A Novel Mechanical Fault Diagnosis Scheme Based on the Convex 1-D Second-Order Total Variation Denoising Algorithm

Convex 1-D first-order total variation (TV) denoising is an effective method for eliminating signal noise, which can be defined as convex optimization consisting of a quadratic data fidelity term and a non-convex regularization term. It not only ensures strict convex for optimization problems, but also improves the sparseness of the total variation term by introducing the non-convex penalty function. The convex 1-D first-order total variation denoising method has greater superiority in recovering signals with flat regions. However, it often produces undesirable staircase artifacts. Moreover, actual denoising efficacy largely depends on the selection of the regularization parameter, which is utilized to adjust the weights between the fidelity term and total variation term. Using this, algorithms based on second-order total variation regularization and regularization parameter optimization selection are proposed in this paper. The parameter selection index is determined by the permutation entropy and cross-correlation coefficient to avoid the interference by human experience. This yields the convex 1-D second-order total variation denoising method based on the non-convex framework. Comparing with traditional wavelet denoising and first-order total variation denoising, the validity of the proposed method is verified by analyzing the numerical simulation signal and the vibration signal of fault bearing in practice.

[1]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[3]  Christopher Edwards,et al.  Nonlinear robust fault reconstruction and estimation using a sliding mode observer , 2007, Autom..

[4]  C. Edwards,et al.  Fault estimation for single output nonlinear systems using an adaptive sliding mode estimator , 2008 .

[5]  Mila Nikolova,et al.  Fast Nonconvex Nonsmooth Minimization Methods for Image Restoration and Reconstruction , 2010, IEEE Transactions on Image Processing.

[6]  Chao Liu,et al.  Wind farm power prediction based on wavelet decomposition and chaotic time series , 2011, Expert Syst. Appl..

[7]  Laurent Condat,et al.  A Direct Algorithm for 1-D Total Variation Denoising , 2013, IEEE Signal Processing Letters.

[8]  Camille Couprie,et al.  Dual constrained TV-based regularization , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[9]  Ivan W. Selesnick,et al.  Convex 1-D Total Variation Denoising with Non-convex Regularization , 2015, IEEE Signal Processing Letters.

[10]  Pengfei Liu,et al.  Efficient multiplicative noise removal method using isotropic second order total variation , 2015, Comput. Math. Appl..

[11]  Pengjian Shang,et al.  The coupling analysis of stock market indices based on cross-permutation entropy , 2015 .

[12]  Ronny Bergmann,et al.  A Second-Order TV-Type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data , 2015, Journal of Mathematical Imaging and Vision.

[13]  Yongbo Li,et al.  A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree , 2016 .

[14]  Cancan Yi,et al.  Research on Mechanical Fault Diagnosis Scheme Based on Improved Wavelet Total Variation Denoising , 2016 .

[15]  Wei-Chiang Hong,et al.  Electric load forecasting by the SVR model with differential empirical mode decomposition and auto regression , 2016, Neurocomputing.

[16]  Jiashu Zhang,et al.  Robust Kronecker product video denoising based on fractional-order total variation model , 2016, Signal Process..

[17]  Ming Liang,et al.  Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications , 2016 .

[18]  Wei Lu,et al.  A novel approach for analog fault diagnosis based on stochastic signal analysis and improved GHMM , 2016 .

[19]  Mohammed Imamul Hassan Bhuiyan,et al.  Computer-aided sleep staging using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and bootstrap aggregating , 2016, Biomed. Signal Process. Control..

[20]  Pavle Boškoski,et al.  Distributed bearing fault diagnosis based on vibration analysis , 2016 .

[21]  Teng Gong,et al.  A novel intelligent method for mechanical fault diagnosis based on dual-tree complex wavelet packet transform and multiple classifier fusion , 2016, Neurocomputing.

[22]  Ming Liang,et al.  Time–frequency analysis based on Vold-Kalman filter and higher order energy separation for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions , 2016 .

[23]  Junsheng Cheng,et al.  An intelligent fault diagnosis model for rotating machinery based on multi-scale higher order singular spectrum analysis and GA-VPMCD , 2016 .