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Algorithms 2018, 11(11), 184; https://doi.org/10.3390/a11110184

Weak Fault Detection of Tapered Rolling Bearing Based on Penalty Regularization Approach

1,* and 1,2
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: 7 October 2018 / Revised: 31 October 2018 / Accepted: 31 October 2018 / Published: 8 November 2018
(This article belongs to the Special Issue Dictionary Learning Algorithms and Applications)
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Abstract

Aimed at the issue of estimating the fault component from a noisy observation, a novel detection approach based on augmented Huber non-convex penalty regularization (AHNPR) is proposed. The core objectives of the proposed method are that (1) it estimates non-zero singular values (i.e., fault component) accurately and (2) it maintains the convexity of the proposed objective cost function (OCF) by restricting the parameters of the non-convex regularization. Specifically, the AHNPR model is expressed as the L1-norm minus a generalized Huber function, which avoids the underestimation weakness of the L1-norm regularization. Furthermore, the convexity of the proposed OCF is proved via the non-diagonal characteristic of the matrix BTB, meanwhile, the non-zero singular values of the OCF is solved by the forward–backward splitting (FBS) algorithm. Last, the proposed method is validated by the simulated signal and vibration signals of tapered bearing. The results demonstrate that the proposed approach can identify weak fault information from the raw vibration signal under severe background noise, that the non-convex penalty regularization can induce sparsity of the singular values more effectively than the typical convex penalty (e.g., L1-norm fused lasso optimization (LFLO) method), and that the issue of underestimating sparse coefficients can be improved. View Full-Text
Keywords: sparse regularization; augmented Huber non-convex penalty regularization (AHNPR); L1-norm regularization; weak fault detection; tapered rolling bearing sparse regularization; augmented Huber non-convex penalty regularization (AHNPR); L1-norm regularization; weak fault detection; tapered rolling bearing
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Li, Q.; Liang, S.Y. Weak Fault Detection of Tapered Rolling Bearing Based on Penalty Regularization Approach. Algorithms 2018, 11, 184.

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