## 1 Introduction  
Fiber-optic sensing has been highly favored by researchers in recent years, and a large number of related studies have shown that fiber-optic sensing has excellent performance in various measurement applications due to its small size, sensitivity, and immunity to electromagnetic interference [1; 2; 3; 4; 5]. Fiber-optic sensors mainly use the position or power changes of specific wavelengths in the spectrum measured after the probing beam reaches the measurement position of the fiber-optic sensor to interrogate changes in various environmental physical parameters. FBGs based on the Bragg grating architecture are simple-to-manufacture fiber-optic sensors made by transversely exposing the core of single-mode fiber to intense ultraviolet light with a periodic pattern [6], which can be used to sense temperature [7], strain [8], pressure [9], vibration [10], acceleration [11], and more. Usually, the strain sensitivity is about a 1 pm wavelength shift with one microstrain (\(\mu\epsilon\)) applied change, and the temperature sensitivity is about a 13 pm wavelength shift with a 1 \({}^{\circ}\)C change in environmental temperature for a standard FBG sensor around the 1550 nm wavelength [12]. On the other hand, the production process of a fiber-optic interferometer is more complicated than that of FBG, which usually requires the use of fiber fusion splicing equipment to splice different types of fibers, taper, side polishing, etching, etc. [13; 14; 15]. By changing the shape of these optical fibers, the path of light beam transmission is altered to form an optical path difference. This allows changes in different environmental physical parameters to shape different light beam paths, creating different interference states for sensing. Fiber-optic interferometers typically exhibit heightened sensitivity in measurements. Their accuracy for sensing temperature [16] and strain [17] is significantly greater--ranging from tens to hundreds of times higher--than that of standard FBGs. In addition, standard FBGs are usually only capable of measuring either strain alike or temperature alone, requiring the use of another FBG for temperature compensation in the case of strain alike measurement [9]. Fiber-optic interferometers can overcome this problem by using the Vernier effect to measure temperature, strain, or other dual parameters simultaneously [18; 19]. However, the main common disadvantages of fiber-optic interferometers are the high optical loss and the complexity of the optical spectrum, which make it difficult to cascade multiple fiber-optic interferometers to perform sensing tasks at the same time. In contrast, multiple FBGs can be cascaded in series to perform multi-point sensing tasks. Thus, if multiple FBGs and fiber-optic interferometers are cascaded in series, it is possible to meet the requirements of measurement conditions that require multiple measurement points, high sensitivity, and diversity of physical parameter measurement. In the previous instance, multiple FBGs cascaded an interferometer for sensing [20]. To increase the number of FBG sensing points, it is necessary to arrange the wavelengths of the FBGs very close to each other, and the overlapping of the wavelengths of the FBGs may occur during the sensing task, making it difficult to interpret the sensing results. In previous studies, it has been demonstrated that the overlapping of FBGs can be solved using machine learning to accurately interpret the sensed information [7; 8]. However, FBGs cascade an interferometer framework for sensing tasks with the wavelength overlap of FBGs, which has not been explored. In this paper, the main goal is to improve the sensing architecture of FBGs cascade with an interferometer by utilizing machine learning technology, specifically the DBN, to address the issue of FBGs' wavelength overlap within this sensing architecture.