Time-frequency analysis of a new aperiodic resonance

Abstract Based on the time-frequency analysis, a piecewise re-scaled method is proposed to realize aperiodic resonance in a Duffing system excited by the nonlinear frequency modulated (NLFM) signal. Based on the aperiodic resonance theory, the weak NLFM signal is enhanced greatly. By short time Fourier transform, numerical simulations are carried out for several kinds of NLFM signal. The results show that the method enhances the NLFM signal effectively. Meanwhile, the effectiveness of the method is still illustrated in the noise background. In addition, the noise and the interference frequency can be removed. Noteworthy, and differently as what happens with the stochastic resonance and vibrational resonance, the aperiodic resonance does not require any auxiliary signal or noise to induce it. This constitutes also a new result of this paper. Next, in order to expand the application of this method, it is used to process the experiment signal of bearing fault under variable speed condition. The validity of the method is illustrated again. The results provide new reference in processing non-stationary frequency-modulated signal. Finally, an adaptive piecewise re-scaled aperiodic resonance scheme is put forward to get optimal parameters to induce stronger aperiodic resonance quickly.

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