Research on a novel weak fault detection method based on vibrational resonance in high-dimensional chaotic system, and variational mode decomposition

This paper constructs a high-dimensional Lorenz–Stenflo model by introducing perturbation parameters based on the Lorenz–Stenflo chaotic system. The theoretical framework of vibrational resonance is established by incorporating both low-frequency and high-frequency excitation signals into the system, where the high-frequency component enhances the system response to low-frequency signal, and thus enable weak-signal detection. Specifically, the dynamical characteristics of chaotic system are modified such that the response amplitude to the low-frequency signal reaches its extremum by tuning the amplitude or frequency of high-frequency signal. The mapping relationship is derived among the response amplitude gain of low-frequency signal, high-frequency excitation parameters, and system parameters. The non-monotonic variation of this relationship with respect to these parameters indicates the occurrence of vibrational resonance in the system. In addition, the output of vibrational resonance system is susceptible to interference under strong noise conditions. To mitigate this issue, the parameterized variational mode decomposition method is employed for preprocessing, effectively suppressing strong noise. Comparative analysis across different evaluation index demonstrates that fractional multiscale phase permutation entropy is suitable for selecting the optimal modal component. Experimental results show that the proposed vibrational resonance system effectively extracts fault features of rolling bearing, thereby validating and extending the applicability of vibrational resonance theory in signal processing.