Symplectic Sparsest Mode Decomposition and its Application in Rolling Bearing Fault Diagnosis

A heated and challenging area of fault diagnostic research has been separating the rolling bearing problem feature information from severe noise disruption. The Symplectic Geometry Mode Decomposition (SGMD) has been effectively applied to rolling bearings with the advantage that it does not involve the subjective definition of parameters and eliminates noise when efficiently reconstructing the modes. Yet, it possesses the following shortcomings the invalid symplectic geometry component (SGC) affects the decomposition accuracy, and the physical meaning of the decomposition results is unclear. Inspired by nonparametric adaptive signal decomposition methods such as SGMD and Matching Pursuit (MP), the paper proposes the Symplectic Sparsest Mode Decomposition (SSMD) method. SSMD first constructs a library of symplectic geometry atoms and constrains the number of atoms by energy threshold, which effectively improves the decomposition speed; then, the quality of atoms and the robustness of the algorithm are improved by initialized adaptive noise reduction of symplectic geometry atoms; finally, symplectic geometry atoms are optimally reconstructed by genetic algorithms with the regularized locally narrowband operator as the optimization target, which obtains the sparsest solution of symplectic geometry mode components while constraining the decomposition result to be locally narrowband signals, so as to make better physical meaning of decomposition results. The comparative analysis results of simulation and experiment show that SSMD has obvious advantages in decomposition accuracy and noise robustness, and is more efficient relative to the decomposition of SGMD.