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

作　　者：卢恋 任伟新 王世东 LU Lian;REN Weixin;WANG Shidong(College of Civil Engineering,Hefei University of Technology,Hefei 230009,P.R.China;Key Laboratory for Resilient Infrastructures of Coastal Cities,Ministry of Education,Shenzhen University,Shenzhen,Guangdong 518060,P.R.China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009 [2]深圳大学滨海城市韧性基础设施教育部重点实验室(筹),广东深圳518060

出　　处：《应用数学和力学》2022年第8期825-834,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51778204);深圳市科创委项目(KQTD20180412181337494,ZDSYS20201020162400001,GJHZ20200731095802007)。

摘　　要：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.

关 键 词：分数阶FOURIER变换 非平稳信号 瞬时频率 伸缩平移窗 时变结构 

分 类 号：TN911.6[电子电信—通信与信息系统] TU311.3[电子电信—信息与通信工程]