A Novel Fault Diagnosis Method for Rolling Bearing Based on Improved Sparse Regularization via Convex Optimization

Dongjie Zhong,Cancan Yi,Houzhuang Zhang,Han Xiao,Anding Wu

doi:10.1155/2018/2169364

Abstract

Structural health monitoring and fault state identification of key components, such as rolling bearing, located in the mechanical main drive system, have a vital significance. The acquired fault signal of rolling bearing always presents the obvious nonlinear and nonstationary characteristics. Moreover, the concerned features are submerged in strong background noise. To handle this difficulty, a novel fault signal denoising scheme based on improved sparse regularization via convex optimization is proposed to extract the fault feature of rolling bearing. In this paper, the generalized minimax-concave (GMC) penalty is firstly researched to promote the sparsity of signal, which is based on traditional L1-norm and Huber function. It is designed to estimate the sparse solutions more accurately and maintain the convexity of the cost function. Then, the GMC penalty is extended to 1-D first-order total variation (TV) as nonseparability and nonconvex regularizer. Thus, a convex optimization problem, which involves a quadratic data fidelity term and a convex regularization term, is developed in this paper. To accelerate the convergence of the algorithm, it is solved by forward-backward (FB) iterative algorithm and thus the denoised signal can be obtained. In order to demonstrate its performance, the proposed method is illustrated for numerical simulation signal and applied in the feature extraction of the measured rolling bearing vibration signal.

Highlights

In the field of prognostics and health management (PHM) to mechanical equipment, the actual collected vibration signal contains wealthy information about operating status [1,2,3]
Inspired by the idea of jointing the nonconvex penalty and convex optimization algorithm, the traditional L1-norm regularization term is replaced by generalized MC (GMC) penalty in the total variation (TV) denoising scheme in this paper so as to effectively realize fault state identification
Where A is an oversampled inverse discrete Fourier transform, ψB:RN → R is the generalized MC (GMC) penalty defined by (7), λ is the regularization parameter, and the symbol of Dx stands for the TV operator

Summary

Introduction

In the field of prognostics and health management (PHM) to mechanical equipment, the actual collected vibration signal contains wealthy information about operating status [1,2,3]. Variational mode decomposition (VMD) [15, 16] is proposed based on Wiener filtering, one-dimensional Hilbert transform, and heterodyne demodulation analysis It is still affected by the selection of penalty parameter and the number of signal components. The novel denoising method based on convex optimization and sparsity has publicly employed in signal processing and image enhancement [19, 20] It has been successfully applied in the field of mechanical fault diagnosis [21], spectral data processing, and baseline correction [22]. Inspired by the idea of jointing the nonconvex penalty and convex optimization algorithm, the traditional L1-norm regularization term is replaced by GMC penalty in the TV denoising scheme in this paper so as to effectively realize fault state identification.

Theory Descriptions

Simulation Signal Analysis

Experimental Analyses

Conclusions

Conflicts of Interest