## 5 Performance Testing of Hydraulic Support FBG Inclinometers
### Analysis of Test Results  
Upon the conclusion of the experiment, the recorded data were meticulously sorted and tabulated. The experimental data obtained from the first-cycle test of the cantilever-beam hydraulic support FBG inclinometer are presented in Table 1 below. Figure 11: The diagram of performance measurement system. The experimental data from the second cycle of the hydraulic support FBG inclinometer test are shown in Table 2 below. Following multiple repetitions of the experiments, the experimental process curve was plotted based on the data results acquired. Given that the wavelength change in the unstressed FBG3 is exceedingly minimal, the temperature effect could not be accounted for. Figure 12 depicts the experimental process curve of the cantilever-beam-type hydraulic support FBG inclinometer during the first cycle. Here, the abscissa represents the tilt angle of the hydraulic support FBG inclinometer, while the ordinate denotes the change in the central wavelength of the hydraulic support FBG inclinometer. From the cyclic experiment of the hydraulic support FBG inclinometer in the tilt angle between \(-15^{\circ}\) and \(15^{\circ}\) in Figure 11, it can be concluded that when the hydraulic support FBG inclinometer is tilted to the right (\(0^{\circ}\)-\(15^{\circ}\)), in the series double gratings symmetrically arranged on the cantilever beam, the left grating (\(\Delta\lambda_{1}\)) will grow linearly due to tension, and the linear equation is \(y=65.8\)x, and the right grating (\(\Delta\lambda_{2}\)) will change non-linearly due to compression. The right grating (\(\Delta\lambda_{2}\)) is non-linear due to compression; when the hydraulic support FBG inclinometer is tilted to the left (\(-15^{\circ}\)-\(0^{\circ}\)), the right grating (\(\Delta\lambda_{2}\)) will grow linearly due to stretching, and the linear equation is \(y=-67.4\)x, while the left grating (\(\Delta\lambda_{1}\)) is non-linear due to compression. \begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Angle of Inclination/\({}^{\circ}\)**} & **Positive-Cycle Test** & **Reverse-Cycle Test** \\  & **Grating Wavelength/nm** & **Grating Wavelength/nm** \\ \hline \(-15\) & 1526.9561 & 1533.9687 \\ \(-12\) & 1526.9455 & 1532.7696 \\ \(-9\) & 1526.8883 & 1532.5848 \\ \(-6\) & 1526.8036 & 1532.3725 \\ \(-3\) & 1526.9067 & 1531.1588 \\ \(0\) & 1527.1012 & 1531.9577 \\ \(3\) & 1527.2963 & 1531.7665 \\ \(6\) & 1527.4985 & 1531.6698 \\ \(9\) & 1527.7141 & 1531.7346 \\ \(12\) & 1527.8962 & 1531.7915 \\ \(15\) & 1527.0882 & 1531.8066 \\ \hline \end{tabular}
\end{table} 
Table 1: First-cycle test data. \begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Angle of Inclination/\({}^{\circ}\)**} & **Positive-Cycle Test** & **Reverse-Cycle Test** \\  & **Grating Wavelength/nm** & **Grating Wavelength/nm** \\ \hline \(-15\) & 1537.0703 & 1543.1503 \\ \(-12\) & 1537.0587 & 1542.9692 \\ \(-9\) & 1536.9914 & 1542.7845 \\ \(-6\) & 1536.9186 & 1542.5584 \\ \(-3\) & 1537.0383 & 1542.3633 \\ \(0\) & 1537.2254 & 1542.1521 \\ \(3\) & 1537.4182 & 1541.9634 \\ \(6\) & 1537.6367 & 1541.8556 \\ \(9\) & 1537.8295 & 1541.9363 \\ \(12\) & 1538.0372 & 1541.9814 \\ \(15\) & 1538.2223 & 1541.9871 \\ \hline \end{tabular}
\end{table} 
Table 2: Second-cycle test data. Further, all of the above operations were performed on the hydraulic support FBG inclinometers arranged with FBG1 and FBG2 within a \(\pm 15^{\circ}\) inclination range, and the results of the repeated tests are shown in Figure 13.  
From Figure 13, the second-cycle test of the hydraulic support FBG inclinometer at \(\pm 15^{\circ}\) shows that when the hydraulic support FBG inclinometer is tilted to the right (0\({}^{\circ}\)\(\sim\)15\({}^{\circ}\)), among the double gratings symmetrically arranged on the cantilever beam, the left grating (\(\Delta\lambda_{1}\)) will grow linearly due to stretching, and the linear equation is y = 66.4x, whereas the right grating (\(\Delta\lambda_{2}\)) will show a non-linear change due to compression.