## 5 Structure Measured Temperature and Deformation Analysis
### Measured Deformation of Main Beam  
Based on the obvious difference in signal frequency and amplitude between the train load effect and temperature load effect, the adaptive filtering method proposed in the literature [34] is adopted in this paper to extract the deformation of the bridge under the action of temperature in the structural response data, as shown in Figure 17.  
As can be seen from Figure 17, under the influence of temperature change, the deformation trend of the main beam in winter and summer is similar, but the specific values are different, and the deformation on the east side is greater than that on the west side. The high temperature in summer causes thermal expansion of the material, resulting in the increase in the transverse deformation of the main beam, and the maximum transverse deformation is 36.4 mm, which appears around 16:00. The shrinkage of the material caused by low temperature in winter causes the lateral deformation to fluctuate around the reference point. In the hottest summer, the vertical deformation of the main beam continues to increase, reaching a maximum value of \(-\)274.4 mm at about 15:00. In the coldest winter, the vertical deformation of the main beam reaches a maximum value of \(-\)203.6 mm at about 18:00. Due to the lag effect of temperature, the time when the maximum deflection appears is different from that in summer, and the value is smaller. Under the action of temperature difference and temperature gradient of the system, the deformation of the main beam with the same section is compared. It is found that the deformation of the main beam with section of the main beam span is \(-\)29.7 mm when the temperature rises. Under the positive temperature difference, the deformation of the main beam of section of the main beam span is \(-\)119.2 mm, while the vertical deformation of the main beam is \(-\)274.4 mm at 15:00. Figure 16: Ambient temperature and east and west box temperature. (**a**) Ambient temperature and east and west box temperature on January 18. (**b**) Ambient temperature and east and west box temperature on 18 January 2023. The temperature has a significant effect on the deformation of the main beam, especially in the vertical deformation. It is found that the deformation of the main beam with  
Figure 17: Transverse, vertical and longitudinal deformation of the main beam under temperature load. (**a**) Transverse deformation on 17 August 2023 on the east side of the middle section of the main beam span. (**b**) Transverse deformation on 17 August 2023 on the west side of the middle section of the main beam span. (**c**) Vertical deformation on 17 August 2023 on the east side of the middle section of the main beam span. (**d**) Vertical deformation on 17 August 2023 on the west side of the middle section of the main beam span. (**e**) Transverse deformation on 18 January 2023 on the east side of the middle section of the main beam span. (**f**) Transverse deformation on 18 January 2023 on the west side of the middle section of the main beam span. (**g**) Vertical deformation on 18 January 2023 on the east side of the middle section of the main beam span. (**h**) Vertical deformation on 18 January 2023 on the west side of the middle section of the main beam span. the same section under the action of temperature difference and temperature gradient is far greater than that of a single temperature change under the action of ambient temperature and solar radiation. The high temperature in summer results in thermal expansion of the main beam material, the vertical and transverse deformation increase, and the overall deformation trend is downward. In the coldest winter, the transverse deformation fluctuates around the base point, the degree of change is less than that in summer, and the vertical deformation changes in the same trend, only decreasing in numerical value.