## 2 Measuring Setup, Principle, and Results  
The main equipment used in the experiments was an FBG interrogator (Citpo Technologies Co., Taipei, Taiwan) with a wavelength scanning range of 1528-1568 nm, an FSO device (Thorlabs Inc. F810 FC-1550 in Newton, NJ, USA), and a vibration generator (Pasco  
Figure 1: The application vision (upper part) and the experimental setup (lower part) of the FSO-based FBG sensing system for simultaneous monitoring of vibration and temperature. (FBGI: fiber Bragg grating interrogator; PC: personal computer; VG: vibration generator; SG: signal generator). SF-9324, Pasco, Roseville, CA, USA). Other equipment, such as the personal computer, standard FBG, temperature bath, and signal generator, are commonly available on the market. The lower part of Figure 1 shows the experimental setup. First, the FBG interrogator sends the probing beam from the optical fiber via the collimator to the air path, i.e., the 2 m FSO, and then from the collimator to the FBG sensor for sensing. The optical fiber on the side of the FBG is tied to a heavy object and immersed in a temperature bath. The signal generator-driven vibration generator generates different frequencies of vertical vibrations to pull the optical fiber so that the FBG generates a dynamic strain over time. Consequently, this setup allows the FBG to simultaneously measure different vibrations and temperatures. The measured vibration and temperature signals are returned to the FBG interrogator for data acquisition. Subsequently, the sampled data is then used to train a machine learning model to recognize the FBG's signal-sensing information. The computer for machine learning is equipped with a CPU of Intel(R) Core (TM) i7-9700k speed @ 3.60 Hz, installed RAM of 16 GB, and a graphics card of NVIDIA GeForce RTX 2080 Ti. FBG is a periodic grating structure; in temperature measurement, the thermal expansion of the fiber material due to the change of ambient temperature changes the spacing of the grating period and the refractive index of the core material, which results in the Bragg wavelength of the FBG changing with the temperature. In terms of vibration measurement, it relies on the applied dynamic mechanical stress to cause fiber deformation, which dynamically changes the grating period and refractive index, resulting in the FBG Bragg wavelength changing with vibration. That is to say, the FBG sensing temperature and vibration mechanism are different due to the fiber deformation mechanism being different and can be superimposed, so the simultaneous measurement of vibration and temperature will be feasible. Generally speaking, a single FBG cannot measure the strain and temperature change at the same time because the wavelength shift of the FBG when subjected to strain (strain sensitivity is 1 pm/\(\mu\varepsilon\)) will overlap with the wavelength shift of the FBG when subjected to ambient temperature change (temperature sensitivity is 10-13 pm/\({}^{\circ}\)C) [15], and it is not possible to recognize the exact amount of the strain and temperature change. However, the difference is that the vibration is a continuous periodic strain response; a vibration signal corresponding to the FBG wavelength change and a temperature change corresponding to the FBG wavelength change will be able to be recognized. The data collection process consists of two segments: one involving the FSO link, employing an FBG interrogator with a 3 Hz sweeping laser (equivalent to three sampling points per second), and the other without the FSO link, utilizing an FBG interrogator with a 200 Hz sweeping laser (equivalent to 200 sampling points per second). As per the Nyquist sampling theorem [16], the maximum sampling frequencies are restricted to 1.5 Hz and 100 Hz, respectively. In the FSO connection scenario, the FSO collimator may cause wavelength disturbance of the high-speed sweep laser.