## 1 Introduction  
Fiber optic sensing, renowned for its small size, sensitivity, precision, rapid response, and immunity to electromagnetic interference, holds significant promise for a wide range of manufacturing [1; 2], biomedical [3; 4], and transportation sensing applications [5; 6]. The performance of fiber optic sensing technology has witnessed continual enhancements. Despite being typically employed to measure a single physical parameter, fiber optic sensors also possess the capability to concurrently measure multiple parameters if required [7; 8; 9]. This feature yields cost savings by obviating the necessity for additional sensors. However, swift identification of the measured parameter's value is imperative when assessing diverse physical parameters. Theoretically, as long as the optical transceiver is functioning properly and the data sampling points and ranges are appropriate, fiber optic sensors are capable of accurately measuring the frequency of vibrations [10]. Furthermore, fiber optic sensors can be operated over a wide range of temperatures due to the nature of the glass, making fiber optic sensors a very suitable tool for simultaneous monitoring of vibration and temperature. Simultaneous monitoring of vibration and temperature in electromechanical systems, especially within large public facilities, represents a highly effective strategy for ensuring their proper functionality and preventing potential accidents. This study mainly focuses on the simultaneous measurement of temperature and vibration using a solitary FBG sensor. In fiber optic sensing measurements, fiber optic interferometer sensors are the most sensitive choice [11], and they can measure both physical parameters simultaneously [7; 8]. Nevertheless, using multiple fiber optic interferometer sensors in tandem is difficult due to complex spectral and optical loss problems. In addition, distributed fiber optic sensing can measure vibration and temperature simultaneously [9]. However, the system equipment is more complicated, and the cost is certainly higher, so it is not cost-effective when the measurement is not over a large area (fiber length of 1 km or more). Standard FBGsensors are capable of measuring a wide range of parameters accurately and can cascade multiple FBG sensors for simultaneous measurements [2]. Furthermore, FBG sensing systems can be integrated with FSO [12; 13], allowing the fiber to be easily routed over geographic obstructions and thus eliminating cable routing and maintenance costs. The top half of Figure 1 shows the potential application of an FSO-based FBG sensing system for simultaneous measurement of vibration and temperature. The light emitted from the central office can be passed through the FSO instead of a fiber optic so that the sensed signal is transmitted directly over the air and over obstructions to the target location to be measured. Simultaneous vibration and temperature monitoring by FBGs can play a key role in the proper functioning and safety of tunnels and green energy-related applications. In a previous study, FBG vibration sensing in a link containing an FSO was demonstrated by a single-frequency laser [14]. However, the previous framework relied on optical power measurement and was incapable of conducting simultaneous multi-site measurements and simultaneous measurements of vibration and temperature. The present work on FBG vibration sensing with FSO link architecture is based on the FBG decoder using wavelength mode signaling, which is capable of measuring vibration and temperature simultaneously and allows simultaneous measurement of multiple points. Moreover, the acquired signals can be learned by machine learning to quickly determine the temperature and vibration frequency, obviating the need for a fast Fourier transform to analyze the vibration frequency. This enhancement renders it more effective for timely vibration and temperature monitoring.