# An Incentive Factor-Based Dynamic Comprehensive Evaluation on a High-Speed Railway Track
## 4 Case Study
### An Incentive Factor-Based DCE  
Based on the method described in Section 2 and the processed data obtained in Section 4.1, the SCE matrix can be calculated, and the results are shown in Table 7. The values of the incentive factor-based DCE parameters are shown in Table 8. Moreover, Table 9 shows the values of the optimal incentive point and the negative incentive point. Table 10 shows the optimal incentive and the negative incentive control module values. The values \(h^{+}\) and \(h^{-}\) calculated by Equations (20) and (21) were 0.5063 and 0.4937, respectively. Then we can get the DCE value (Table 11) and the total DCE value based on the time factor (\(\lambda_{k}=e^{k/2n}\)) (Table 12). The value of TQI for each track section obtained by the traditional method is shown in Table 13. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time** & \(\mathbf{y_{i}(t_{1})}\) & \(\mathbf{y_{i}(t_{2})}\) & \(\mathbf{y_{i}(t_{3})}\) & \(\mathbf{y_{i}(t_{4})}\) & \(\mathbf{y_{i}(t_{5})}\) & \(\mathbf{y_{i}(t_{6})}\) \\ \hline \(C_{1}\) & 0.98877 & 0.93517 & 0.99274 & 0.941 & 0.98782 & 0.98499 \\ \(C_{2}\) & 0.99389 & 0.96277 & 0.99492 & 0.95289 & 0.99579 & 0.99565 \\ \(C_{3}\) & 0.98738 & 0.92913 & 0.98881 & 0.91674 & 0.98675 & 0.98954 \\ \(C_{i}\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \(C_{394}\) & 0.99233 & 0.94992 & 0.99302 & 0.92156 & 0.99355 & 0.99337 \\ \(C_{395}\) & 0.99724 & 0.98378 & 0.99784 & 0.95515 & 0.99692 & 0.99482 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Static comprehensive evaluation (SCE) matrix (unit: mm). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameters** & \(\mathbf{\eta^{max}}\) & \(\mathbf{\eta^{min}}\) & \(\bar{\mathbf{\eta}}\) & \(\mathbf{\eta^{+}}\) & \(\mathbf{k^{+}}\),\(\mathbf{k^{-}}\) & **r** \\ \hline Value & 0.0294 & \(-\)0.0259 & \(-\)0.0012 & 0.00795 & 0.3 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The values of the incentive factor-based dynamic comprehensive evaluation (DCE) parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{\(\mathbf{t}_{2}\)} & \multicolumn{2}{c}{\(\mathbf{t}_{3}\)} & \multicolumn{2}{c}{\(\mathbf{t}_{4}\)} & \multicolumn{2}{c}{\(\mathbf{t}_{5}\)} & \multicolumn{2}{c}{\(\mathbf{t}_{6}\)} \\ \hline
**OIP** & **BIP** & **OIP** & **BIP** & **OIP** & **BIP** & **OIP** & **BIP** & **OIP** & **BIP** \\ \(\mathbf{y_{i}^{+}(t_{2})}\) & \(\mathbf{y_{i}^{-}(t_{2})}\) & \(\mathbf{y_{i}^{+}(t_{3})}\) & \(\mathbf{y_{i}^{-}(t_{3})}\) & \(\mathbf{y_{i}^{+}(t_{4})}\) & \(\mathbf{y_{i}^{-}(t_{4})}\) & \(\mathbf{y_{i}^{+}(t_{5})}\) & \(\mathbf{y_{i}^{-}(t_{5})}\) & \(\mathbf{y_{i}^{+}(t_{6})}\) & \(\mathbf{y_{i}^{-}(t_{6})}\) \\ \hline
0.99672 & 0.98015 & 0.94312 & 0.92655 & 1.00069 & 0.98412 & 0.94895 & 0.93238 & 0.99577 & 0.9792 \\
1.00185 & 0.98526 & 0.97072 & 0.95415 & 1.00288 & 0.98630 & 0.96084 & 0.94427 & 1.00374 & 0.98717 \\
0.99533 & 0.97876 & 0.93708 & 0.92051 & 0.99676 & 0.98019 & 0.92469 & 0.90812 & 0.99470 & 0.97813 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
1.00178 & 0.98521 & 0.96024 & 0.94367 & 1.00133 & 0.98476 & 0.92489 & 0.90832 & 0.99912 & 0.98255 \\
0.99106 & 0.97449 & 0.85593 & 0.83936 & 0.97400 & 0.95743 & 0.77636 & 0.75979 & 0.98538 & 0.96881 \\ \hline \hline \end{tabular} Note: OIP and BIP are the abbreviations for optimal incentive points and negative incentive points.  
\end{table} 
Table 9: Value of the optimal and negative incentive points (unit: mm). For a comparison of the two methods, the values shown in Tables 12 and 13 are plotted in Figure 2. The curve representing the time factor-based DCE showed fluctuations on \(C_{254}\sim C_{269}\), \(C_{338}\sim C_{369}\), and \(C_{30}\sim C_{52}\), which suggests that there may be three risky sections. The corresponding sections were K1023\(\sim\)K1024, K1004\(\sim\)K1005, K1067\(\sim\)K1068, which are partly shown in this paper.