## 5 Performance Testing of Hydraulic Support FBG Inclinometers
### Instrument Fit Analysis  
Instrument linear fitting pertains to the establishment of a linear relationship between the tilt angle of the instrument and the wavelength drift. To enhance the accuracy of the hydraulic support FBG inclinometer, the fitting curve is derived from the data of the two-cycle tests for fitting analysis, with linearity being fitted only when the grating is under tension.  
Figure 12: The relationship between the wavelength change in the tilt sensor and the angle of tilt in the first test.  
Figure 13: The relationship between the wavelength change in the tilt sensor and the angle of tilt in the second test.  
First, the grating wavelength drift and inclination angle were fitted for gratings FBG1 and FBG2 during their tensile phase in the first-cycle test. The resulting fitted curves are presented in Figures 14 and 15 below.  
In the fit analysis of the stretched grating in the first-cycle test, when the hydraulic support FBG inclinometer is tilted to the right, the left grating is in the stretched state, the left grating (\(\Delta\lambda_{1}\)) grows linearly due to stretching, and the linear equation is \(\mathrm{y}=65.8\mathrm{x}\), with a fit coefficient of 0.9997; when the hydraulic support FBG inclinometer is tilted to the left, the right grating is in the stretched state, and the right grating (\(\Delta\lambda_{2}\)) grows linearly due to stretching, and the linear equation is \(\mathrm{y}=-67.4\mathrm{x}\), with a fit coefficient of 0.9995. The right grating (\(\Delta\lambda_{2}\)) grows linearly due to stretching, and the linear equation is \(\mathrm{y}=-67.4\mathrm{x}\), with a fitting coefficient of 0.9995.  
Next, during the second-cycle test, when gratings FBG1 and FBG2 are under tension, the grating wavelength drift and tilt angle are subjected to fitting and analysis. The corresponding fitted curves are presented in Figures 16 and 17 below.  
Figure 14: The fitting curve of the change in the left grating wavelength and the inclination angle of the first positive-loop test inclinometer.  
Figure 15: Fitting curve of the right grating wavelength and inclination angle of the first reverse-circulation test inclinometer.  
The fit analysis of the tensile grating in the second-cycle test shows that when the hydraulic support FBG inclinometer is tilted to the right, the left grating is in a tensile state, the left grating (\(\Delta\lambda_{1}\)) grows linearly due to the tensile force, and the linear equation is \(y=66.4x\), with a fit coefficient of 0.9996; when the hydraulic support FBG inclinometer is tilted to the left, the right grating is in a tensile state, and the right grating (\(\Delta\lambda_{2}\)) grows linearly due to the tensile force, with a fit coefficient of \(y=-66.5x\), and a fit coefficient of 0.9994. The right grating (\(\Delta\lambda_{2}\)) grows linearly due to stretching, and the linear equation is \(y=-66.5x\), with a fitting coefficient of 0.9994.  
In summary, with the hydraulic support FBG inclinometer in a \(\pm 15^{\circ}\) tilt range, and the hydraulic support FBG inclinometer in the stretched state of the FBG1 or FBG2 on the fiber grating wavelength, the value of the fit is greater than 0.9994, indicating that the amount of change in the wavelength of the optical fiber grating and the tilt angle has a good degree of linearity.