Real-time demodulation of complex FBG spectra via dictionary-enhanced sparse Bayesian learning

We propose a dictionary Gaussian sparse Bayesian learning (DG-SBL) framework for the comprehensive demodulation of complex fiber Bragg grating (FBG) spectra, particularly those characterized by multi-peak structures, non-standard shapes, and significant overlap. The framework consists of two distinct stages: dictionary learning and real-time demodulation. In the dictionary learning stage, an alternating iterative optimization of atoms and coefficients is employed to successively approximate the signal. By incorporating a determinate number of fiber gratings as a natural K-sparsity constraint, the complexity of this learning phase is significantly reduced, yielding both a calibrated dictionary and a noise precision estimate. In the real-time demodulation stage, the spectra are reconstructed using the learned dictionary atoms. A hybrid tracking strategy is utilized: if the reconstruction error falls within the estimated noise precision, a direct translational matching is applied; otherwise, a covariance-free Bayesian algorithm is invoked to re-search for optimal atoms within the dictionary. This covariance-free property drastically lowers the computational complexity of waveform reconstruction. Experimental results on grating spectral signals (30 nm range, 0.01 nm resolution) demonstrate the method's effectiveness: waveform reconstruction achieves a cosine similarity of >99.99%, with an average processing time of 0.021 s per frame during learning and a tracking latency below 0.2 ms. Furthermore, the proposed directional weighting strategy effectively separates overlapping signals, offering a scalable solution for real-time sparse recovery in industrial monitoring applications.