Double-Refined Symplectic Geometry Mode Decomposition

Symplectic geometric mode decomposition (SGMD) can preserve signal structure more stably and robustly than traditional amplitude modulated and frequency modulated (AM-FM) based mode decomposition algorithms. However, it focuses solely on the oscillatory modes of the signal, overlooking the presence of trends and noise, which leads to inaccurate oscillatory mode isolation and mode mixing. To address these issues, the double-refined symplectic geometric mode decomposition (DRSGMD) is proposed. DRSGMD establishes a refined signal-decomposition framework that supersedes single-oscillatory-mode framework of SGMD by explicitly incorporating trend and noise modes. Within this framework, the trend mode is proactively extracted to preliminarily refine the oscillatory mode and alleviate mode mixing. Furthermore, the oscillatory mode undergoes further refinement: the noise mode is isolated via the principal component analysis properties of singular value decomposition, and single components are merged using time-frequency domain information. Simulation results demonstrate that DRSGMD accurately decomposes all components of the simulated signal, yielding superior decomposition fidelity and robustness. Empirical validation on real-world datasets further confirms that DRSGMD effectively extracts artifact-free oscillatory modes from EEG recordings and attains high accuracy in fault detection of measured bearing dataset.