## 2 Research and Design of Slope Displacement Monitoring System
### Principle of Calculation of Wall Inclination Angle Discrimination  
Following the video image processing, a segmented video image is generated. This segmented section includes the monitored target--in this case, the retaining wall surface adorned with reflective strips. The primary purpose of the monitoring system is to continuously assess the displacement of the retaining wall surface. It accomplishes this by tracking changes in the positions of the reflective strips. When these strips shift, the monitoring system employs an algorithm to calculate real-time offset displacements and angles, thus predicting the tilt angle of the retaining wall surface.  
The calculation principle for determining the displacement of the retaining wall surface is based on the arrangement of two cameras with different orientations. Simultaneously monitoring the retaining wall surface in real-time, this setup enables the precise prediction of deformations in the wall surface at the same angle orientation. Figure 4 illustrates the geometrical relationship between the monitoring areas of the two cameras and the displacement of the wall surface.  
The formulas for calculating the vertical and horizontal displacements of the reflective strips are as follows:  
\[H_{ij}=\Delta H_{1}+\Delta H_{2}+\Delta H_{3}+\ldots+\Delta H_{j} \tag{2}\]  
Figure 4: Geometric relationship between camera monitoring surface and wire rope deflection.  
\[x_{ij}=\Delta x_{1}+\Delta x_{2}+\Delta x_{3}+\ldots+\Delta x_{j} \tag{3}\]  
where \(H_{ij}\), \(x_{ij}\) denote the vertical displacement and horizontal deflection displacement of the reflective strip monitored by camera \(i\) (\(i\) = 1, 2) for the \(j\)th time, respectively.  
The formula for calculating the reflective strip displacement angle is as follows:  
\[x_{1j}=x_{j}\sin\alpha_{1} \tag{4}\]  
\[x_{2j}=x_{j}\sin\alpha_{2} \tag{5}\]  
\[H_{1j}=H_{2j}=H_{j} \tag{6}\]  
\[\alpha_{1}+\alpha_{2}=\alpha\;or\;\pi-\alpha \tag{7}\]  
where \(H_{j}\), \(x_{j}\) are the vertical displacement and horizontal deflection displacement of the reflective strip monitored by the camera for the \(j\)th time, respectively.  
The resulting reflective strip displacement angle \(\theta_{j}\) is obtained:  
\[\theta_{j}=\arctan\frac{x_{j}}{H_{j}} \tag{8}\]  
Then, the predicted angle of deformation of the retaining wall face \(\alpha_{j}\) is:  
\[\alpha_{j}=\arctan\frac{H_{j}\tan\theta_{j}-h\sin\theta_{j}}{h\cos\theta_{j}} \tag{9}\]  
The author has taken into thorough consideration the recommendations provided by the reviewers. The criteria for adding the deformation angle (\(\alpha_{j}\)) of the retaining wall are now as follows.  
Typically, when designing retaining walls, deformation limits are established in alignment with engineering requirements and relevant standards. One common criterion pertains to the maximum inclination of the retaining wall surface, often falling within the range of 1% to 2%. Consequently, this paper adopts 2% as the threshold for the ultimate deformation standard of the retaining wall. To account for this standard, multiple video monitoring areas are defined. If the retaining wall exceeds a tilt angle of \(\alpha_{j}>2\%\), indicating an excessive wall angle, and when more than 50% of the wall monitoring system detects that the retaining wall exceeds the 2% limit, the control system will activate an alarm. This alarm will trigger the evacuation of personnel and initiate emergency rescue procedures.