## 6 Optimal Features for Earthquake-Induced Structural Displacement Monitoring
Each data point of the normalized RMSE with respect to the normalized tile dimension (\(D/\Delta_{\mathrm{GT,max}}\)) is depicted with gray symbols. As previously presented in Table 2, a larger overall peak roof displacement in the Y-direction is observed compared to the X-directionfor the nine tests in this study. In addition, very large peak roof displacements in the Y-direction are recorded during the 100% and 110% \(\mathrm{MCE_{R}}\) Northridge earthquake tests (MID 8 and 18). Therefore, both RMSEs and tile dimensions after normalization (in the Y-direction) are less than the values in the X-direction. For each direction, data points are divided into multiple bins based on the normalized tile dimension with a fixed bin width of 10%, which are indicated by the red and white background in the plot. The statistics of the data within each bin are presented by a box and whisker plot in Figure 16. As the normalized tile dimensions (\(D/\Delta_{\mathrm{GT,max}}\)) increase, the normalized RMSEs decrease from 5.78% to 3.56% in the X-direction and decrease from 2.68% to 1.46% in the Y-direction. For both X- and Y-direction, a relatively stable RMSE can be achieved when the normalized tile dimensions (\(D/\Delta_{\mathrm{GT,max}}\)) are greater than 50% (i.e., the actual tile dimension of the target is greater than 50% of the peak displacement during the earthquake). Figure 16: Statistics for normalized root-mean-square errors (RMSEs) with respect to normalized tile dimension (\(D/\Delta_{\mathrm{GT,max}}\)) of black-and-white checkerboard targets. Note that the box plot is the statistics for the data points within each bin. Numbers in red represent the medians for data in the first and last bin. Figure 15: Root-mean-square error (RMSE) statistics for various reference target patterns in displacement tracking of the 6-story mass timber building specimen under 67% and 100% \(\mathrm{MCE_{R}}\) tests (\(n\) is the number of RMSE data points for each pattern; numbers in red color indicate the median value of each data group). * **Intensity Contrast**: In the proposed target detection and tracking algorithm, the colored ROI image is converted into grayscale for the convenience of thresholding and the reduced computational cost. Type 3 (black-and-white) and Type 3\({}_{\text{R}}\) (red-and-white) targets are both 2-tile checkerboard patterns with the same geometric shape and dimension but with different colors. Five pairs of contrasting colors involved in target detection and tracking for these two patterns are listed below in descending order of intensity difference within the color pairs in the grayscale image: (1) black and white, (2) red and white, (3) white and background, (4) black and background, and (5) red and background. As previously discussed in Section 3.1, the two corner points between red squares and background are suppressed for the Type 3\({}_{\text{R}}\) pattern in feature point detection and tracking. Therefore, displacement tracking for the Type 3\({}_{\text{R}}\) pattern relies largely on the red-to-white and white-to-background contrast which have relatively large intensity differences within each color pair. However, displacement tracking for the Type 3 targets relies on black-to-white, white-to-background, and black-to-background contrasts, where the intensity difference between the black region and the background is relatively low and it may reduce the performance of feature point localization. This insight is reflected by the slightly larger results in the RMSE statistics for the Type 3 targets compared to the Type 3\({}_{\text{R}}\) targets. * **Pattern shape**: Square checkerboard patterns and concentric circular patterns are included for the structural displacement monitoring of the 6-story mass timber building specimen. The square checkerboard patterns provide orthogonal features with explicit feature points, while the concentric circular pattern only provides circular shapes without any explicit point for tracking.