Vibrational resonance in coupled self-learning Duffing oscillators and its application in noisy radio frequency signal processing

TL;DR

This work introduces a network of frequency-adaptive, self-learning Duffing oscillators to push vibrational resonance into high-frequency regimes and to robustly denoise signals in noisy settings. By coupling a learning rule that updates the natural frequency with the external excitation and an amplification factor $\beta$, the array achieves broad VR and improved amplification across multiple oscillators. The authors derive approximate VR conditions, show how parameters like $A$, $B$, $\epsilon$, and network size influence resonance, and validate the approach through simulations and two RFID-based experiments, where it outperforms wavelet and Kalman denoising. The results suggest practical potential for high-frequency signal processing, fault diagnosis, and vibration sensing in noisy environments, with future work focusing on analytical methods, more complex signals, and hardware realization.

Abstract

This work presents a new coupled array of frequency-adaptive Duffing oscillators. Based on learning rules, the natural frequency of each oscillator changes with the external excitation to achieve the frequency-adaptive capability in the response. The frequency range of vibrational resonance in the response is greatly extended through the frequency-adaptive learning rule. Moreover, the theoretical condition for vibrational resonance is derived and its validity is verified numerically. The coupled self-learning Duffing oscillators can also perform signal denoising in strong noise environment, and its performance in signal denoising has been verified through processing the simulated signal and the wireless radio frequency signal under two scenarios. The superiority of vibrational resonance to the conventional denosing methods such as wavelet transform and Kalman filter has also been illustrated by experimental radio frequency signal processing. The combination of broadband frequency adaptability and strong noise-reduction capability suggests that these oscillators hold considerable potential for engineering applications.

Figures (20)

• Figure 1: The structure of the coupled self-learning Duffing oscillators.
• Figure 2: Influence of the amplification factor $\beta$ on vibrational resonance of Eq. (3) in the $B-\beta$ plane. The simulation parameters are $\zeta=0.25$, $b=1$, $k_\omega=10$, $A=0.1$, $\Omega_1=10$, $\Omega_2=10\Omega_1$ and $\epsilon=1$. Panels (a)-(d), $Q_i$ versus $B$ and $\beta$, $i=1$, 2, 3, 4 in turn.
• Figure 3: Influence of the characteristic frequency $\Omega_1$ on vibrational resonance of Eq. (3) in the $B-\Omega_1$ plane. The continuous lines in purple color are the theoretical results and the numerical results are covered due to the consistent of the two kinds of results. The simulation parameters are $\zeta=0.25$, $b=1$, $\beta=10$, $k_\omega=10$, $A=0.1$, $\Omega_2=10\Omega_1$ and $\epsilon=1$. Panels (a)-(d), $Q_i$ versus $B$ and $\Omega_1$, $i=1$, 2, 3, 4 in turn. This figure corresponds to Fig. A1 of the Appendix which removes the theoretical results of the resonance ridge line.
• Figure 4: Influence of the learning rate $k_\omega$ on vibrational resonance of Eq. (3) in the $B-k_\omega$ plane. The continuous lines in purple color are the theoretical results and the numerical results are covered due to the consistent of the two kinds of results. The simulation parameters are $\zeta=0.25$, $b=1$, $\beta=10$, $A=0.1$, $\Omega_1=10$, $\Omega_2=10\Omega_1$ and $\epsilon=1$. Panels (a)-(d) show $Q_i$ as a function of $B$ and $k_\omega$ for $i = 1, 2, 3, 4$, respectively. This figure corresponds to Fig. A2 of the Appendix which removes the theoretical results of the resonance ridge line.
• Figure 5: $Q$ versus $B$ of the first four oscillators of Eq. (3). The simulation parameters are $\zeta=0.25$, $b=1$, $\beta=10$, $k_\omega=10$, $A=0.1$, $\Omega_1=10$, $\Omega_2=10\Omega_1$ and $\epsilon=1$.