# Categorization of the Condition of Railway Embarments Using a Multi-Attribute Utility Theory
## 3 Case Study Example
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Attribute** & **Label** & **Mean** & **SD** & \begin{tabular}{c} **Calculated Weight** \\ **of Importance (w)** \\ \end{tabular} \\ \hline Supervision Center & \(\mathrm{QV}_{\mathrm{C}1}\) & 9.30 & 0.78 & 0.243 \\ \begin{tabular}{c} National Assessment \\ \end{tabular} & \(\mathrm{QV}_{\mathrm{C}2}\) & 5.60 & 1.19 & 0.146 \\ \begin{tabular}{c} Ballast depth \\ (ballast pockets) \\ \end{tabular} & \(\mathrm{QV}_{\mathrm{C}3}\) & 8.40 & 0.91 & 0.219 \\ \
\begin{tabular}{c} Ballast fouling \\ (ballast quality) \\ \end{tabular} & \(\mathrm{QV}_{\mathrm{C}4}\) & 8.70 & 0.94 & 0.227 \\
\begin{tabular}{c} Irregularities in \\ sub-ballast and \\ embankment fill \\ \end{tabular} & \(\mathrm{QV}_{\mathrm{C}5}\) & 6.30 & 1.21 & 0.164 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean values, standard deviations, and calculated weight of importance for attributes. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  
The sum of all weights of importance concerning attribute parameters, based on Equation (9), equals 1:  
\[\sum_{\text{i}=1}^{5}\text{w}_{\text{i}}=0.243+0.146+0.219+0.227+0.164=1. \tag{14}\]  
Finally, the overall utility function values \(\text{U}(\text{S}_{\text{j}}^{\text{k}})\) for each alternative was calculated by combining five weights of attribute importance with the normalized utility functions for the five (\(n\)) attributes and the (\(m\)) alternatives of specific section using Equation (10). The overall utility function values give the ranking for each alternative. For example, it is calculated for the fifth subsection within the first section:  
\[\text{U}\Big{(}\text{S}_{\text{5}}^{\text{1}}\Big{)}=\sum_{\text{i}=1}^{5} \text{w}_{\text{i}}\cdot\overline{\text{U}_{\text{i}}}\Big{(}\text{S}_{\text{ 5}}^{\text{1}}\Big{)}. \tag{15}\]  
After the overall utility function was calculated for each alternative within each section (railway line), the development of the final ranking list followed. A classification scheme, as shown in Table 4, was assigned to each subsection and the results are presented in the form, shown in Figure 7, for a 500 m length where the overall condition of the embankment was in the range from very poor to adequate and a second 500 m section where the overall condition of embankment was in the range from adequate to very good. The implementation of the multi attribute utility theory thus provided classification of the condition for the investigated railway embankments. The overall classification results, given in Figure 8, represent the summation of classification results for lines selected by each Supervision Center (SC), as well as averaged values, in the form of an overall utility function--an overall percentage graph. As it can be seen from Figure 8, the categorization results show that most of the investigated embankments, 41.8%, are in an adequate condition and that 33.7% of the embankments are in poor condition, while 12.6% are in a very poor condition. On the other hand, 10% of the investigated embankments are in good condition, with only 1.9% is in a very good condition. The categorization results are consistent for line sections within each Supervision Center. The described procedure of implementing MAUT for railway embankment categorization gave the solid basis for decision-makers to plan further detailed investigation works and monitoring programs as well as remediation measures. Figure 7: A graphical representation of: (**a**) a 500 m long line section with very poor to adequate condition and (**b**) a 500 m long line section with adequate to very good condition.