## 6 Conclusions  
In this paper, the stress inversion method for a goat driven by optical fiber data is studied using the key stratum theory and optical fiber monitoring principles. A novel inversion formula for goat stress is derived, enabling precise monitoring of the pressure distribution within the goat. The method was rigorously verified through comprehensive physical model experiments. Compared with traditional detection methods, distributed fiber sensing technology has the characteristics of real-time monitoring, and the analysis of data can be synchronized through computer programming. It can significantly improve the efficiency and response speed of goat pressure monitoring. The main conclusions are as follows:  
1. A pioneering goat pressure inversion model has been developed, driven by distributed optical fiber monitoring data, which effectively characterizes critical layer subsidence through distinct pre-fracture and post-fracture phases. The sophisticated mathematical framework captures the intricate coupling relationship between optical fiber sensors and rock mass deformation, revealing a definitive correlation between key stratum failure locations and peak stress positions within the goat area. This fundamental understanding substantially advances our knowledge of the internal mechanisms governing rock mass deformation and stress redistribution patterns during mining operations.
2. The innovative implementation of a dual monitoring system, integrating BOTDA and DIC technologies, demonstrates exceptional reliability in predicting overburden rock fracture patterns and quantifying critical deformation thresholds. Through rigorous experimental investigations, we have conclusively established a critical strain threshold of 4000 \(\mu\epsilon\) for key stratum fracture initiation, with pre-fracture rock mass strain consistently maintaining values below this threshold. This precise quantitative parameter marks a significant advancement in mining safety monitoring, enabling the development of accurate early warning systems and facilitating proactive risk management through continuous, real-time strain measurements.
3. Through systematic physical model experiments, we have comprehensively validated the effectiveness of our optical fiber monitoring data inversion methodology in characterizing both spatial distribution and temporal evolution of goat stress patterns. The experimental results conclusively demonstrate a characteristic \"U-shaped\" pressure distribution across the goat area, with measurement deviations consistently maintained within 8.88% across various advancement stages. This thorough validation not only confirms the theoretical framework's accuracy but also provides crucial insights into the dynamic evolution of mining-induced stress fields. These findings establish a robust foundation for enhanced mining safety assessment and control strategies, offering immediate practical applications in real-world mining operations.  
Conceptualization, J.C. and Z.Y.; methodology D.Z. and Y.O.; data curation, Z.Y. and J.Y.; writing--original draft preparation, G.Y. and C.M.; writing--review and editing, Z.Y. All authors have read and agreed to the published version of the manuscript.  
This work was supported by financial support from the Henan Province Science and Technology Projects (Grants No. 252102211032, 242102220091, 252102210090 and 242102211010), the Key Projects of Water Conservancy Science and Technology in Henan Province (Grant No. GG202441), and the National Level General Project Cultivation Project (Grant No. 23 HNCDJ49, School Level).  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in this article; further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The research content in this paper is experimental and there are no conflicts of interest.