Bearing incipient fault diagnosis based upon maximal spectral kurtosis TQWT and group sparsity total variation denoising approach

Localized faults in rolling bearing tend to result in periodic shocks and thus arouse periodic responses in the vibration signal. In this paper, a novel fault diagnosis method based on maximal spectral kurtosis tunable Q-factor wavelet transformation (TQWT) and group sparsity total variation denoising (GS-TVD) is proposed to address the issue of bearing incipient failure. Firstly, the range of Q-factor was pre-selected according to the spectral distribution of impulse component, and bearing vibration signal was transformed by the TQWT method. Then, the spectral kurtosis of each scale transform coefficients was calculated, and the optimal Q-factor and decomposition scale can be selected according to the kurtosis maximum principle. In order to remove the interference components and high-frequency noise from the reconstructed vibration signal generated by inverse TQWT, the GS-TVD approach is employed, thus the cyclic periodicity characteristic and transient impulses can be detected obviously. The two cases experimental results indicate that the proposed technique is more effective and applicable for bearing incipient fault diagnosis compared with traditional method

A Convex-Nonconvex Strategy for Grouped Variable Selection

This paper deals with the grouped variable selection problem. A widely used strategy is to augment the negative log-likelihood function with a sparsity-promoting penalty. Existing methods include the group Lasso, group SCAD, and group MCP. The group Lasso solves a convex optimization problem but is plagued by underestimation bias. The group SCAD and group MCP avoid this estimation bias but require solving a nonconvex optimization problem that may be plagued by suboptimal local optima. In this work, we propose an alternative method based on the generalized minimax concave (GMC) penalty, which is a folded concave penalty that maintains the convexity of the objective function. We develop a new method for grouped variable selection in linear regression, the group GMC, that generalizes the strategy of the original GMC estimator. We present an efficient algorithm for computing the group GMC estimator and also prove properties of the solution path to guide its numerical computation and tuning parameter selection in practice. We establish error bounds for both the group GMC and original GMC estimators. A rich set of simulation studies and a real data application indicate that the proposed group GMC approach outperforms existing methods in several different aspects under a wide array of scenarios.Comment: 33 pages, 4 figure

On Solving SAR Imaging Inverse Problems Using Non-Convex Regularization with a Cauchy-based Penalty

Synthetic aperture radar (SAR) imagery can provide useful information in a multitude of applications, including climate change, environmental monitoring, meteorology, high dimensional mapping, ship monitoring, or planetary exploration. In this paper, we investigate solutions to a number of inverse problems encountered in SAR imaging. We propose a convex proximal splitting method for the optimization of a cost function that includes a non-convex Cauchy-based penalty. The convergence of the overall cost function optimization is ensured through careful selection of model parameters within a forward-backward (FB) algorithm. The performance of the proposed penalty function is evaluated by solving three standard SAR imaging inverse problems, including super-resolution, image formation, and despeckling, as well as ship wake detection for maritime applications. The proposed method is compared to several methods employing classical penalty functions such as total variation ($TV$) and $L_1$ norms, and to the generalized minimax-concave (GMC) penalty. We show that the proposed Cauchy-based penalty function leads to better image reconstruction results when compared to the reference penalty functions for all SAR imaging inverse problems in this paper.Comment: 18 pages, 7 figure

SWAGGER: sparsity within and across groups for general estimation and recovery

Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within arbitrary overlapping groups in a vector. This allows one to enforce mutual exclusivity between components within solutions to optimization problems. We show multiple example use cases (including a total variation variant), demonstrate synergy between it and other regularizers, and propose an algorithm to efficiently solve problems regularized or constrained by the proposed penalty.First author draf