## 4 Bridge Degradation Identification and Model Update Results
### Analysis of Crack Detection Results
#### 4.2.1 Determination of the Threshold Range for Crack Detection Parameters  
When determining the threshold range for parameters during the crack detection process, this study established a standard control group and selected data file sizes based on computational capacity. Furthermore, by comparing the relevant results, the study determined that the proximity threshold for neighboring points in density estimation should be set at 0.1, and a factor of 1.5 times the standard deviation was chosen as the tuning parameter for sparsity threshold The highlighted sections in the three parts of Figure 13, respectively, show the areas with a higher likelihood of crack occurrence within the various projection planes of the bridge point cloud data, with the red areas indicating a higher probability of crack formation. The detection results revealed one crack in the bridge, with the following characteristics: Crack 1: length: 915.65 mm; width: 1.15 m; depth: 7.07 m.  
The following images represent the results of the analysis, showing the regions with a higher probability of sparse areas in the x-y, x-z, and y-z planes after adjusting the threshold for the distance between adjacent points. Additionally, the connected regions along the X-axis, after parameter adjustment, have been visualized and marked. Figure 14A-C and Table 2 illustrate the varying sensitivity in detecting areas with a higher probability of crack presence on the bridge as the distance threshold between neighboring points increases during the density calculation. Among these, Figure 14B shows the highest sensitivity. After several tests involving the fine-tuning of the distance threshold between neighboring points, it was found that the optimal threshold n should be between 0.01 and 1.0, using the first 2000 rows of the dataset from these tests. The following are combined results showing the visualization of sparse locations after each adjustment of the sparsity threshold, along with the visualization and marking of the connected regions on the X-axis after the adjustments. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Experiment Number** & **1** & **2** & **3** \\ \hline Proximity Threshold for Neighboring Points in & 0.01 & 0.08 & 1.0 \\ Density Estimation & & 1.5 & 1.5 \\ Tuning Parameter for Sparsity Threshold & 0 & 1 & 1 \\ Fracture Count & 0 & 1 & 1 \\ Length of Potential Crack Area Detected/mm & 0 & 1028.58 & 947.60 \\ Width of Potential Crack Area Detected/m & 0 & 0 & 0 \\ Depth of Potential Crack Areas Detected/m & 0 & 7.60 & 6.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Program execution parameters and result data. Figure 13: Standard control group operation results. Figure 15A-C and Table 3 show the gradually decreasing sensitivity in detecting areas with a higher probability of crack presence on the bridge as the sparsity threshold adjustment factor increases during the density calculation. Based on several fine-tuning tests of the sparsity threshold, it was found that the optimal threshold k should be between 0.5 and 2.0, using the first 2000 rows of the dataset from these tests. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Experiment Number** & **1** & **2** & **3** \\ \hline Proximity Threshold for Neighboring & 0.1 & 0.1 & 0.1 \\ Points in Density Estimation & 0.5 & 1.0 & 2.0 \\ Tuning Parameter for Sparsity Threshold & 1 & 1 & 0 \\ Fracture Count & 185.54 & 1028.53 & 0 \\ Detected/mm & 0 & 0 & 0 \\ Depth of Potential Crack Areas Detected m & 9.47 & 9.47 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Program execution parameters and result data. Figure 14: Results of the crack detection program based on different proximity thresholds for neighboring points in density estimation: (**A**) Results with a parameter selection of 0.01, (**B**) Results with a parameter selection of 0.08, (**C**) Results with a parameter selection of 1.0. Based on the comprehensive results, the length and height of the sparse regions suggest potential areas for crack occurrence in the inspected bridge.