# Resilience Assessment of Beijing Subway Lines under Extreme Precipitation Weather
## 4 Case Study
### Resilience Assessment Results  
Here, the proposed approach for subway line resilience assessment is applied to estimate the resilience level of the Changping Line under heavy rainfall. We construct the Bayesian network model for each of the obtained five key performance indicators \"escalators, moving walks and barrier-free\" access, \"low-voltage power distribution system\", \"traction power supply system\", \"switch equipment\", and \"vehicle connection system\". The child node and the parent node represent the resilience value of each indicator and the daily rainfall amount, respectively. Here, the child node has discrete values of re  
Figure 8: Risk matrix of the Changping Line.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**System** & **Coding** & **Secondary Sub-Function** & **Failure Mode** & **Failure Mode** & **Importance** \\  & 0105 & Automatic fire alarm system & Fire alarm failure & 0.04\% & 9 \\ \hline
0106 & Water supply and drainage and fire extinguishing system & Failure of fire extinguishing equipment & 0.00\% & 9 \\ \hline
0107 & Platform door & Platform door & failure & \(-\)0.27\% & 10 \\ \hline
0108 & Access control system & Water supply and drainage failure & 0.00\% & 8 \\ \hline
0109 & Ventilation air conditioning and heating & HVAC equipment failure & 0.00\% & 8 \\ \hline \hline \end{tabular}
\end{table}
Table 8: _Cont._silience areas for each indicator, and the parent node has continuous values of daily rainfall amounts. Based on the failure data in extreme rainfall days in 2022, we calculate the fitted Gaussian mixture distribution over the parent and child nodes for each Bayesian network to obtain the conditional expectation of the child node given the observed value of the parent node. This is the estimated resilience value of each key performance indicator given the information of a new rainstorm event.  
As the first case in this paper, we use the last day with extreme rainfall in 2022 (22 August) to test our resilience evaluation approach. The daily rainfall amount of this day is 31.5 mm, which is the input of each Bayesian network we constructed here. Then, the estimated resilience values for all key performance indicators are obtained, and the resilience percentage score for each key performance indicator is calculated as 1 minus the ratio between the estimated resilience value and the maximal resilience value of this indicator in the historical data. A weighted average of the resilience scores for the five key performance indicators is calculated, where the weights are determined based on the risk matrix of the Changing Line obtained from the FMEA, to obtain the overall resilience score for the Changing Line under a new rainstorm event. In the case considered here, the resilience scores, weights, and weighted average resilience scores of each indicator are shown in Table 9. In this case, the resilience score is 98.96 for \"escalators, moving walks and barrier-free\" access, and 100 for all the other indicators. Then, the overall resilience score of the Changping Line is 99.88. Finally, based on some discretization method, the resilience scores of the five key performance indicators are transformed into the resilience levels. At the same time, the weighted average of the line's resilience score is also transformed into a grade classification to obtain the overall resilience level of the Changping Line in this extreme rainfall event.  
As the second case in this paper, we also estimate the resilience of the Changping Line on another day with extreme rainfall (28 July 2022), as shown in Table 10. The daily rainfall amount of this day is 55.5 mm. In this case, we find that \"Escalators, moving walks and barrier-free\" access has a resilience score of 91.49, which is slightly smaller than the first case. All the other four key indicators have resilience scores of 100. Thus, the resilience score of the entire Changping Line is 99.05 on this day. All of these resilience scores were also transformed into resilience levels.