Noise Suppression in Nonstationary Signals by Integrating an Improved VMD With the Hilbert Transform

This paper proposes an improved variational mode decomposition (VMD) framework integrated with the Hilbert transform (HT) for decomposing and reconstructing nonstationary signals in high-noise, multi-frequency environments. Unlike traditional VMD methods, the proposed framework introduces a soft data fidelity constraint and a frequency alignment scheme to mitigate the effects of heavy-tailed noise and reduce mode mixing. Employing adaptive regularization in the transform domain further refines intrinsic mode extraction, capturing finer multi-scale details. An additional amplitude matching stage, driven by an LMS-based mechanism, adjusts gain factors to rebuild each component accurately. Experiments on synthetic signals demonstrate improved noise suppression and mode separation, as evidenced by lower RMSE/MAE and higher SNR and correlation values compared to traditional VMD. Across SNRs of 10, 15, and 20 dB, the proposed method consistently outperforms traditional VMD in RMSE/MAE, SNR, and correlation. Hilbert spectra for the two-tone signal and the real bearing signal exhibit sharper ridges and more concentrated energy, indicating improved mode separation and noise suppression. Furthermore, the HT-based timefrequency representation clearly illustrates energy concentration and instantaneous frequency variations, enabling time-frequency analysis of complex, nonstationary signals. These results underscore the potential of the improved VMD-HT framework for a wide range of applications in engineering, energy, and biomedical contexts, where robust, adaptive, and precise signal processing is critical.