## 4 Results and Discussion  
The calibration curves of the sensor are shown in Figure 15. According to the calibration test data and the standard National Metrological Verification Regulation JJG860-2015  
Figure 14: Calibration test of the sensor: a, calibration device; b, sensor; c, FBG demodulation; d, weights. Pressure Sensor (Static) of China, the sensing characteristic index and measurement error index of the sensor were investigated. The sensing characteristic indexes include the maximum working range, the output value of the full range, and the sensitivity, etc., whereas the measurement error indexes include the linearity index, the zero drift index, the hysteresis index, and the repeatability index, etc. The specific definitions of each index are as follows. The output value of the full range is defined as:  
\[\lambda_{f}=\frac{1}{n}\sum_{i=1}^{n}\left(\lambda_{i\max}-\lambda_{i\min}\right) \tag{10}\]  
where \(\lambda_{f}\) is the output value of the full range, n is the total number of calibration loading and unloading cycles, and \(\lambda_{i\max}\) (\(\lambda_{i\min}\)) is the wavelength output value at the upper (lower) limit of the measurement when the sensing unit is under the \(i^{th}\) cycle. Zero drift refers to the fluctuation of the output value of the calibrated sensor in the absence of external load, which is defined as:  
\[d=\frac{\left|d_{i}-d_{1}\right|_{\max}}{\lambda_{f}}\times 100\% \tag{11}\]  
where \(d\) is zero drift, \(di\) is the \(i_{th}\) zero output record, and \(d_{1}\) is the first zero output record. The linear fitting formula of the sensing unit can be obtained by fitting the calibration test curve with the least square method:  
\[y=k_{x}+\lambda_{B} \tag{12}\]  
where \(y\) is the output wavelength, \(x\) represents the external load, \(k\) is the slope of the fitting curve, and \(\lambda_{B}\) is the initial wavelength of the sensor. Then, the linearity is defined as:  
\[\xi_{L}=\frac{\left|\overline{y}_{i}-y_{i}\right|_{\max}}{\lambda_{f}}\times 1 00\% \tag{13}\]  
where \(\overline{y}_{i}\) is the average value of the output wavelength at the \(i_{th}\) calibration point and \(y_{i}\) is the corresponding value of the calibration point on the fitted line. Repeatability refers to the repetition degree of the output data of the calibrated sensor. It is used to investigate the reliability and stability of the sensor, and is defined as:  
\[\xi_{K}=\frac{3K}{\lambda_{f}}\times 100\% \tag{14}\]  
Figure 15: Stability testing curves of the sensor. where \(K\) is the standard deviation over the entire range, and is defined as:  
\[ \begin{split} K&=\sqrt{\frac{1}{2m}\sum\limits_{i=1}^{m} \left(K_{Li}^{2}+K_{Uli}^{2}\right)}\\ K_{Li}&=\sqrt{\frac{1}{n-1}\sum\limits_{j=1}^{n} \left(y_{Lij}-\overline{y}_{Li}\right)^{2}}\\ K_{Li}&=\sqrt{\frac{1}{n-1}\sum\limits_{j=1}^{n} \left(y_{Uij}-\overline{y}_{Uli}\right)^{2}}\end{split}  \tag{15}\]  
where \(K_{Li}\) is the standard deviation for \(i_{th}\) calibration point during loading, \(K_{Uli}\) is the standard deviation for \(i_{th}\) calibration point during unloading, \(n\) is the number of calibration cycles, \(i\) is the sequence number of the calibration point, \(j\) is the sequence number of the calibration cycles, \(y_{Lij}\) is the output wavelength for the \(j_{th}\) cycle at the \(i_{th}\) calibration point during loading, \(\overline{y}_{Li}\) is the average wavelength at the \(i_{th}\) calibration point during loading, \(y_{Uij}\) is the output wavelength for the \(j_{th}\) cycle at the \(i_{th}\) calibration point during unloading, \(\overline{y}_{Uli}\) is the average wavelength at the \(i_{th}\) calibration point during unloading, and m is the number of calibration points. Hysteresis refers to the difference between the output wavelength of the sensor at the calibration point, which mainly reflects the accuracy and assembly performance of the sensor.