## 4 Performance and Economic Feasibility of a Retaining Wall Displacement Measurement System  
### System Performance  
A testbed for analyzing the displacement measurement performance of the developed system was constructed, as shown in Figure 9. A laboratory experiment was performed in the following sequence: (1) collection of reference point cloud data, (2) collection of deformation point cloud data after attaching a deformation plate to the wall with the aim of causing an artificial deformation, and (3) evaluation of the distance between the reference and deformation point cloud data using a distance analysis algorithm. In the experiment, the distance between the hardware and analysis target was 20 m. The deformation of the retaining wall with a width and height of 600 and 1500 mm, respectively, was simulated by connecting five wooden plates with thicknesses of 7.15, 13.24, 20.13, 24.48, and 30.25 mm, as shown in Figure 9b. Figure 8: Structure of the 3D point cloud data collected by the hardware. Figure 7: Software for hardware control. The main parameters of the displacement measurement hardware were set as shown in Table 3. The Multiple Model-to-Model Cloud Comparison (M3C2) algorithm, which is sensitive to sensor noise and more accurate than other algorithms (C2C and C2M), was used to evaluate the distances between the point cloud data. The M3C2 algorithm developed by [PERSON] et al. [30] selected core points from the reference point cloud as distance analysis targets and set the direction of deformation by generating the normal vector of the plane, which was fitted using the neighboring points, and included the diameter \(D_{\text{M3C2}}\) for each core point. A cylinder with diameter \(d_{\text{M3C2}}\) and height \(H_{\text{M3C2}}\) was then created according to the normal vector direction of individual core points. The reference and deformation point cloud data inside the cylinder were projected onto the normal vector, and the average distances between the projected data were calculated. Table 3 presents the parameters of the M3C2 algorithm used in this study. The displacement measurement performance of the developed system was evaluated using the root-mean-square error (RMSE) as expressed by Equation (2). \[RMSE(Root\ Mean\ Square\ Error)=\sqrt{\frac{\sum_{i=1}^{n}(PV_{i}-GT_{i})^{2}}{n}} \tag{2}\]  
GT = Ground Truth, PV = Predicted Value  
Figure 10 shows the reference and deformation point cloud data collected using testbed. Figure 11 shows the ground truth of lateral displacement and the displacement analysis results based on the M3C2 algorithm. The ground truth in the wooden plate position in the analysis target is the thickness of the wooden plate, and in the other areas, the ground \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Value** \\ \hline \multirow{2}{*}{2D LiDAR sensor} & Resolution & 0.1667\({}^{\circ}\) \\  & Frequency & 25 Hz \\ \hline \multirow{2}{*}{Servomotor} & Rotation speed & 2\({}^{\circ}\)/s \\  & Number of rotations & 1 \\ \hline \multirow{4}{*}{M3C2 algorithm} & Core points & All point cloud data \\  & \(D_{\text{M3C2}}\) (normal scale) & 300 mm \\ \cline{1-1}  & \(d_{\text{M3C2}}\) (projection scale) & 300 mm \\ \cline{1-1}  & \(H_{\text{M3C2}}\) (height) & 3000 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main parameters of the retaining wall displacement measurement hardware and M3C2 algorithm. Figure 9: Testbed for evaluating the performance of the retaining wall displacement measurement system. (**a**) Scene of the performance test; (**b**) simulation of retaining wall deformation. truth is set to 0. The \(x\)-axis shows the wall width (width of the analysis target), while the \(y\)-axis shows the wall height (height of the analysis target). The color bar made of red and blue shows the lateral displacement. In the displacement analysis results, the lateral displacement gradually decreased as the wall height increased, which is like the ground truth, while the displacement measurement position was like the ground truth.