## 3 Experimental Setup
(b) Response curve of wavelength variation of \(\Delta\lambda_{\text{L}}\), \(\Delta\lambda_{\text{S}}\) and \(\Delta\lambda_{\text{R}}\) of the FBG relative to force variation. (c) \(\Delta\lambda_{\text{R}-\text{L}}\) under different load pressures. It can be seen from Figure 9a that the wavelength of the left peak is almost consistent with the central wavelength of the FBG without stress, while the split point and right peak drift to the right as stress increases. As can be seen from the figure, the depth of the split point deepens with increasing stress. This is because as the stress increases, the right peak gradually drifts towards a longer wavelength, while the left peak's wavelength hardly changes. This results in a decrease in the overlapping area of the two peaks, resulting in a decrease in the intensity of the reflection and an increase in the depth of the split point. The fact that the reflectance of the right peak decreases with increasing pressure can also be explained. There can be seen a similar trend in Figure 10a. Combined with the data in Table 1, Figures 9b,c and 10 were plotted. It can be noticed that the left peak moves into shorter wavelengths, but the range of movement is small, at about \(-3.14\) pm/N. In contrast, the split point and right peak move into longer wavelengths, with a sensitivity of \(16.57\) pm/N and \(45.14\) pm/N, respectively. Furthermore, it can be seen from Figures 9c and 10c that the sensitivity is the largest when using the difference between the two peaks. Additionally, error analysis of the experimental data was carried out and is recorded in Figure 1:1 It can be inferred from the table and figure that there is hysteresis in the FBG measurement. When the measured pressure is \(5.0\) N, the split point hysteresis error of FBG is the largest, at \(0.028\) nm. When the measured pressure is \(5.5\) N, the right peak hysteresis error of the FBG reflection spectrum is the largest, at \(0.028\) nm. The interquartile range (IQR) method was used to analyze the sensor repeatability, and the boxplot results shown in Figure 1:2 As can be seen from the figure, the wavelength of the right peak fluctuates gradually with increasing pressure, and its stability is slightly lower than that of the split point. As a result, for following research in the future, when conducting the analysis, it is feasible for us to focus primarily on the correlation between pressure and the change in the wavelength of the split point. The return error and hysteresis in pressure measurement were discovered based on analysis of the pressure loading and unloading experiment data for the FBG. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Force/N**} & \multicolumn{3}{c}{**Left Peak (\(\Lambda_{\mathrm{L}}\))/nm**} & \multicolumn{3}{c}{**Split Point (\(\Lambda_{\mathrm{S}}\))/nm**} & \multicolumn{3}{c}{**Right Peak (\(\Lambda_{\mathrm{R}}\))/nm**} \\ \cline{2-10}  & **Loading** & **Unloading** & **Error** & **Loading** & **Unloading** & **Error** & **Loading** & **Unloading** & **Error** \\ \hline
4.0 & 1546.444 & 1546.448 & 0.004 & 1546.632 & 1546.648 & 0.016 & 1546.752 & 1546.776 & 0.024 \\
4.5 & 1546.440 & 1546.440 & 0.000 & 1546.644 & 1546.664 & 0.020  
In order to obtain reasonable measurement results, further error analysis was carried out on the data. The arithmetic mean is  
Figure 1:3  
where \(\mathrm{k}_{i}\) represents the sensitivity corresponding to the i-th measurement. The residual error of each measured value is  
Figure 1:4  
The standard deviation \(\sigma\) of a single measurement is obtained according to [PERSON]'s formula  
Figure 1:5  
Through further data analysis, the residual distribution of the wavelength drift is shown in Figure 12, and conforms to the 3\(\sigma\) criterion. However, it can be seen from the picture that the maximum wavelength drift residual of the split point is 42.67 pm, while that of the right peak is 58 pm, so the right peak wavelength's stability is lower than that of the split point.