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基于分数阶Fourier变换的结构瞬时频率识别

卢恋 任伟新 王世东

卢恋,任伟新,王世东. 基于分数阶Fourier变换的结构瞬时频率识别 [J]. 应用数学和力学,2022,43(8):825-834 doi: 10.21656/1000-0887.420241
引用本文: 卢恋,任伟新,王世东. 基于分数阶Fourier变换的结构瞬时频率识别 [J]. 应用数学和力学,2022,43(8):825-834 doi: 10.21656/1000-0887.420241
LU Lian, REN Weixin, WANG Shidong. Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform[J]. Applied Mathematics and Mechanics, 2022, 43(8): 825-834. doi: 10.21656/1000-0887.420241
Citation: LU Lian, REN Weixin, WANG Shidong. Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform[J]. Applied Mathematics and Mechanics, 2022, 43(8): 825-834. doi: 10.21656/1000-0887.420241

基于分数阶Fourier变换的结构瞬时频率识别

doi: 10.21656/1000-0887.420241
基金项目: 国家自然科学基金(51778204);深圳市科创委项目(KQTD20180412181337494;ZDSYS20201020162400001;GJHZ20200731095802007)
详细信息
    作者简介:

    卢恋(1994—),女,博士生(E-mail:lulian@mail.hfut.edu.cn

    任伟新(1960—),男,教授,博士(通讯作者. E-mail:renwx@szu.edu.cn

    王世东(1994—),男,博士生(E-mail:2017110600@mail.hfut.edu.cn

  • 中图分类号: TN911.6; TU311.3

Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform

  • 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。

  • 图  1  时频面旋转

    Figure  1.  Rotation of the time-frequency plane

    图  2  FRFT识别一般信号的原理示意图

    Figure  2.  Schematic diagram of general signal identification based on the FRFT

    图  3  任意非平稳信号关于频率的三维曲面图

    Figure  3.  The 3D surface of any non-stationary signal with respect to the frequency

    图  4  任意非平稳信号时频曲线

    Figure  4.  The time-frequency distribution of arbitrary nonstationary signals

    图  5  加噪信号时域波形:(a) SNR为−10 dB;(b) SNR为10 dB;(c) SNR为20 dB

    Figure  5.  Time domain waveforms of noised signals: (a) SNR is −10 dB; (b) SNR is 10 dB; (c) SNR is 20 dB

    图  6  FRFT对信号瞬时频率的识别过程:(a) α与最佳$\hat{u} $关系曲线;(b) 时间与α关系曲线;(c) 时间与最佳$\hat{u} $关系曲线

    Figure  6.  The FRFT identification process of signal instantaneous frequencies: (a) the relationship curve between α and $\hat{u} $; (b) the relationship curve between t and α; (c) the relationship curve between t and $\hat{u} $

    图  7  FRFT与STFT对信号瞬时频率的识别与理论值的对比:(a) SNR为−10 dB; (b) SNR为10 dB; (c) SNR为20 dB

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  7.  The comparison between FRFT and STFT identification values of signal instantaneous frequencies and theoretical values: (a) SNR is −10 dB; (b) SNR is 10 dB; (c) SNR is 20 dB

    图  8  三自由度线性系统

    Figure  8.  The 3DOF linear system

    图  9  刚度线性变化时结构固有频率

    Figure  9.  Natural frequencies of the structure with linearly changing stiffness

    图  10  质量1的位移响应

    Figure  10.  The displacement response of mass 1

    图  11  FRFT识别及理论结构第一阶固有频率

    Figure  11.  The FRFT-based identification and the 1st-order theoretical natural frequencies of the structure

    图  12  FRFT识别及理论结构第二阶固有频率

    Figure  12.  The FRFT-based identification and the 2nd-order theoretical natural frequencies of the structure

    图  13  FRFT识别及理论结构第三阶固有频率

    Figure  13.  The FRFT-based identification and the 3rd-order theoretical natural frequencies of the structure

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出版历程
  • 收稿日期:  2021-08-12
  • 录用日期:  2021-12-01
  • 修回日期:  2021-11-25
  • 网络出版日期:  2022-06-30
  • 刊出日期:  2022-08-01

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