# Bridge Displacements Monitoring Method Based on Pixel Sequence
## 3 Experimental Structure Composition
The camera outputs images with a resolution of 8688 \(\times\) 5792 pixels for photography and 1920 \(\times\) 1080 pixels for videography, capturing static and dynamic loading, respectively. The camera is a full-frame camera with a sensor size of 36 \(\times\) 24 mm. The required focal length for the shooting process can be calculated using the following formula:  
\[\mathrm{f}=\frac{\mathrm{d}\times\mathrm{s}}{\mathrm{w}} \tag{9}\]  
where f represents the focal length of the camera, d represents the distance from the camera to the object being photographed, s represents the width of the sensor, and w represents the width of the object being photographed. In the experiment, the distance from the test beam to the camera is 5 m, the sensor width is 36 mm, and the width of the test beam is 6 m. Therefore, it can be determined as follows:  
\[f=\frac{5\mathrm{m}\times 0.036\,\mathrm{m}}{6\,\mathrm{m}}=0.03\,\mathrm{m} \tag{10}\]  
Therefore, in the validation experiments for the algorithm presented in this paper, fixing the camera's focal length at 30 mm ensures that the proportion of the structure in the image is maximized while also guaranteeing that the mechanical characteristics of the structure can be effectively captured. To simulate the bridge's response to loadings under real working conditions, loading is applied continuously over a short period, starting from  
Figure 6: Machine vision measurement system. Figure 7: Pinhole camera model. the unloaded state to extract bridge displacement. Subsequently, the captured images and videos are transmitted to the data processing terminal via the camera data transmission cable for further processing. 2. To validate the accuracy of the algorithm proposed in this paper, LVDT displacement sensors are used to obtain precise displacement data for comparison. The displacement data from the seven LVDT sensors, which are in contact with the main beam, are collected using a Donghua tester (Table 1, Figure 8). Subsequently, the displacement extracted using the DoG algorithm proposed in this paper is compared with the accurate data obtained from the LVDT sensors to assess the accuracy and reliability of the algorithm's displacement measurements [24]. 3. The loading is manually applied using weights of 10 kg and 5 kg during the experiment. A model car is used to simulate the force applied to the bridge under working conditions. 4. In this study, the algorithm will be used for deformation recognition based on image signals, where the smallest unit in the image is the pixel. Therefore, the minimum resolution in the algorithm system corresponds to the pixel factor in the experiment. The specific calculation method and value of the pixel factor will be provided in Section 4.3.1. 5. The sampling rates of the LVDT and the camera offer multiple options. To select the most appropriate rates, the Nyquist-Shannon theory was referenced, which states that for band-limited signals, the sampling frequency must be at least twice the highest frequency to avoid aliasing. Before the validation experiments, finite element software Midas Civil 2022 was used to analyze the simply supported beam in the experiment, and the first five modal frequencies of the structure were calculated as 0.511 Hz, 2.035 Hz, 4.544 Hz, 7.995 Hz, and 12.317 Hz. Based on this, the camera sampling rate was set to 25 Hz, and the LVDT sampling rate was set to 500 Hz, ensuring accurate extraction of the structural response.