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• A novel iteratively reweighted accurate sparse low-rank (IRASLR) matrix estimation algorithm is proposed. • An equivalent variant of minimax concave penalty (MCP) is constructed. • The equivalent weighted MCP and equivalent weighted matrix γ - n o r m are defined with their proximal operators provided. • The simulation and experiment signal proved that the proposed IRASLR method shows better reconstruction accuracy. Bearing fault diagnosis is significant to ensure the safe functioning of mechanical systems. One of the key issues in bearing fault diagnosis is the accurate and effective extraction of fault characteristic features. In order to further explore the construction of penalty function, further alleviate the problem of bias estimation and enhance the capabilities of the sparse low-rank (SLR) method in effectively diagnosing bearing faults, in this paper, an iteratively reweighted accurate sparse low-rank (IRASLR) matrix estimation algorithm is proposed. Taking the sparse and low-rank properties of fault transient signals in time–frequency domain into account, an optimization problem is formulated. Two penalty functions, derived from a core minimax-concave penalty (MCP), induce sparse and low-rank properties, respectively. Specifically, to facilitate the design of weighting schemes, we construct an equivalent variant of MCP (EVMCP). By separately extending EVMCP to matrix elements and singular values, we obtain equivalent weighted MCP and equivalent weighted matrix γ - n o r m. Finally, based on the proximal operators of the two penalty functions, we deduce an IRASLR algorithm under the alternating direction method of the multipliers (ADMM) framework. The performance of IRASLR is verified by processing simulated and experimental signals, while the superiority of the algorithm is confirmed through comparative experiments. [ABSTRACT FROM AUTHOR]

The bearing fault impact impulses induced by the contact between components with drawback, is difficult to be detected at sprouting stage due to the interference of background noise, harmonics, random shocks, etc. In this paper, an impulse feature enhanced weighted sparse representation (IFEWSR) algorithm is proposed to accurately detect the weak bearing fault impact feature from incipient stage condition monitoring (CM) signal. Firstly, a modified fault period estimation method is presented to improve the robustness and reduce the computational complexity of recently proposed algorithms. Secondly, a novel weighting strategy on wavelet coefficients, indicated by the period-assisted corelated kurtosis of envelope spectrum (CKSES), is presented to denote the contribution of subband signals for sparse representation calculation framework. In addition, the mean normalized energy-weight deviation (MNEWD) rule is proposed to evaluate the performance of the weighting algorithm on subband signals which is blank at present. Thirdly, a novel fault feature enhancement technique is developed to better capture the bearing fault feature information. The effectiveness and superiority of the proposed method are proved by simulation and experiments. Results show that the proposed IFEWSR method provides higher accuracy for incipient fault feature extraction and outperforms other state-of-the-art methods. [ABSTRACT FROM AUTHOR]