## 2 Measuring Setup, Principle, and Results
Consequently, when employing a 200 Hz FBG interrogator, this faster sweeping speed and stability issues with the 200 Hz FBG interrogator result in pronounced wavelength fluctuation, impacting the accurate interrogation of vibration signals. Therefore, to measure higher vibration frequencies in FSO links, in addition to a high-speed swept laser, it must also be stable and prevent wavelength fluctuations. Due to site constraints in the experimental environment, the FSO system has a length of only 2 m, whereas, in normal operation, the theoretical length of the FSO can extend to several kilometers [17; 18]. The length discrepancy necessitates a higher laser power to compensate for transmission path loss. Additionally, environmental turbulence in the FSO path will add noise to the FBG spectrum [19], which will cause errors in the read wavelength and produce vibration signals with noise. This issue can be effectively addressed through the application of denoising techniques [20]. Figure 2 shows the results of simultaneous vibration and temperature measurements without the participation of the FSO link. Figure 2a-d display the vibration frequencies of 20 Hz, 40 Hz, and 80 Hz, and the temperatures of 30 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C are measured for different vibration frequencies. The findings indicate that the vibration signals at various temperatures can be differentiated. The prominently displayed red  
line represents the vibration signal smoothed using the Savitzky-Golay filter [21], which theoretically will be very close to the wavelength of the FBG under the actual ambient temperature measurement. Since the temperature measurement is without the vibration signal, the corresponding wavelength would be exactly in the middle of the wavelengths corresponding to the peaks and valleys of the hypothetical vibration signal since the vibration is a harmonic motion. It should be clarified that the FBG sensor used for the measurements is used to measure both vibration and temperature, so it is not possible to use the same FBG to measure only the temperature but not the vibration. Also, there may be small temperature differences each time of temperature bath adjustment, and small changes in the fiber optic tension and the water level in the sink may cause the wavelength of the FBGs to fluctuate. Therefore, the FBG wavelength may not fall perfectly in the center of the amplitude level of the vibration signal if the temperature data are measured at different times, so the results of temperature measurement alone are not shown in Figure 2. In addition, one of the main ideas of the scheme is to use the vibration signal directly to recognize the frequency of the vibration and temperature value by machine learning, so consideration of the vibration signal only indicates that the temperature and vibration can be differentiated. Figure 2 shows that the measured vibration frequency is not affected by the temperature change. The temperature measurements are generally less affected by the frequency of vibration, with wavelengths of 1536.2 nm, 1536.3 nm, 1536.4 nm, and 1536.5 nm for 30 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C, respectively. Some of the deviations in the temperature  
Figure 2: Simultaneous measurements of vibration and temperature at 30 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C without FSO participation: (**a**) 20 Hz vibration frequency, (**b**) 40 Hz vibration frequency, (**c**) 60 Hz vibration frequency, and (**d**) 80 Hz vibration frequency. measurements are due to the small differences in fiber tension and water level of the bath, as mentioned earlier. Also, the water temperature may not be the same every time the temperature bath is adjusted to the same temperature.