Real-Time Surface Temperature Reconstruction of Thermal Protection Structures via Deep-Embedded Sensors Without Explicit Thermophysical-Property Information

Monitoring the surface thermal state of thermal protection structures (TPS) is essential for the safe operation and health assessment of hypersonic vehicles. However, direct sensor deployment on heated surfaces suffers from poor survivability, while many model-based approaches require prescribed thermophysical properties and boundary conditions. This study proposes an AutoRegressive with eXogenous input (ARX)-based surface temperature reconstruction method using deep-embedded sensors. By identifying a local equivalent dynamic mapping among internal temperature responses, the method reconstructs the near-surface temperature through virtual-point recursive extrapolation without requiring explicit thermophysical-property or boundary-condition information. Numerical simulations show high accuracy under adiabatic, natural-convection, and forced-convection rear-surface boundaries, with the global RRMSE remaining within 1.09%. Further analyses demonstrate tolerance to moderate temperature- and space-dependent variations in equivalent thermophysical properties; simulations using realistic LI-900 thermal conductivity variations confirm its applicability under different effective conductivity conditions. Single-sided heating experiments with two sensor-embedding layouts validate the method, yielding RRMSE values of 1.74% for the 5-point model and 4.27% for the 9-point model in the main validation case. The applicable conditions are further clarified through analyses of internal temperature-difference SNR, recursive error accumulation, and sensor-layout constraints. The proposed method provides a low-cost and long-life solution for online TPS surface temperature monitoring.