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.

在时频分析的基础上，提出了一种分段重新定标的方法，以实现由非线性调频（NLFM）信号激发的Duffing系统的非周期性共振。根据非周期性共振理论，弱NLFM信号得到了极大的增强。通过短时傅立叶变换，对几种NLFM信号进行了数值模拟。结果表明，该方法有效地增强了NLFM信号。同时，该方法的有效性仍在噪声背景中示出。另外，可以去除噪声和干扰频率。值得注意的是，与随机共振和振动共振不同，非周期性共振不需要任何辅助信号或噪声来诱导它。这也是本文的新成果。下一个，为了扩展该方法的应用范围，用于处理变速条件下轴承故障的实验信号。再次说明了该方法的有效性。研究结果为处理非平稳调频信号提供了新的参考。最后，提出了一种自适应分段重新定标的非周期性共振方案，以获取最佳参数，以快速地引发更强的非周期性共振。