# BOPVis: Bridge Monitoring Data Visualization for Operational Performance Mining
## 5 Case Studies
### Cause of the Operational Deformation  
The dominant factors driving the operational deformation of the background bridge are further investigated. For a long-span highway bridges, the traffic load is much smaller than the dead load. Additionally, the hourly averaging can filter out the traffic-related high-frequency components in the measured displacements. Consequently, traffic measurements are not considered in interpreting the bridge's deformation. Instead, structural temperature, ambient temperature, relative humidity, and wind speeds are incorporated into the analysis as explanatory variables. The bridge has 32 temperature sensors to measure the steel girder's temperature distribution. Four top-plate temperature sensors at two cross-sections of the girder, namely TMP1, TMP2, TMP3, and TMP4, are selected. By clicking the plus sign in the upper left corner of the correlation panel, the scatter plot matrix is used to display all pairwise relationships between these four temperature variables, as shown in Figure 7. The correlation coefficients are all greater than 0.97, indicating a high level of uniformity in structural temperatures due to the steel's excellent heat transfer performance. This uniformity is also evident in the time-series plot Figure 8.  
As a result, the average of all 32 temperature measurements is selected as the representative structural temperature, denoted as TS. Similarly, the representative variables of the ambient temperature, wind speeds, and relative humidity are determined as TA, WS, and RH, respectively. To explore the cause of the operational deformation, the vertical  
Figure 6: The interaction of the scatter plot matrix. and horizontal-axis variables in the scatter plot matrix correspond to the structural displacements (GPS 1-X, GPS 2-Z, GPS 3-Z, and GPS 4-X) and environmental actions (TS, TA, WS, and RH), respectively, as shown in Figure 9. When the \"fitted lines\" option is enabled, the best-fitted lines overlay the scatter plot where the absolute values of correlation coefficients are greater than 0.8. These lines serve as a guide to the tendency of variations in structural displacements with environmental actions. Based on the distribution patterns of scattered points in Figure 9, the correlations for each pairwise variable combination can be intuitively compared. Moreover, the correlation coefficients in each plot are mapped to colors in the colormap, determining the scattered points' color. Obviously, the correlations of the structural displacements with TS and TA are much higher than those with WS and RH, suggesting that temperature changes primarily govern the concerned structural deformations. When the temperature increases, the midpoint of the main girder can be observed to move downward and simultaneously, both tower tops move toward the central span. A linear regression analysis shows that the sensitivity coefficients of GPS1-X, GPS2-Z, GPS3-Z and GPS4-X with regard to TS are, respectively, 5.30 mm/\({}^{\circ}\)C, \(-\)41.1 mm/\({}^{\circ}\)C, \(-\)44.2 mm/\({}^{\circ}\)C, and \(-\)4.2 mm/\({}^{\circ}\)C, indicating that the girder vertical displacement is much larger than the tower-top horizontal displacement for the same temperature changes. The above findings in BOPVis are a good agreement with the previous results in the bridge engineering community. According to [29], the temperature-induced deformation of a suspension bridge can be estimated by the formula \(L_{E}\theta_{\text{C}}\times\delta T_{\text{C}}\), where \(L_{E}\), \(\theta_{\text{C}}\) and \(T_{\text{C}}\) are the equivalent length, linear expansion coefficient and temperature variation. The equivalent length \(L_{E}\) varies  
Figure 7: The scatter plot matrix showing all the pairwise relationships among the four top-plate temperature sensors at two cross-sections of the girder. The structural temperatures generally exhibit a high level of uniformity. for different displacements.