Adaptive thermal-mechanics decoupled Fiber Bragg grating Sensors Based on the Fundamental Solutions and Measurements

This paper introduces a adaptively fundamental solutions (AFS) that incorporates an undetermined parameter and is based on the mirror image method and uncertainty handling strategies.  This approach utilizes fiber Bragg grating (FBG) technology for the simultaneous measurement of temperature, thermal stress, and external stress.  The core of this method involves adaptively fitting an AFS using temperature data from any point within the object.  Once fitted, the AFS can accurately calculate and capture the temperature distribution data of the object.  These data are then used as inputs for the temperature component of the FBG sensors, facilitating precise interpretation of the FBG's responses to thermal stress and external loads. To validate the high precision and practical applicability of this method, we conducted numerical simulations using finite element software.  These simulations verified the accuracy of our temperature calculations across all spatial and temporal domains, with the Normalized Mean Bias Error (NMBE) consistently within the range of [-5\%, 5\%].  Further, experimental validation confirmed that the thermal stress and external loads calculated using this method had NMBEs of 2.52\% and 1.37\%, respectively, compared to experimental results. The integration of advanced computational methods with high-precision measurement techniques is poised to effectively address thermal-mechanical coupling issues in applications such as tactile sensing, aircraft monitoring, and device protection.  This synergy is expected to significantly advance the development and application of these technologies.