Adaptive calibration iTMB2-iFEM for thermal-mechanical coupling deformation monitoring

Abstract

Accurate deformation monitoring of aircraft wing beams under thermal-mechanical coupling loads is vital to flight safety and structural performance optimization. Fiber Bragg Grating (FBG) sensors combined with the inverse finite element method (iFEM) are promising for real-time strain-based deformation reconstruction. However, conventional iFEM neglects thermal-mechanical coupling, and FBG's temperature-strain cross-sensitivity degrades monitoring accuracy in practical aerospace environments. To address these issues, this study proposes an adaptive calibration iTMB2-iFEM framework for complex beam structures under thermal-mechanical coupling loads. A novel two-node inverse thermal-mechanical beam element (iTMB2) is developed, which integrates thermal-expansion degrees of freedom into the displacement-field expression of 1D inverse beam elements for synchronous reconstruction of mechanical and thermal deformation. An adaptive calibration strategy based on the Quasi-Newton method is designed to optimize the FBG strain-sensitivity coefficients by minimizing the error between the Digital Image Correlation (DIC)- measured displacement and the iTMB2-iFEM-reconstructed displacement under reference loads. Numerical simulations on a civil wing beam structure verify that the proposed iTMB2-iFEM outperforms the traditional iHB2-iFEM, with a reconstruction RMSE of 0.09 mm for thermal-mechanical coupling deformation. Experimental validation at 25 °C, 40 °C, and 60 °C with a 5 kN mechanical load shows that the adaptive calibration iTMB2-iFEM achieves a deformation reconstruction RMSE of <0.12 mm, verifying its high accuracy and engineering applicability for thermal-mechanical coupling deformation monitoring of complex beam structures.