基于分数阶Fourier变换的结构瞬时频率识别

Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform

为识别时变信号的瞬时频率,由分数阶Fourier变换定义推导出了一般信号的频率与单一变量旋转角度α的关系式,从理论上解释了分数阶Fourier变换本质上是一种普通Fourier变换结合伸缩平移窗的算法,进而在分数阶Fourier域建立了非平稳信号瞬时频率的一般表达式,实现了结构瞬时频率的识别.采用任意非线性调频信号仿真算例和三自由度有阻尼时变结构系统的数值算例对提出的方法进行了比较分析.结果表明,该文提出的方法与理论值吻合良好,并具有一定的抗噪性,验证了方法的可靠性和实用性,可以应用于时变结构瞬时频率的识别.

To identify the instantaneous frequencies of time-varying signals,the theoretical relationship between the frequency and rotational angleαin a signal was derived based on the definition of the fractional Fourier transform.Then the fractional Fourier transform was interpreted to be essentially an algorithm combining the ordinary Fourier transform with the dilation and translation window.A general expression of the signal instantaneous frequency in the fractional Fourier domain was thereafter formulated so that the structural instantaneous frequency can be extracted accordingly.The feasibility and reliability of the proposed method were verified with a simulated nonlinear frequency modulation signal and a numerical example of a 3DOF damped time-varying structure system.The results show that,the results of the proposed method are in good agreement with the theoretical values,and the method has a certain degree of anti-noise capability.Subsequently,the proposed method is applicable to the identification of the instantaneous frequencies of time-varying structures.