# Sequential-Fault Diagnosis Strategy for High-Speed Train Traction Systems Based on Unreliable Tests
## 3 Methodology
### Evaluation Method of Test Reliability Based on the Cloud Model  
(1) Basic theory of the cloud model  
The cloud model is a model that describes the transformation between qualitative concepts and their corresponding values based on a probability theory and fuzzy mathematics theory. \(A=(Ex,En,He)\), \(Ex\), \(En\) and \(He\) represent the three digital features of the cloud model, respectively. (2) Determination of the evaluation set  
We divide each index into five levels of language evaluation vectors, which together can form an evaluation set. Assuming that the domain of an index in the evaluation set is \(U=[X_{\text{min}},X_{\text{max}}]\), five clouds are generated in the domain \(U\) according to the language scale of the index via the normal cloud model, and the clouds are used to represent the evaluation languages of different levels. It refers to the evaluation level and is expressed as the cloud scale. Considering the detection accuracy of the sensor, we set the index universe as \(U=[90,100]\) and divide it into five rating ranges using the golden section method. The hyper entropy \(He_{0}\) of the central cloud is taken as 0.05, so the five cloud models are \(C_{1}=(90,1.031,0.13)\), \(C_{2}=(93.09,0.64,0.08)\), \(C_{3}=(95,0.39,0.05)\), \(C_{4}=(96.91,0.64,0.08)\) and \(C_{5}=(100,1.031,0.13)\), respectively. We set the number of cloud droplets \(N\) to 5000, and the generated cloud map is shown in Figure 3. From left to right are \(C_{1}\), \(C_{2}\), \(C_{3}\), \(C_{4}\), \(C_{5}\). (3) Determine expert weights  
We determined the expert weight by judging the similarity between the evaluation information given by the maintenance technician and the evaluation information given \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Evaluation** & **Influence of** & **Threshold Setting** & **Impact of** & **Influence of** & **Influence of Working** \\
**Level** & **Test Error** & **Rationality Influence** & **Environmental Noise** & **Sensor Reliability** & **Condition Disturbance** \\ \hline
1 & great & great & great & great & great \\
2 & larger & larger & larger & larger & larger \\
3 & common & common & common & common & common \\
4 & less & less & less & less & less \\
5 & very small & very small & very small & very small & very small \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation criteria for test-influencing factors. Figure 3: Cloud model corresponding to each evaluation level. by all other maintenance personnel. We can use cloud similarity to calculate the similarity evaluated by maintenance technicians, and then calculate the weight. The concept of cloud similarity can be understood as: assuming that two evaluation clouds are \(C_{1}=(Ex_{1},En_{1},He_{1})\) and \(C_{2}=(Ex_{2},En_{2},He_{2})\), and their three digital features constitute vectors \(\vec{C_{1}}\) and \(\vec{C_{2}}\). The cosine value between them can be regarded as the similarity of the two clouds. We conclude that \(\vec{C_{1}}=(Ex_{1},En_{1},He_{1})\), \(\vec{C_{2}}=(Ex_{2},En_{2},He_{2})\), and the similarity is \(\partial(C_{1},C_{2})=\cos(\vec{C_{1}},\vec{C_{2}})\). In the cloud evaluation matrix, assuming that there are \(k\) maintenance technicians, the cloud evaluation matrix can be expressed as \(E^{k}=\left(E_{ij}\right)_{n\times m}(k=1,2,\ldots)\); then, the calculation formula of the evaluation similarity of the \(u\) maintenance technician can be obtained as follows:  
\[S_{u}=\sum_{u\
eq v}\sum_{i=1}^{n}\sum_{j=1}^{m}\partial(E_{ij}^{u},E_{ij}^{v })(v=1,2,\ldots,k) \tag{2}\]  
where \(\partial(E_{ij}^{u},E_{ij}^{v})\) represents the cloud similarity of corresponding clouds in the evaluation matrix of different maintenance technicians. After obtaining the evaluation similarity of each maintenance technician, the expert weight can be determined:  
\[P_{U}=\left(S_{u}\right)/\sum_{k=1}^{K}\left(S_{u}\right) \tag{3}\]  
where \(k\) represents the number of maintenance technicians.