Fault feature extraction of sun gears using combined higher-order nonconvex total variation with overlapping group sparsity

Maintaining the health and safety of the sun gears is critical because these provide an essential part of the transmission power in planetary gearboxes. Firstly, to reduce the influence of planetary motion that introduces phase delay into the fault vibration signals of sun gears, this paper applies the vibration separation method for preprocessing. Then, the higher-order nonconvex total variation model based on overlapping group sparsity theory is developed, and thus overcomes the recognition problem of information error caused by the traditional total variation model under noise interference. The studied model of this paper incorporates regularization terms from different perspectives; the overlapping group sparsity well characterizes the intercrossing relationship between adjacent elements, while the high-order nonconvex norm improves solution smoothness. Therefore, the above two regularization terms are introduced into the total variation model to effectively improve the noise reduction performance of the model and make the fault feature of sun gears more prominent than those of other components. In addition, the variable-splitting strategy is employed to iteratively solve each subproblem and obtain the optimal solution of the model. Finally, the cyclic autocorrelation function is adopted to further process the model output, leveraging the noise suppression capability of cyclic cumulants. The fault-related spectral lines of the sun gears are more pronounced than other interference components. The studied method analyzes analysis of fault test vibration data demonstrates that the studied method effectively addresses the fault diagnosis problem of sun gears.