# Bridge Displacements Monitoring Method Based on Pixel Sequence
## 4 Experimental Results and Analysis
### Structure Displacement Extraction
#### 4.3.1 Static Load Structural Displacement Extraction  
In order to validate the feasibility of the proposed algorithm under static load conditions, the edge extraction algorithm was applied to each scenario to acquire the baseline for every case. The initial state was the bridge structure without any load. The results of structural deformation and edge detection under different conditions were merged using MATLAB, resulting in a series of images. Through the fusion algorithm, the deformation of the results was reflected by the displacement of pixels (Figure 21). Next, the number of pixel displacements \(\mathrm{S_{P}}\) along the edge line in the image was calculated. Then, the pixel scale factor \(\mathrm{Z}\) was utilized to convert the pixel displacement into the image displacement \(\mathrm{S_{S}}\). In this experiment, targets with a size of 48 mm \(\times\) 48 mm were used. In the figure below, \(\mathrm{D}\) represents the actual size of a component of the structure, and \(\mathrm{d}\) represents the corresponding length in terms of the number of pixels in the image. In the image acquisition process, these targets occupied 72-75 pixels, with an average of approximately 74 pixels for multiple points. Therefore, the scale factor used in the experiment is calculated as follows:  
\[\mathrm{Z}=\frac{\mathrm{D}}{\mathrm{d}}=\frac{48}{74}=0.6486\;\mathrm{mm}/ \mathrm{pixel} \tag{11}\]  
The \(\mathrm{S_{S}}\) calculation formula is as follows:  
\[S_{s}=S_{p}\times Z \tag{12}\]  
To validate the accuracy of this algorithm, each \(1/8\) point is considered a reference point. We calculated the relative error between the image displacement \(\mathrm{S_{S}}\) obtained through the above method for each condition at seven reference points and the actual displacement \(\mathrm{S_{S}}\) obtained from the LVDT displacement sensor. The error calculation formula is as follows:  
After extracting the overall displacement of the bridge using the algorithm proposed  
\[\frac{|S_{s}-S_{l}|}{S_{l}}\times 100\% \tag{13}\]  
earlier, the displacement curve of the structure at a specific moment is obtained as follows (Figure 22):  
Figure 21: Pixel displacement extraction image. By performing the aforementioned operations, the error between the image displacement and the actual displacement for each scenario can be calculated as follows (Tables 4-6):  
More commonly used methods for identifying structural deformation include the Canny edge detection method and the improved Canny edge detection method with sub-pixel correction. According to existing algorithms, the results of the 10 kg, 20 kg, and 30 kg experiments in this study were calculated. In Figure 23, the blue sections depict the error of the Canny operator and the improved Canny operator sub-pixel algorithm, respectively. The yellow sections represent the error of the DoG algorithm proposed in this paper. It can be seen that under static loading conditions, the DoG algorithm has higher accuracy compared to other algorithms. It can accurately extract mechanical data on structural deformation, enabling the assessment of structural safety. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Reference Points** & **1**\$ **L** & **2**\$ **L** & **3**\$ **L** & **4**\$ **L** & **5**\$ **L** & **6**\$ **L** & **7**\$ **L** \\ \hline S\({}_{\text{P}}\)/pixel & 4.0667 & 7.3333 & 10.6667 & 13.0000 & 12.0000 & 8.9000 & 4.6000 \\ S\({}_{\text{s}}\)/mm & 2.6378 & 4.7568 & 6.9189 & 8.4324 & 7.7838 & 5.7730 & 2.9838 \\ S\({}_{\text{I}}\)/mm & 2.5184 & 4.5440 & 6.7134 & 8.5034 & 7.9379 & 5.8329 & 3.1568 \\ Deviation & 4.74\% & 4.68\% & 3.06\% & 0.83\% & 1.94\% & 1.03\% & 5.48\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The image structure recognition results under a 40 kg load.