Symplectic weighted sparse support matrix machine for gear fault diagnosis

Abstract For gear fault diagnosis, it is often encountered that the input samples are naturally constructed as two-dimensional feature matrices with rich structure information. Support matrix machine (SMM) is an effective classifier for these matrix data, which fully leverages the matrix structure information. However, it is indispensable for SMM to artificially extract fault features and select the useful features, which requires plenty of professional knowledge. Hence, a symplectic weighted sparse SMM (SWSSMM) model is proposed in this paper. Under the concept of symplectic geometry, SWSSMM automatically extracts the symplectic weighted coefficient matrix (SWCM) as the fault feature representation. Meanwhile, the sparsity constraint and low-rank constraint are used in SWSSMM to eliminate the redundant fault features and capture the geometry structure information of SWCM, respectively. Besides, we derive an effective solver for SWSSMM with fast convergence. The experiment results demonstrate the superiority of SWSSMM for gear fault diagnosis.

[1]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[2]  Zhaowei Shang,et al.  Scattering transform and LSPTSVM based fault diagnosis of rotating machinery , 2018 .

[3]  Xin Li,et al.  An early fault diagnosis method of gear based on improved symplectic geometry mode decomposition , 2020 .

[4]  David Chelidze,et al.  Statistical Characterization of Nearest Neighbors to Reliably Estimate Minimum Embedding Dimension , 2014 .

[5]  Liu Yang,et al.  Fault diagnosis of gearbox based on RBF-PF and particle swarm optimization wavelet neural network , 2019, Neural Computing and Applications.

[6]  Jian Liu,et al.  Data-driven time-frequency analysis method based on variational mode decomposition and its application to gear fault diagnosis in variable working conditions , 2019, Mechanical Systems and Signal Processing.

[7]  Kup-Sze Choi,et al.  Deep stacked support matrix machine based representation learning for motor imagery EEG classification , 2020, Comput. Methods Programs Biomed..

[8]  Yuan Yan Tang,et al.  Low-rank matrix regression for image feature extraction and feature selection , 2020, Inf. Sci..

[9]  Edgard M. Maboudou-Tchao Wavelet Kernels for Support Matrix Machines , 2019, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health.

[10]  Hao Zheng,et al.  A new fault diagnosis method for planetary gear based on image feature extraction and bag-of-words model , 2019, Measurement.

[11]  Phillip L. De Leon,et al.  The Instantaneous Spectrum: A General Framework for Time-Frequency Analysis , 2018, IEEE Transactions on Signal Processing.

[12]  Xin Li,et al.  A novel deep stacking least squares support vector machine for rolling bearing fault diagnosis , 2019, Comput. Ind..

[13]  Pheng-Ann Heng,et al.  Robust Support Matrix Machine for Single Trial EEG Classification , 2018, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[14]  Yu Yang,et al.  Kernel flexible and displaceable convex hull based tensor machine for gearbox fault intelligent diagnosis with multi-source signals , 2020 .

[15]  Xin Li,et al.  Non-parallel least squares support matrix machine for rolling bearing fault diagnosis , 2020 .

[16]  G. Kotliar,et al.  Spectral density functionals for electronic structure calculations , 2001, cond-mat/0106308.

[17]  Pheng-Ann Heng,et al.  Multiclass support matrix machine for single trial EEG classification , 2018, Neurocomputing.

[18]  Niaoqing Hu,et al.  Fault diagnosis of sun gear based on continuous vibration separation and minimum entropy deconvolution , 2019, Measurement.

[19]  Richard G. Baraniuk,et al.  Fast Alternating Direction Optimization Methods , 2014, SIAM J. Imaging Sci..

[20]  Haiyang Pan,et al.  Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis , 2019, Mechanical Systems and Signal Processing.

[21]  Chao Yang,et al.  Some Remarks on the Complex J-Symmetric Eigenproblem , 2018 .

[22]  Xuejun Li,et al.  Gear fault diagnosis based on support vector machine optimized by artificial bee colony algorithm , 2015 .

[23]  Baoping Tang,et al.  A novel fault diagnosis model for gearbox based on wavelet support vector machine with immune genetic algorithm , 2013 .

[24]  Yongbo Li,et al.  A method based on refined composite multi-scale symbolic dynamic entropy and ISVM-BT for rotating machinery fault diagnosis , 2018, Neurocomputing.

[25]  Xiao-Sheng Si,et al.  A rotating machinery fault diagnosis method based on multi-scale dimensionless indicators and random forests , 2020, Mechanical Systems and Signal Processing.

[26]  Cheng Zhang,et al.  Transient extraction based on minimax concave regularized sparse representation for gear fault diagnosis , 2020 .

[27]  Mohamed-Jalal Fadili,et al.  A Generalized Forward-Backward Splitting , 2011, SIAM J. Imaging Sci..