A Novel Signal Denoising Method Using an Analytical Signal-Based SVD and Its Applications in Bearing Fault Diagnosis

The use of singular value decomposition (SVD) under the Hankel matrix has emerged as a powerful technique for denoising non-stationary signals. The efficacy of the denoising process is significantly influenced by the structure of the Hankel matrix and the selection of subsignals. This article systematically investigates these factors and introduces an analytical signal-based SVD (A-SVD) method. Initially, the analytical signal is introduced. This is based on the observed correlation between subsignals, aiming to reduce this correlation. Subsequently, a parameter unit energy change index (ECI) is introduced for assessing the decomposition's stability across different Hankel matrices, aiming to optimize the structure of the Hankel matrix. Moreover, the group Gini index (GGI) of the reconstructed signal is utilized to select the optimal denoised signal. Lastly, the envelope spectrum is utilized for the analysis and extraction of relevant fault features. The effectiveness and superiority of the A-SVD method are confirmed through its application to both simulated bearing fault signals and two actual bearing fault cases.