Bearing Fault Diagnosis via Robust PCA With Nonconvex Rank Approximation

Feature extraction is an essential part of bearing fault diagnosis. Robust principal component analysis (RPCA) provides a general technique for extracting fault features. However, although the convex relaxed RPCA is convex and easy to optimize, the global optimal solution obtained may deviate significantly from reality. To address this issue, we propose a nonconvex RPCA method for bearing fault diagnosis, utilizing the
$\gamma $
norm penalty. Leveraging the unitary invariance property of the
$\gamma $
norm and the Moreau–Yosida operator, we transform the original equation into a singular value optimization problem using a difference of convex programming to obtain a feasible solution. The most important advantage of Nonconvex RPCA over conventional filtering methods is that it can improve fault feature extraction while decreasing noise interference, which results in substantially enhanced estimation accuracy of the bearing fault signal. Simulation analysis and experimental results confirm the effectiveness of the developed approach. Comparison experiments demonstrate that nonconvex RPCA provides more accurate extraction results compared to L1-norm regularization, variational mode decomposition (VMD), and feature mode decomposition (FMD).