## 3 Results and Discussion
### Sensitivity of the Mechanochromic Sensor and Prediction of Displacement  
To investigate the quantitative sensitivity in discoloration of each color, the relationship between the normalized intensity of the color and the displacement in each stage was expressed as a linear function. Figure 8 shows the linear trend (dotted lines) of the normalized intensities of colors as a function of displacement. Table 1 summarizes the results of linear function fitting for each color and displacement values at each stage. The linear function is defined as follows:  
\[\Delta C=a\cdot d+b, \tag{2}\]  
Figure 7: Changes in HSV depending on displacement. where a and b are the coefficients of the linear function, and a stands for sensitivity, demonstrating the relationship between displacement (d) and discoloration (\(\Delta\)C). b is the y-intercept, i.e., this initial value of \(\Delta\)C at each stage. \(\Delta\)C is normalized R, G, B, H, S, and V values. For instance, in the case of R, \(\Delta\)C indicates the ratio of the R values at different displacement to its initial value. Each RGB color exhibited varying sensitivity (a) and goodness of a fit (R\({}^{2}\)), depending on the displacement stage. In the initial displacement (stage I), B exhibited the highest sensitivity and R\({}^{2}\) values, implying high linearity. However, the linearity of B decreased in stage II, wherein R and G showed high sensitivity and R\({}^{2}\). Furthermore, R showed high linearity in stage III. In the case of HSV, all three (H, S, and V) exhibited high R\({}^{2}\) values, while S showed the highest sensitivity, for the initial displacement. H showed significant linearity in the subsequent behavior. At the beginning of displacement, B and V exhibited high linearity; however, as displacement increased, R and H exhibited significant discoloration behavior. Specifically, the color element for predicting displacement may vary depending on the displacement level, resulting in a complicated post-processing process for displacement prediction. Therefore, in this study, displacement was predicted using the ViT-s model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Normalized Color**} & \multicolumn{3}{c}{**I (0-1 mm)**} & \multicolumn{3}{c}{**II (1-3 mm)**} & \multicolumn{3}{c}{**III (3-4 mm)**} \\ \cline{2-10}  & **a** & **b** & **R\({}^{2}\)** & **a** & **b** & **R\({}^{2}\)** & **a** & **b** & **R\({}^{2}\)** \\ \hline R & \(-0.012\) & 1 & 0.64 & 0.015 & 0.979 & 0.89 & 0.020 & 0.962 & 0.90 \\ G & \(-0.009\) & 1 & 0.38 & \(-0.020\) & 1.016 & 0.88 & 0.007 & 0.942 & 0.47 \\ B & \(-0.028\) & 1 & 0.93 & \(-0.001\) & 0.975 & 0.09 & 0.021 & 0.913 & 0.94 \\ H & \(-0.027\) & 1 & 0.89 & 0.051 & 0.912 & 0.96 & 0.028 & 0.980 & 0.78 \\ S & \(-0.076\) & 1 & 0.87 & \(-0.048\) & 0.950 & 0.69 & \(-0.004\) & 0.828 & 0.00 \\ V & \(-0.028\) & 1 & 0.93 & \(-0.001\) & 0.974 & 0.02 & 0.020 & 0.914 & 0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sensitivity value according to loading stage. Figure 8: Result of linear curve fitting between displacement and normalized color at each stage; (**a**) RGB colors, (**b**) HSV colors. ViT-s is a deep learning model that applies a transformer architecture to computer vision tasks. ViT-s processes input images by splitting them into fixed-size patches, embedding each patch, and leveraging a self-attention mechanism to capture global relationships across the entire image. Unlike CNNs, which rely heavily on local feature extraction, ViT-s excels in learning comprehensive correlations throughout an image [18]. In particular, the ViT-s used in this study demonstrated an effective predictive performance on small datasets by employing a shift patch tokenization structure, which enhanced the spatial relationships between adjacent pixels during the image tokenization process and the locality self-attention structure to strengthen local attention.