Inverse heat transfer for real-time thermal evaluation of aircraft thermal protection structure with embedded FBG sensors

Thermal Protection Structures (TPSs) are indispensable parts of aircraft. In the context of high-speed aviation vehicles, surface thermal information of the TPS is vital to ensuring the safe operation of the aircraft. However, the real-time measurement of surface thermal information becomes a great challenge due to the complex and volatile flight environment. In this paper, we propose a method for real-time monitoring of the TPS' surface temperature by using embedded temperature sensors processed with inverse heat conduction model. In the investigation, tube packaged FBG (TP-FBG) sensors that were insensitive to strain and vibration were employed as embedded sensors in thermal protection composites. In the signal processing, thermal hysteresis correction model based on the Fourier heat conduction theory was established. After that, the data processing method of Auto-Regression with eXtra inputs was used to process the data of the sensors. The measurement error and response delay of bare FBG sensor, thermocouple and TP-FBG sensors are compared by a transient thermal shock experiment. The experiment results show that thermal hysteresis effect of the TP-FBG sensors is significant. However, the correction model can effectively correct the measurement errors of TP-FBG caused by thermal hysteresis. Building upon the model, two inverse heat conduction methods with adaptive boundaries were proposed. These methods can retrieve surface thermal information by processing the measured temperatures from embedded sensors. Numerical simulations demonstrate that while the instantaneous heating moment may exhibit significant relative errors, the average relative error remains below 5.54%. Experimental validation using a quartz lamp to heat real TPS materials further confirms the effectiveness of the inversion method. The method successfully mitigates the influence of process deviations during sensor embedding and material preparation, maintaining an average relative error of less than 8.53%. These findings suggest the potential for the proposed correction model and inversion methods in practical engineering applications. Particularly, their applicability to dynamic high temperature monitoring of thermal protection composites.