## 3 Testing Set-Up and Data Acquisition
### Experiments to Measure Vertical Displacement
#### 3.2.2 Vertical Displacement Measurement Using LiDAR  
To verify the proposed measurement method, the displacement of the PC test specimens was measured during the vertical static loading tests. Figure 11 shows the test set-up of the specimen. In the test, the LiDAR devices were conveniently installed 800 mm in front of the test specimen, a distance unaffected by potential damage and failure of the specimen. On the other hand, twenty LVDTs were directly installed on the specific location of the specimen surface, and they required many complicated assistant devices. Thus, when severe damage occurred, the errors in measurement were significantly affected. In this study, the center of the specimen, including the joint with two beams, was selected to measure the vertical displacement. An Intel LiDAR L515 was used to collect data in the form of Bin files and JPEG images. In the PC-C specimen, a total of 1923 bin files and 1923 JPEG images were collected with image qualities of 1280 \(\times\) 720 pixels. In the PC-P specimen, a total of 883 bin files and 883 JPEG images were collected with image qualities of 1280 \(\times\) 720 pixels. The average LVDT1 (L1) and LVDT2 (L2) was used for validation with LiDAR. On the other hand, the displacement of the test specimens was measured simultaneously with LiDAR processing time.  
Figure 11: Conventional displacement (LVDT) set-up.  
Using the proposed LiDAR method, the vertical displacement of the beam-column joint and the beam end rotation angle were measured. Firstly, the boundary of the specimen was extracted from the original point cloud data by applying data filters. The M-estimator Sample Consensus (MSAC) algorithm is a robust parameter estimation method commonly used in computer vision and image processing tasks. It is an extension of the Random Sample Consensus (RANSAC) algorithm, designed to handle data with outliers and noise. In this study, MSAC was used to delineate the specimen's plane by specifying the maximum allowed distance and the maximum angular distance from the stationary point to the plane as well as setting a reference vector for that plane. For noise handling, the remaining noise from the previous step was removed by using the DBSCAN algorithm. The DBSCAN algorithm can remove remove uninterest regions with low point clouds density from the expected region of interest. Image binarization, also known as image thresholding, is a fundamental image processing technique used to convert a grayscale or color image into a binary image, where each pixel is assigned either a black or white value. The goal of image binarization is to separate the foreground objects (the objects of interest) from the background. The image binarization method was applied to the final extracted result, which included the background and specimen. Finally, the boundary of the specimen was generated by using a Sobel operator, which detected an edge on the binary images. Figure 12 shows the tracking points and the extracted boundary of the test specimen. Based on the extracted boundary of the test specimens, the vertical displacement of the beam-column joint was calculated as follows:  
\[\mathbf{Y_{def}}=(\mathbf{Y_{i+1}}-\mathbf{Y_{i}})\times\mathbf{R_{v}} \tag{1}\]  
where \(\mathbf{Y_{def}}\) is the deflection of the specimen (unit in mm); \(\mathbf{Y_{i+1}}\) and \(\mathbf{Y_{i}}\) are the tracking points at the Y axis of the i-th and i + 1-th frames, respectively (unit in mm); and \(\mathbf{R_{v}}\) is the vertical resolution (unit in mm).  
Figure 13 directly compares the vertical displacement measured by the conventional LVDTs and the proposed LiDAR method. The vertical displacement measured by the LiDAR method is shown as a variation range, since it was calculated from all of the tracking points on the boundary of the specimen. Nevertheless, the tendency of vertical displacement was significantly similar regardless of the measurement method.  
Figure 12: Tracking points for vertical displacement of the specimen: (**a**) PC-C; (**b**) PC-P.