## 3 Data Collection Setup and Analysis  
In the strain sensing experiment, the initial center wavelength of both FBGs was 1544.73 nm. The setup used was to fix the center wavelength of one of the FBGs at 1545.1 nm by applying strain. The other FBG was subjected to the strain from the initial center wavelength position of the FBG, and a total of 12 steps of strain application were performed. Finally, the center wavelength position of the FBG was located at 1545.45 nm. Each step was about 60 \(\mu\epsilon\) of strain application with a 0.06 nm wavelength shift, since the wavelength shift of 1 pm corresponds to about 1 \(\mu\epsilon\) of strain application. The 60 \(\mu\epsilon\) strain was realized by shifting the LS by 20 \(\mu\)m. Since the distance between the fixed points on both sides of the FBG was 33 cm, the microstrain on the FBG was 20 \(\mu\)m divided by 33 cm, which is equal to 60 \(\mu\epsilon\). However, the moving operation of LS was via manual adjustment of the micrometer head, and with the limitations of the actual resolution of the OSA, there may have been an error of 5 \(\mu\epsilon\) to 10 \(\mu\epsilon\) in the application of each strain. From this setup, the spectrum of FBGs can be obtained with no overlap, partial overlap, and  
Figure 1: An experimental framework for two FBGs cascading an interferometer for sensing. The sensing data are used for model training and testing of machine learning (BLS: broadband light source; Cir. : circulator; TDI: tunable delay-line interferometer; OSA: optical spectral analyzer; PC: personal computer). almost complete overlap. In order to verify that the overlapped spectra of FBG wavelengths can be successfully interpreted in different interference patterns obtained by fiber-optic interferometry, three different interferometric states of TDI were used to verify the success of the FBG spectra. Figure 2 shows the spectra of the FBG from 0 \(\upmu\epsilon\) to 720 \(\upmu\epsilon\) strain and the unstrained FBG in three different interferometric settings of TDI. The appearance of the interference spectrum is very similar to that of a sinusoidal wave, which shows periodic power modulation as the wavelength changes, and the displacement between the wavelength positions of the troughs is defined as the free spectral range (FSR). Here, the FSR of the three different interference states set by TDI is 2 nm. It can be observed that in the cases of Figure 2a-c, the wavelengths of the unstressed FBGs fall in the left, center, and right halves of one of the 2 nm wide lobes in the interference pattern. The FBG energy is higher in the case of Figure 2b and lower in the cases of Figure 2a,c because the interference power tunes the reflected power of the FBG. Therefore, it can be found that the power of the other FBG under strain will be modulated according to the wavelength position of the FBG and the corresponding power of the set interference. From the above, it can be seen that even if the FBG wavelengths are at the same position, they will be affected by different interferences and thus show different spectra. Figure 3 shows this concept more clearly. Figure 3a-c show the FBG spectra of the first, eighth, and last steps of the strain in three different interferometric states, respectively. It can be seen that the spectra of the two FBGs, both superimposed and un-superimposed, are very different in the three different interference states. Furthermore, as mentioned before, optical sensing mainly utilizes specific wavelength variations for sensing, and sensing based on interferometric spectroscopy either utilizes the wavelength at a certain peak of the spectrum to obtain sensing information or utilizes the wavelength at a certain dip of the spectrum to obtain sensing information. Hence, in this scheme, the wavelength value at the peak of the interference's lobe on the right side of the FBGs in Figure 3 is assumed to be the main wavelength for determining the sensed information during sensing.