Generalized Multivariate Symplectic Sparsest United Decomposition for Rolling Bearing Fault Diagnosis

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The non-stationary characteristics of the vibration signals of rolling bearings will be aggravated under variable speed conditions. Meanwhile, multichannel signals can provide a more comprehensive characterization of state information, providing multiple sources of information that facilitate information fusion and enhancement. However, traditional adaptive signal decomposition methods generally assume that the frequency information is constant and stationary, and it is difficult to achieve a unified decomposition when dealing with multichannel time-varying signals. Therefore, the intention of this paper is to propose a multichannel signal adaptive decomposition method applicable to variable speed conditions. Specifically, this paper takes advantage of the strong adaptability and robustness of symplectic geometric mode decomposition (SGMD). To improve its applicability to multichannel time-varying signals at variable rotational speeds, a generalized multivariate symplectic sparsest united decomposition (GMSSUD) method is proposed. In GMSSUD, firstly, the completely adaptive projection (CAP) method is employed to achieve a unified representation of the multichannel signals. Then, the generalized demodulation method is introduced to stabilize the signal and subsequently reduce the noise through component screening and reconstruction. Finally, with the new proposed operator as the optimization objective, the constructed sparse filter parameters are optimized to achieve the frequency band segmentation. The analysis results demonstrate that the GMSSUD method possesses higher decomposition precision for multichannel signals with variable speeds and also has a stronger diagnosis ability for variable-speed bearing faults.