Thus, we only selected the features which carry important information, and eliminated the irrelevant features for prediction.