## 3 Case-Based Model Validation
### Running State Prediction  
After combing the overall data of the two road sections, the data can be imported into the model to predict the state occurrence probability and formulate the overall operation and maintenance strategy. By analyzing the number of times each degradation state occurs and the completion of manual operation and maintenance, and considering the maintenance code specific to the mechanical and electrical facilities industry, the initial state transfer probability of the electromechanical system can be calculated as \(\lambda_{01}=0.98\%\), \(\lambda_{12}=4.76\%\), \(\lambda_{2F}=3.70\%\). The repair completion rates of minor fault state \(S_{0}\), general fault state \(S_{2}\), and serious fault state \(S_{\text{F}}\) are 95.24%, 96.30%, and 100%, respectively. First, the study calculates the situation when the maintenance strategy is not considered. In this case, the probability of \(I_{0}\), \(I_{1}\), and \(I_{2}\) is 0, the total number of known devices is 4289, and the number of fault data is 131. Combined with the numbers of slight fault state, general fault state, and serious fault state in Table 1, the steady-state probability of each state of electromechanical system follows Equation (7):  
\[X=[0.9695,0.0098,0.0189,0.0018,0,0,0] \tag{7}\]  
Combined with Figure 4 and Table 1, the state transition matrix P can be obtained, as shown in matrix (8). \[P= \begin{bmatrix}0.9902&0.0098&0&0&0&0&0\\ 0&0.9524&0.0476&0&0&0&0\\ 0&0&0.9630&0.0370&0&0&0\\ 0&0&0&0&0&0&1\\ 0.9902&0.0098&0&0&0&0&0\\ 0.9524&0&0.0476&0&0&0&0\\ 0.9630&0&0&0.0370&0&0&0\end{bmatrix}  \tag{8}\]  
Taking Formula (7) as the initial state and iterating Formula (8) to the steady state with MATLAB R2022a, the steady-state probability calculation results of each state of the electromechanical system without considering overmaintenance strategy can be obtained, as shown in Equation (9). \[\Pi=[0.6846,0.1049,0.1813,0.0070,0,0] \tag{9}\]  
Then, the situation considering the maintenance strategy is calculated. If the initial frequency of manual inspection in the maintenance strategy is set to 1/month (the working time of a working day is 8 h, and a month is calculated according to 30 working days) and analyzed, then the initial state transition matrix (10) of the electromechanical system \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**Status**} & \multicolumn{2}{c}{**Quantity**} \\ \hline \multirow{3}{*}{Minor fault status: \(S_{1}\)} & \multirow{3}{*}{Completed} & Field maintenance & 36 \\ \cline{3-4}  & & Remote processing & 4 \\ \cline{2-4}  & & Unfinished & 2 \\ \hline \multirow{3}{*}{General failure status: \(S_{2}\)} & Completed & 78 \\ \cline{2-4}  & Unfinished & 3 \\ \hline \multicolumn{2}{c}{Serious failure status: \(S_{\text{F}}\)} & 8 & 8 \\ \hline \end{tabular}
\end{table} 
Table 1: Maintenance record data. can be obtained. The state transition model of the multistate Markov process considering maintenance is shown in Figure 5.  
\[P= \begin{bmatrix}0.9569&0.0153&0&0&0.0333&0&0\\ 0&0.9191&0.0526&0&0&0.0333&0\\ 0&0&0.9297&0.0555&0&0&0.0333\\ 0&0&0&0&0&0&1\\ 0.9847&0.0153&0&0&0&0&0\\ 0.9474&0&0.0526&0&0&0&0\\ 0.9445&0&0&0.0555&0&0&0\end{bmatrix}  \tag{10}\]  
By extracting the state transition matrix of the electromechanical system and the probability initial values of each state into MATLAB R2022a to iteratively calculate to the steady state, the limit distribution of the Markov chain fault prediction model considering maintenance can be obtained, as shown in Equation (11):  
\[\Pi=[0.7936,0.0993,0.0695,0.0028,0.0264,0.0033,0.0051] \tag{11}\]  
In the operation and maintenance process of the electromechanical system, regular manual inspection can help ensure the normal operation of the equipment, reduce maintenance costs, improve production efficiency, and increase the life of the equipment. Thus, this study gradually increases the frequency of manual inspection of the electromechanical system to formulate a better operation strategy.