LAUSR

This study proposes a fiber Bragg grating (FBG) sensing system integrated with the conjugate beam method (CBM) and frequency analysis to reconstruct the deformation of cantilever beams. Distributed strain data from the FBG array were transformed into displacement profiles and subsequently validated against beam theory and finite element method (FEM). The reconstructed deformation exhibited close agreement, with root-mean-square error (RMSE) typically below 2% under static loading, confirming the accuracy and reliability of the FBG-CBM methodology in static deformation measurement. Besides, in the dynamic domain, the extracted modal frequencies closely matched FEM predictions, while frequency-domain analysis demonstrated the system’s ability to capture broadband resonant responses up to 14 kHz. Modal amplitudes obtained via (short-time) fast Fourier transform were incorporated into the reconstruction, enabling dynamic displacement estimation, accurate modal identification, and damping ratio. The resonant frequency and mode shape have an RMSE of less than 0.2% and 4.41%, respectively, compared to the FEM and theoretical solutions. These results highlight the dual capability of the proposed FBG sensing technology for both displacement reconstruction and frequency characterization, demonstrating its suitability for compact and scalable structural health monitoring (SHM) in beam structures.