Double-layer non-negative matrix factorization for vibration-impulse separation

Abstract Accurate separation of transient impulses from vibration responses is fundamental for mechanical-defect identification. Whereas non-negative matrix factorization (NMF) inherently supports component separation through low-rank approximation, conventional implementations relying on direct time–frequency distribution clustering show constrained performance in complex scenarios. Based on the advantages of multilayer NMF, this study proposes a double-layer NMF model that integrates adaptive band decomposition, periodic feature weighting, and feature-band fusion. The first layer applies a smooth orthogonal robust NMF to obtain full frequency-band decomposition, followed by autocorrelation kurtosis-based weighting, which amplifies the periodic components of the coefficient matrix. The second layer implements a sparse weighted NMF with Euclidean distance for feature clustering, thus generating a consolidated impact-sensitive frequency band. This approach shifts the separation criterion from band-energy dominance to fault characteristic guidance. Validation via simulated and experimental case studies confirms that the model effectively resolves overlapping transient components and outperforms conventional decomposition methods in terms of impulse-source separation.