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Symmetry 2018, 10(7), 243; https://doi.org/10.3390/sym10070243

Weak Fault Detection for Gearboxes Using Majorization–Minimization and Asymmetric Convex Penalty Regularization

1
College of Mechanical Engineering, Donghua University, Shanghai 201620, China
2
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
*
Author to whom correspondence should be addressed.
Received: 5 June 2018 / Revised: 14 June 2018 / Accepted: 16 June 2018 / Published: 26 June 2018
(This article belongs to the Special Issue Symmetry in Computing Theory and Application)
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Abstract

It is a primary challenge in the fault diagnosis community of the gearbox to extract the weak fault features under heavy background noise and nonstationary conditions. For this purpose, a novel weak fault detection approach based on majorization–minimization (MM) and asymmetric convex penalty regularization (ACPR) is proposed in this paper. The proposed objective cost function (OCF) consisting of a signal-fidelity term, and two parameterized penalty terms (i.e., one is an asymmetric nonconvex penalty regularization term, and another is a symmetric nonconvex penalty regularization term).To begin with, the asymmetric and symmetric penalty functions are established on the basis of an L1-norm model, then, according to the splitting idea, the majorizer of the symmetric function and the majorizer of the asymmetric function are respectively calculated via the MM algorithm. Finally, the MM is re-introduced to solve the proposed OCF. As examples, the effectiveness and reliability of the proposed method is verified through simulated data and gearbox experimental real data. Meanwhile, a comparison with the state of-the-art methods is illustrated, including nonconvex penalty regularization (NCPR) and L1-norm fused lasso optimization (LFLO) techniques, the results indicate that the gear chipping characteristic frequency 13.22 Hz and its harmonic (2f, 3f, 4f and 5f) can be identified clearly, which highlights the superiority of the proposed approach. View Full-Text
Keywords: sparse regularization; majorization minimization (MM); asymmetric convex penalty regularization (ACPR); gearbox weak; gearbox sparse regularization; majorization minimization (MM); asymmetric convex penalty regularization (ACPR); gearbox weak; gearbox
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Li, Q.; Liang, S.Y. Weak Fault Detection for Gearboxes Using Majorization–Minimization and Asymmetric Convex Penalty Regularization. Symmetry 2018, 10, 243.

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