## 4 Load Effect Separation Experiment  
### Analysis of Train Load Effect Based on Influence Line  
The stiffness or elastic modulus of the bridge structure will change after damage. As an inherent characteristic of the bridge, the influence line [24; 25; 26; 27; 28; 29] will also have different degrees of influence with the change in the structural characteristics of the bridge. The Chongqing Nanjimen track bridge's health monitoring system enables the real-time acquisition of response data, including vertical displacement of the main beam, longitudinal displacement of the main tower, and stress of the main beam, during the operation of a train. Considering that the train is running at a constant speed during the crossing of the bridge (the impact of different speeds is minimal) and the duration is brief (the effect of temperature and wind is stable), bridge influence lines of various indexes can be obtained through monitoring data analysis and compared with the finite element analysis results to achieve a bridge state assessment. The analysis results are shown in Figures 10-14. As can be seen from Figures 10-14, based on the response data such as vertical displacement of the main beam, longitudinal displacement of the main tower, and stress of the main beam collected by the health monitoring system of the Chongqing Nanjimen track bridge, the temperature load is removed by the above separation method and the response data under the action of the train load are obtained. A comparison of the influence line obtained by Midas/Civil 2023 simulation with the measured maximum vertical displacement of the main beam reveals that the measured maximum vertical displacement of the main beam is 92.00 mm and the theoretical maximum is 92.4 mm, both of which occur at 67.80 m from the left side of the span. The measured maximum longitudinal displacement of the P2 main tower is 34.00 mm, and the theoretical maximum is 34.4 mm, both of which occur at 106.28 m from the left side of the span. The measured maximum longitudinal displacement of the P3 main tower is 18.80 mm, and the theoretical maximum is 19.20 mm, both of which occur at 11.42 m from the left side of the span. The measured maximum stress of the main beam roof is \(-\)0.70 Mpa, and the theoretical maximum stress is \(-\)0.70 Mpa at 67.80 m from the left side of the span. The measured maximum stress of the main beam floor is 3.80 Mpa; the theoretical maximum stress is \(-\)0.70 Mpa, and the stress is 9.32 m from the left side of the span. Figure 9: Vertical displacement of the main beam under temperature load (unit: mm). Figure 11: Comparative analysis of longitudinal displacement of P2 tower top and finite element influence line. Figure 12: Comparative analysis of longitudinal displacement of P3 tower top and finite element influence line. Figure 10: Comparative analysis of vertical displacement of the main beam and finite element influence line. Figure 13: Comparative analysis of roof stress and finite element influence line in the center section of the main beam closing section. Meanwhile, normalized cross-correlation (NCC) was employed to assess the degree of similarity between the two entities [30,31]. For each lag (\(k\)), we calculated the number of normalized cross-relations:  
\[R(k)=\frac{\sum_{i=1}^{n}(y_{1}(i)-\overline{y}_{1})\cdot(y_{2}(i+k-n)-\overline {y}_{2})}{\sqrt{\sum_{i=1}^{n}(y_{1}(i)-\overline{y}_{1})^{2}}\cdot\sqrt{\sum_{ i=1}^{n}(y_{2}(i+k-n)-\overline{y}_{2})^{2}}} \tag{1}\]  
where  
\(n-\)Sample size;  
\(\overline{y}_{1}\), \(\overline{y}_{2}-\)Mean of samples \(y_{1}\) and \(y_{2}\), respectively. The larger the NCC value, the better the fitting. As can be seen from Table 2, the normalized cross-correlation values are 0.9457, 0.9531, 0.8873, 0.9098, and 0.9101 indicating a high degree of fitting between the measured values and the theory.