## 1 Introduction  
The stability control of goal areas remains a critical challenge in underground longwall mining operations. During the mining process, pressure variations in a goaf can trigger catastrophic safety incidents, including roof collapse and roadway deformation [1, 2, 3]. Moreover, abnormal pressure distributions may compromise the stability of surrounding coal pillars through stress transfer mechanisms, potentially affecting adjacent mining zones [4, 5]. These safety concerns are particularly pronounced in modern mining operations, where increasing mining depths and expanding production scales amplify the complexity of stress regime management. Therefore, comprehensive characterization and precise prediction of stress magnitude and distribution patterns in goaf regions have become imperative for ensuring operational safety in longwall mining environments. Previous investigations have examined the mechanical response and geomaterial deformation patterns in goaf environments through analytical frameworks and computational modeling approaches [6; 7; 8]. [PERSON] et al. [9] demonstrated that subsurface mass movement profiles more accurately reflect field conditions when characterized by negative exponential functions. [PERSON] et al. [10] performed a coupled analysis of mining-induced stress regimes and the characteristics of bifurcated zones (fragmented and fractured domains) within an overburden sequence by simulating their distinct features, revealing exponential pressure evolution during waste material consolidation. [PERSON] et al. [11] categorized stress distributions within rock masses into five domains based on principal stress extrema. [PERSON] et al. [12] established a computational methodology for stress field determination in room-and-pillar environments utilizing superposition principles. [PERSON] et al. [13] introduced concepts including the \"confined roof behavior principle\", \"quaternary temporal phases\", and the strata-floor mass interaction under spatiotemporal conditions through field observations. While these studies elucidated the failure mechanisms of superincumbent strata and constitutive behavior in goaf regions, the practical implementation of stress monitoring remains challenging due to the limitations of conventional monitoring approaches. In addition, the goaf treatment method has a significant impact on the surrounding stress distribution, and the filling method can effectively regulate the stress state of the surrounding rock. Compared with the alternating distribution of the stress concentration and pressure relief zone caused by the natural collapse method, the backfill method can reduce the stress of the original rock by 30-70% by actively supporting the surrounding rock. The primary challenge in goaf stress monitoring lies in sensor deployment and data acquisition. Traditional monitoring methods rely on instruments installed directly in the coal seam floor, making them vulnerable to damage from roof caving during mining operations. Furthermore, conventional physical simulation experiments typically employ discrete monitoring devices, such as extensometers and surveying instruments [14; 15; 16], which provide only localized resolution and exhibit operational complexity. These limitations have motivated the exploration of alternative monitoring technologies, particularly the implementation of distributed optical fiber sensing technology (DOFS) [17; 18; 19]. DOFS presents several distinctive advantages for goaf stress field monitoring. First, by installing optical fibers in the key stratum that experiences relatively less impact, rather than in the coal seam floor, the system achieves stable continuous monitoring throughout the entire mining process. Second, the technology offers superior durability and reliability, with optical fiber materials demonstrating strong corrosion resistance and an operational lifespan exceeding 20 years under normal conditions.