Reweighted Dual Sparse Regularization and Convex Optimization for Bearing Fault Diagnosis

Abstract

Performing early and accurate bearing fault diagnosis is of great significance. However, accurate extraction of the repetitive transients from noisy vibration signals is a critical issue. In this article, a reweighted dual sparse regularization (RDSR) method is proposed for bearing fault diagnosis, and the RDSR is a unified framework of the reweighted generalized minimax-concave (reGMC) penalty and the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm regularization. To be specific, the reGMC penalty and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm are both introduced in the sparse coding model. The reGMC is utilized to enhance the sparsity and overcome the underestimation deficiency of the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm while restraining the interference. Moreover, the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm is employed to simplify the model and overcome the overfitting problem, which can make the optimization process rapid and stable. Therefore, it can observably enhance the accuracy of bearing fault diagnosis and preserve the amplitude of the fault transient component. Comparisons with ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization model and the conventional spectral kurtosis (SK) show that the proposed method can preserve the spectral peak of the periodic transient components and improve the signal-to-noise ratio (SNR). Experimental case studies further verify that the proposed method can accurately estimate the periodic transient component from vibration signals, which demonstrates that the proposed method is feasible for bearing fault diagnosis.