Improvement of VMD for anomalous collision disturbance based on nonlinear l 1/2 norm

Abstract

Abstract Variational mode decomposition (VMD) is widely used in the fault diagnosis of rotating equipment. The kurtosis index is typically utilized as the objective function to determine the optimal decomposition mode in conventional VMD. However, kurtosis is easily interfered with by abnormal impact signals, seriously affecting the accuracy of VMD in the fault extraction process. Therefore, the instability of the kurtosis index for anomalous disturbances should be addressed. In addition, the number of modal decompositions K and the penalty factor α are not wisely selected, exerting a significant influence on the decomposition effect of VMD. In this study, we propose an enhanced method for fault diagnosis of rotating machineries under abnormal impact interference, namely the improved nonlinear VMD method based on the l 1/2 norm (INVL). Initially, we employ the whale optimization algorithm to optimize the combination of parameters [ K , α ] with the aim of achieving the most favorable decomposition outcomes. Subsequently, the decomposed modes undergo preprocessing using the nonlinear tanh function to mitigate the impact of amplitude shocks. Furthermore, we utilize the sparse l 1/2 norm to select fault feature components, thereby evaluating the sparse distribution of modes. The modes exhibiting the lowest l 1/2-norm values are chosen for information reconstruction and envelope analysis. To assess the effectiveness of the proposed method, we conduct simulations and experimental verifications. The results demonstrate that the INVL method effectively suppresses abnormal shocks and successfully extracts bearing fault features in the presence of anomalous collision disturbances.