Periodic sparse joint deconvolution and its application to bearing fault detection

Abstract

Rolling bearing fault detection under strong background noise remains a challenging task because fault-induced repetitive transients are usually weakened by the transmission path and masked by random interference. To address this issue, this paper proposes a periodic sparse joint deconvolution (PSJD) method for extracting weak bearing fault impulses from vibration measurements. The proposed method formulates bearing fault detection as an inverse filtering problem, in which the deconvolved signal is expected to exhibit both strong periodicity and high sparsity. Specifically, a multi-period correlation term is constructed to enhance repetitive impulses occurring at the fault characteristic period, while a logarithmic sparsity term is introduced to promote impulsive structures and suppress noise-related components. In addition, a regularization term is imposed on the inverse filter to improve numerical stability and avoid excessive oscillation of filter coefficients. The inverse filter is updated using a gradient-ascent scheme with normalization to remove scale ambiguity. The effectiveness of the proposed method is verified using simulated signals and experimental bearing vibration signals. The results demonstrate that the proposed method can effectively recover weak periodic transients and highlight fault characteristic frequencies in the envelope spectrum, even when the original signal is contaminated by strong noise. Compared with conventional deconvolution methods, the proposed method provides better capability in enhancing repetitive impulsive features and improving the reliability of bearing fault identification.