## 4 Conclusions  
During the past several decades, statistical process control has been proven to support safe and efficient management and operations of transportation infrastructure. However, the existing research mainly applied the statistical process control to the analysis of continuous monitoring data. The high-speed railway track systems are large-span structures with complicated forms. In SHM of the track systems, data loss is an unavoidable consequence of wireless sensor networks. While several methods have been proposed to recover the data loss, reconstruction of signals is effective only under certain conditions. Hence, in this study, an improved SPC framework was introduced to analyze the discontinuous monitoring data of a high-speed railway track system. Based on this framework, common-cause variations in the discontinuous monitoring data were first separated by using statistical models, and special events were then detected by the utilization of control charts. The main conclusions are drawn as follows:  
1. With respect to the girder displacement and track slab-girder relative displacements, the displacement variations were mainly caused by the temperature effects and linear trends. The variations of the observation were consistent with the one caused by the temperature effects, indicating that temperature is a key factor for the displacement variations. The proportions of these variations caused by the linear trends to the ones caused by the temperature effects almost exceed 10%, suggesting that linear trends were also unneglectable components in the measurement sequences. 2. The ACF values of regression residuals were large with lag \(\geq\) 1, and vary regularly with lags, indicating the serial dependence in the discontinuous monitoring data. The ACF values of difference equation residuals showed the opposite variation rules with lags, and fell mostly in the 95% confidence interval, which validates the feasibility of the TSDE model for capturing the serial dependence. 3. As for the rail-track slab relative displacement 15 and track slab-girder relative displacement 17, numerous outliers were detected by control charts. This suggested that the track system at these two measuring points was sensitive to special causes. With regard to the special causes triggering the anomalous responses of local and overall \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Date**} & **Measuring Points with** & **Number of** & **Date** & **Measuring Points with** & **Number of Measuring Points** \\  & **Outliers Detected** & **Points** & & **Outliers Detected** & **Points** \\ \hline
2015.8.4–2015.85 & R-S-R-D13, S-G-R-D16, S-G-R-D17, S-G-R-D18, G-D21 & 5 & 2017.1.20 & R-S-R-D13, R-S-R-D15, S-G-R-D18, G-D21 & 4 \\ \hline
2015.8.6 & S-G-R-D16, S-G-R-D17, S-G-R-D18, G-D21 & 4 & 2017.2.20 & R-S-R-D13, R-S-R-D15, S-G-R-D16, G-D21 & 4 \\ \hline
2015.9.1 & S-G-R-D16, S-G-R-D17, S-G-R-D18, G-D21 & 4 & 2017.4.19 & R-S-R-D10, R-S-R-D13, R-S-R-D15, S-G-R-D17 & 4 \\ \hline
2016.1.23 & R-S-R-D13, R-S-R-D14, R-S-R-D15, S-G-R-D16 & 4 & 2017.8.28 & S-G-R-D16, S-G-R-D17, S-G-D21 & 4 \\ \hline
2016.1.24 & R-S-R-D14, R-S-R-D15, S-G-R-D15, S-G-R-D16, S-G-R-D17, G-D21 & 4 & 2018.3.15 & R-S-R-D10, S-G-R-D16, S-G-R-D16, S-G-R-D18, G-D21 & 5 \\ \hline
2016.5.2–2016.5.3 & R-S-R-D10, S-G-R-D16, S-G-R-D16, S-G-R-D18, G-D21 & 4 & 2018.4.3 & R-S-R-D10, R-S-R-D14, S-G-R-D16, S-G-R-D18, G-D21 & 5 \\ \hline
2016.5.12–2016.5.13 & R-S-R-D15, S-G-R-D16, S-G-R-D18, G-D21 & 4 & 2018.4.4 & R-S-R-D10, R-S-R-D13, S-G-R-D16, S-G-R-D17, G-D21 & 5 \\ \hline
2016.5.14 & R-S-R-D10, S-G-R-D16, S-G-R-D16, S-G-R-D18, G-D21 & 4 & 2018.4.21 & R-S-R-D10, S-G-R-D16, S-G-R-D18, G-D21 & 4 \\ \hline
2016.5.15 & R-S-R-D10, S-G-R-D16, S-G-R-D16, S-G-R-D18, G-D21 & 5 & 2018.7.24 & R-S-R-D13, R-S-R-D15, S-G-R-D17, S-G-R-D18 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._track systems, sixteen and twenty-eight significant special events were detected, respectively.