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研究了Duffing振子信号检测过程中混沌、间歇混沌和大周期状态的时频特征,提出了一种基于检测统计量的任意频率信号检测方法。通过对系统不同状态下的输出序列进行短时傅里叶变换(STFT)发现,等幅线和三维时频分布能够体现出不同状态的显著差异,且可以完全区分出每一种状态。从构造统计量的易实现性出发,用三维时频分布中的幅时曲线作为衡量不同状态的依据,并将不同频率对应的幅时曲线的均值最大量作为检测统计量,该统计量的计算可以借助快速傅里叶变换(FFT)操作提高时效性。在此基础上,引入频率控制单元,给出了任意频率信号的检测方法步骤,方法的关键是将检测统计量最大值处所在的频率作为待测信号频率范围的一个端点,另一个端点为毗邻的两个检测统计量值较大者所在频率点。实验给出了不同状态的检测统计量范围,进而以此范围为判据,实现了振子对任意频率信号的检测,说明了方法的可行性,为Duffing振子信号检测问题的研究提供了一种新的思路。
The time-frequency characteristics of chaos, intermittent chaos and large-cycle state in Duffing oscillator signal detection are studied. An arbitrary frequency signal detection method based on detection statistics is proposed. By short-time Fourier transform (STFT) of the output sequence under different states of the system, it is found that the same amplitude and three-dimensional time-frequency distribution can show significant differences between different states and can completely distinguish each state. Based on the easy realization of construction statistics, the amplitude-time curve in the three-dimensional time-frequency distribution is used as the basis for measuring different states. The maximum mean value of the amplitude-amplitude curve corresponding to different frequencies is taken as the test statistic. You can improve timeliness with Fast Fourier Transform (FFT) operations. On this basis, the frequency control unit is introduced and the method of detecting the arbitrary frequency signal is given. The key point of the method is that the frequency at the maximum value of the detection statistic is taken as one end of the frequency range of the signal under test and the other end is adjacent The two test statistics greater frequency of the frequency. The range of detection statistic for different states is given in the experiment, and then the detection of any frequency signal by the oscillator is realized based on this range, which shows the feasibility of the method. This provides a new method for the study of Duffing oscillator signal detection Train of thought.