# Sequential-Fault Diagnosis Strategy for High-Speed Train Traction Systems Based on Unreliable Tests
## 4 Case Study
### Comparative Analysis  
The fault diagnosis strategies of traction systems under reliable tests and unreliable tests are constructed, respectively, and the two are compared and analyzed. From the traction system fault diagnosis tree under reliable tests and unreliable tests, the fault set corresponding to the root node is \(F=\{f_{0},f_{1},f_{2},\cdots,f_{28}\}\). After calculating the value of the evaluation function, \(t_{7}\) is the test that maximizes the value of the evaluation function; therefore, \(t_{7}\) is selected as the next test under both the reliable tests and the unreliable tests. Two branches are obtained from \(t_{7}\), and the failures of the reliable tests and the unreliable tests are \(F=\{f_{0},f_{9},f_{10},\cdots,f_{28}\}\) if they pass the test. The reliable tests and the unreliable tests again use the evaluation function value to obtain values of \(t_{20}\) and \(t_{18}\), respectively, in the next tests. When there are only leaf nodes left, the first isolated \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault** & **Steps Required for Isolation** & **Fault** & **Steps Required for Isolation** \\ \hline \(f_{1}\) & 24 & \(f_{15}\) & 19 \\ \(f_{2}\) & 27 & \(f_{16}\) & 21 \\ \(f_{3}\) & 28 & \(f_{17}\) & 20 \\ \(f_{4}\) & 28 & \(f_{18}\) & 20 \\ \(f_{5}\) & 26 & \(f_{19}\) & 19 \\ \(f_{6}\) & 26 & \(f_{20}\) & 21 \\ \(f_{7}\) & 23 & \(f_{21}\) & 7 \\ \(f_{8}\) & 23 & \(f_{22}\) & 8 \\ \(f_{9}\) & 16 & \(f_{23}\) & 10 \\ \(f_{10}\) & 16 & \(f_{24}\) & 9 \\ \(f_{11}\) & 15 & \(f_{25}\) & 12 \\ \(f_{12}\) & 4 & \(f_{26}\) & 11 \\ \(f_{13}\) & 6 & \(f_{27}\) & 13 \\ \(f_{14}\) & 5 & \(f_{28}\) & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fault diagnosis strategy of traction system under reliable test. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault** & **Steps Required for Isolation** & **Fault** & **Steps Required for Isolation** \\ \hline \(f_{1}\) & 25 & \(f_{15}\) & 20 \\ \(f_{2}\) & 26 & \(f_{16}\) & 21 \\ \(f_{3}\) & 28 & \(f_{17}\) & 18 \\ \(f_{4}\) & 28 & \(f_{18}\) & 18 \\ \(f_{5}\) & 27 & \(f_{19}\) & 20 \\ \(f_{6}\) & 24 & \(f_{20}\) & 21 \\ \(f_{7}\) & 23 & \(f_{21}\) & 13 \\ \(f_{8}\) & 24 & \(f_{22}\) & 12 \\ \(f_{9}\) & 16 & \(f_{23}\) & 10 \\ \(f_{10}\) & 16 & \(f_{24}\) & 15 \\ \(f_{11}\) & 14 & \(f_{25}\) & 7 \\ \(f_{12}\) & 17 & \(f_{26}\) & 8 \\ \(f_{13}\) & 6 & \(f_{27}\) & 9 \\ \(f_{14}\) & 5 & \(f_{28}\) & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fault diagnosis strategy of traction system under unreliable test. fault in the reliable test is \(f_{12}\), and the first isolated fault in the unreliable test is \(f_{14}\). The isolation fault results obtained under the consideration of unreliable tests and reliable tests are completely contrasting, which further reflects the uncertainty analysis of the traction system testability model during construction. Taking into account the uncertain factors that affect inference diagnosis is of great practical significance to ensure the accuracy of fault diagnosis strategies. According to the analyses shown in Tables 4 and 5, from the number of tests used, it takes 28 steps to locate all faults when the tests are reliable and unreliable. From the number of tests, it can be concluded that there is no difference between reliable tests and unreliable tests regarding the impact of fault isolation. From the perspective of the test sequence, when the test is reliable or unreliable, the test sequence and fault isolation sequence are all different, as shown in Figures 5 and 6. From the test sequence comparison curve, it can be seen that the test sequence is different under the condition of reliable tests and unreliable tests. The tests used in the first step are all \(t_{7}\). When the test is reliable, the test used in the second step is \(t_{20}\), and when the test is unreliable, the test used in step 27 is \(t_{1}\), and when the test is unreliable, the test used in step 27 is \(t_{3}\).