## 5 Conclusions  
With regards to the Nanjing Dashengguan Yangtze River Bridge, the analysis in this study mainly consists of two parts. The first part is an explanation of the behavior of the bridge based on its measured longitudinal displacement data, while the second part is an estimation of the girder end reliability based on the calculated relative transverse displacements and expansion device in an FE model. Four main conclusions are drawn, with the first and second conclusions corresponding to the first part of the study, and the third and fourth conclusions corresponding to the second part.  
(1) The empirical wavelet transform can adaptively decompose the data of bridge longitudinal displacements, and the time-frequency characteristics can be captured to investigate the input-output mechanism of the bridge structure. The bridge longitudinal displacements are mainly influenced by temperature change. The longitudinal displacements of the expansion joints are more sensitive to the temperature variations than those of the bearings, because the longitudinal displacements of the expansion joints develop not only from the main bridge but also due to the ramp bridge.  
(2) The time lag effect between the longitudinal displacement and environmental temperature is small for the bearings and expansion joints. The longitudinal displacements of the bearings and the expansion joints both exhibiting a high degree of correlation with environmental temperature. The bridge bearings at the girder ends generally have the largest longitudinal displacements and may possess insufficient reserve redundancy at the sliding limit. The wear lifetimes of the bridge bearings  
Figure 15: Statistical features of transverse rail deflections based on the kernel density estimation: (**a**) PDF; (**b**) cumulative distribution function (CDF).  
are predicted based on the cumulative longitudinal sliding displacement (50 km) of the design. Ideally, the bridge bearings will exhibit lifetimes in the range of 45-82 years, which are less than the bridge design lifetime (100 year).  
(3) Based on the longitudinal displacement data of the bearings and expansion joints at the bridge ends, the transverse deformation of the main-bridge girder ends, and the relative transverse displacement of the expansion joints between the main-bridge girder-ends and the ramp-bridge girder-ends are calculated. The maximum transverse deformation of each girder end is close to 2 mm, while the maximum relative transverse displacement of the expansion joint is close to 1 mm during long-term bridge operation. Under 1 mm of relative transverse displacement at the main-bridge side of the expansion device, the transverse deflection of the rails is 1.00069 mm, while the stress of the entire structure of expansion device remains at a low level.  
(4) The long-term von Mises stress of the expansion device is at a low level, which should not result in fatigue under the anticipated transverse displacements (due to temperature effects) during bridge operation. However, the transverse rail deflections have approached 1 mm, which will reduce the stability of crossing high-speed trains at the location of the expansion device. Close attention should be paid to the stability of the train crossings. Using kernel density estimation, a non-parametric estimation of long-term transverse rail deflections is conducted. The probability of the transverse rail deflections being under 0.6 mm is estimated to be 99.995%. The reliability threshold of the transverse rail deflection can be used to indicate the deceleration instructions given to high-speed trains and the rapid inspection of expansion devices.  
Conceptualization, Y.D.; Methodology & Analysis, Writing--original draft, H.Z.; Writing--review and editing, S.N. and A.L.  
This research was funded by the National Key R&D Program of China (grant no. 2017 YFC0840200), the National Natural Science Foundation of China (grant nos. 51438002 and 51578138).  
The authors declare no conflict of interest.