## 3 Case-Based Model Validation
### Running State Prediction
The aim is to ensure that all kinds of equipment for the electromechanical system can be kept better in the normal working state to improve the equipment's reliability and the electromechanical system's stability. After the frequency adjustment and calculation of manual inspection, this study proposes to gradually increase the manual inspection frequency of the expressway electromechanical system from once a month to 10 times a month, and different frequencies are introduced into the multistate Markov model for testing. The stationary distribution of the electromechanical system's corresponding multistate Markov fault state is summarized in Table 2, and the trend change in the corresponding state is shown in Figure 6.  
Figure 6 shows that the probability of mild (\(S_{1}\)), general (\(S_{2}\)), and severe (\(S_{\text{F}}\)) failure statuses gradually decreases with the increase in maintenance frequency and the rise in inspection time. The occurrence probability of a normal operation state (\(S_{0}\)) does not maintain a steady upward trend when the inspection frequency is set to three times per month. The occurrence probability of the normal state (\(S_{0}\)) reaches a peak of 82.41%, an increase of 13.95% compared with 68.46% of the expected state probability of the electromechanical system under manual intervention. Figure 5: Diagram of the state transition probability model considering maintenance. In summary, the equipment inspection requires a lot of human and material resources. If the maintenance frequency is too high, the inspection cost, including workforce, time, and maintenance costs, will increase, and the low inspection frequency may affect the system's stability. By optimizing the inspection frequency and keeping it within an appropriate range, the cost can be reduced while ensuring the regular operation of the electromechanical system. Because of the three fault states of \(S_{1}\), \(S_{2}\), and \(S_{\text{F}}\), three times a month, that is, three working days a month, can be taken to conduct a comprehensive investigation of the electromechanical system. This scheme not only can effectively ensure the normal operation rate of the electromechanical system but also save a certain amount of resource investment and maximize benefits. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{2}{c}{**Number of Inspections: n Times**} & \multirow{2}{*}{**1**} & \multirow{2}{*}{**2**} & \multirow{2}{*}{**3**} & \multirow{2}{*}{**4**} & \multirow{2}{*}{**5**} \\ \cline{4-4} \multicolumn{2}{c}{**per Month**} & & & & & & \\ \hline \multirow{4}{*}{\begin{tabular}{c} \multirow{2}{*}{\begin{tabular}{c} \multirow{2}{*}{\begin{tabular}{c} State \\ occurrence probability \\ \end{tabular} \\ \end{tabular} } } & Status: \(S_{0}\) & 79.36\% & 82.26\% & 82.41\% & 81.53\% & 80.18\% \\ \cline{2-6}  & Status: \(S_{1}\) & 9.93\% & 7.52\% & 6.02\% & 5.01\% & 4.28\% \\ \cline{2-6}  & Status: \(S_{2}\) & 6.95\% & 3.68\% & 2.30\% & 1.59\% & 1.17\% \\ \cline{2-6}  & Status: \(S_{\text{F}}\) & 0.28\% & 0.15\% & 0.10\% & 0.07\% & 0.05\% \\ \hline \multicolumn{2}{c}{**Number of inspections: n times**} & \multirow{2}{*}{**6**} & \multirow{2}{*}{**7**} & \multirow{2}{*}{**8**} & \multirow{2}{*}{**9**} & \multirow{2}{*}{**10**} \\ \multicolumn{2}{c}{**per month**} & & & & & & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} \multirow{2}{*}{
\begin{tabular}{c} State \\ occurrence probability \\ \end{tabular} } } & Status: \(S_{0}\) & 78.63\% & 77.00\% & 75.33\% & 73.69\% & 72.07\% \\ \cline{2-6}  & Status: \(S_{1}\) & 3.73\% & 3.31\% & 2.98\% & 2.70\% & 2.47\% \\ \cline{2-6}  & Status: \(S_{2}\) & 0.90\% & 0.72\% & 0.59\% & 0.50\% & 0.42\% \\ \cline{2-6}  & Status: \(S_{\text{F}}\) & 0.04\% & 0.03\% & 0.03\% & 0.02\% & 0.02\% \\ \hline \end{tabular}
\end{table} 
Table 2: State distribution corresponding to manual inspection ratings 1–10. Figure 6: Fault state prediction trend chart of electromechanical systems.