Research on weak signal feature extraction of bearings based on vibrational resonance of a frequency-adaptive Duffing system

Abstract

As pivotal elements in rotating machinery, the health of rolling bearings is fundamentally linked to the overall security and consistent performance of mechanical systems. However, the subtle signatures of incipient defects are frequently overwhelmed by intense environmental interference, making it difficult for conventional methods to achieve accurate extraction under complex working conditions. To address this issue, this paper proposes a vibrational resonance (VR) enhancement method based on a frequency-adaptive monostable Duffing oscillator. First, an adaptive dynamical framework based on a frequency feedback mechanism was constructed. By introducing an energy learning rule, the adaptive capture and dynamic matching of the nonlinear oscillator’s intrinsic frequency to the fault characteristic frequency are achieved. Next, the instantaneous equivalent stiffness of the system was derived utilizing the method of local analysis, establishing the VR induction criterion where the equivalent natural frequency matches the target frequency. On this basis, numerical simulations revealed the influence of key parameters on the spectral amplification factor, and an optimal parameter synergistic configuration for inducing the strongest resonance was determined. Finally, the effectiveness of the proposed method was verified through experiments involving different types of bearing faults. Experimental results demonstrate that the proposed method exhibits favorable performance in weak fault feature enhancement, offering competitive extraction results compared to traditional methods such as wavelet transform and variational mode decomposition. This study provides a robust and efficient technical solution for weak fault feature extraction in complex engineering environments.