Robust identification of impact force acting on composite structures via a single FBG sensor using variational mode decomposition

Identifying impact force on composite structures is crucial for structural integrity assessment, yet it remains a formidable challenge under operational conditions where impact-induced vibrations are corrupted by ambient noise and other dynamic loads. To address this limitation, this paper develops a robust two-stage identification framework that requires only a single Fiber Bragg Grating (FBG) sensor. The core innovation of the proposed methodology lies in leveraging Variational Mode Decomposition (VMD) to decouple the complex, noisy strain signal into its constituent modal strain responses, effectively isolating the impact's signature from operational interference. From these purified modal responses, the uncorrected modal constant vector is extracted to serve as a unique fingerprint for impact localization over a grid of predefined potential impact points. The location is accurately determined by evaluating the cosine similarity between this vector and a pre-computed modal matrix of potential impact sites. Subsequently, with the location identified, the impact force's time history is reconstructed using a sparse deconvolution model, which is efficiently solved by the Alternating Direction Method of Multipliers (ADMM). Experimental validation on a composite plate with simplified airfoil geometry confirms the method's efficacy. The results demonstrate a localization success rate across the ten potential impact points exceeding 90% even under simulated operational conditions (harmonic and white noise excitation) and accurate force reconstruction, demonstrating the framework's promising robustness, efficiency, and practical applicability for in-service structural health monitoring (SHM).