## 2 Measuring Setup, Principle, and Results
In addition, since the sampling point of the FBG interrogator is fixed, the sampling time transients may not necessarily coincide with the peaks and valleys of the mechanical waves generated by the vibration generator, so the waveforms of the data measured at different vibration frequencies may not be perfect sinusoids. This may result in the peaks and valleys of the vibration signal corresponding to the wavelength of the position of the distortion, resulting in the curve of the smoothed vibration signal and the actual temperature measurement of the wavelength of the deviation. Hence, using machine learning to read the vibration signal directly to derive the vibration and temperature information can overcome this problem. Incidentally, the signal amplitude generated by the signal generator is the same, and the length between the FBG and the vibration generator is 30 cm of fiber. Since the resonance length is different for each vibration frequency, the amplitude of the vibration signal will be different. In practical applications, the operation of the electrical system and changes in the ambient temperature can lead to continuous changes in temperature. For this purpose, the vibration measurements under dynamic temperature were collected as shown in Figure 3, and the frequencies of vibration measurements in Figure 3a-d are 20 Hz, 40 Hz, 60 Hz, and 80 Hz, respectively. Temperature conditions are 31 to 36 \({}^{\circ}\)C, 41 to 46 \({}^{\circ}\)C, and 51 to 56 \({}^{\circ}\)C. Similarly, by smoothing the signal, the wavelength curve closest to the temperature information can be obtained, as shown by the white line. The wavelength response is 1536.2 nm to 1536.26 nm for water heating from 31 to 36 \({}^{\circ}\)C, 1536.3 nm to 1536.36 nm for 41 to 46 \({}^{\circ}\)C, and 1536.4 nm to 1536.47 nm for 51 to 56 \({}^{\circ}\)C. The initial water temperature being 1 \({}^{\circ}\)C higher than the condition indicated in Figure 2 has led to a slightly higher corresponding wavelength compared to the measurement result depicted in Figure 2. Additionally, since the water heating time cannot be controlled consistently each time, the sampling time of the signals will be different. The important point is that the level of the vibration signal rises as the temperature rises, indicating that simultaneous measurements of vibration and temperature can still be made under dynamic temperature conditions. The vibration signal and the white smoothed lines indicate minor fluctuations, which are attributed to both the noise from the FBG interrogator itself and the fluctuations in water temperature. Figure 3: _Cont._  
Figure 4 shows the simultaneous measurement of vibration and temperature with the participation of FSO. The measured vibration frequencies in Figure 4a-d are 0.1 Hz, 0.5 Hz, 1 Hz, and 1.5 Hz and correspond to four temperatures, namely, 30 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C. From the results, it can be seen that different vibration frequencies are not affected by temperature changes, and the smoothing result of the vibration signals, i.e., the bright red line, presents temperature-related information that is very close to the measurement results in Figure 2. Besides, the amplitudes of the 0.1 Hz, 0.5 Hz, 1 Hz, and 1.5 Hz vibration signals do not differ much because the vibration frequency is low and cannot cause resonance. The important point is that the FBG can also measure the vibration and temperature signals simultaneously and accurately through the FSO transmission. Figure 4: _Cont_. Figure 3: Simultaneous measurements of vibration and dynamic temperature from 31 to 36 \({}^{\circ}\)C, 41 to 46 \({}^{\circ}\)C, and 51 to 56 \({}^{\circ}\)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. Since the vibration signals are dense, different frequencies can be seen by drawing lines with gradient colors.