## 4 Experiment Verification
### Measurement Error Analysis
#### 4.2.1 Transient Full-Field Displacement Error Analysis  
As mentioned above, the toy truck started at 1.8 s, and finished the trip in 4.8 s at the time of 6.6 s. When the toy truck traveled at the mid-span of the beam at 4.2 s, and the theoretical deflection curve of the simply supported beam and deflection curve calculated using the STMM are shown in Figure 15. The results show that the two curves agree well with each other with a maximum measurement error of 0.72 mm.  
From Equation (2), it can be seen that the deflection curve of the simply supported beam under concentrated force is a segmented cubic equation, so the STMM measurement results are fitted with a cubic equation using the least squares method. The fitted deflection curve and theoretical deflection curve are shown in Figure 16. It is clear that the fitted deflection curve exhibits better consistency with theoretical deflection curve, with a maximum measurement error of 0.17 mm.  
Figure 15: Deflection curves of STMM and theoretical equation with mid-span load.  
The fitted deflection curves could be obtained when the toy truck traveled along the beam at 4.2 s, 4.6 s, 5.0 s, 5.4 s, 5.8 s, and 6.2 s, respectively, as shown in Figure 17.  
At any time, subtracting theoretical deflections of 3770 measurement points from corresponding STMM measured results, the spatial measurement error distribution of the STMM can be obtained. As an example, the spatial measurement error of original STMM deflection and fitted STMM deflection along the beam can be calculated under middle span load and shown in Figure 18.  
When the toy truck traveled to the mid-span, error analysis reveals that the maximum measurement error of STMM occurs near the right end support, specifically with an error of 0.47 pixels and a corresponding measurement error of 0.72 mm, and the maximum measurement error is 0.094 pixels or 0.17 mm for fitted STMM.  
Figure 16: Deflection curves of fitted STMM and theoretical equation under mid-span load.  
Figure 17: The deflection curve from fitted STMM at different time.  
Measurement errors of all measure points at a given time can be quantified using the Root Mean Square Error (RMSE), formulated as follows:  
\[RMSE=\sqrt{\frac{1}{m}{\sum\limits_{1}^{m}{[h(x_{i})-y_{i}]}^{2}}} \tag{5}\]  
where \(h(x_{i})\) and \(y_{i}\) are the measured and theoretical deflection value of point \(I\), respectively. To show the error variation in column width, the measurement error of 1, 3, 5, and 11 pixels width STMM are listed in Table 2, comparing with that of vision-based static deflection measurement in studies [15; 21; 22].  
The results demonstrate that the maximum measurement error of STMM is comparable to that of static deflection measurements reported in the current literature, and the measurement error decreases as the width of template slice increases. It can also be seen that the fitted measurement error decreases to 0.03 pixels or 0.052 mm when the template slice width is 11 pixels. The STMM proposed in this paper is of high precision in displacement measurement and can meet the requirements of engineering measurement.