To improve the mode decomposition capacity of the empirical Fourier transform for time-varying structures, an empirical multi-synchroextracting decomposition method has been proposed and applied to mode analysis of time-varying structures. The multi-synchroextracting transform is introduced to obtain the time–frequency coefficients and the time–frequency spectra of response signals. Then, the time–frequency energy of an arbitrary frequency line is obtained by summing the time–frequency coefficients along the entire time history. Due to the total time–frequency energy within the characteristic frequency band is larger than the energy within an adjacent region outside the frequency band, an energy segmentation operator is constructed to determine the energy spectrum boundaries for each mono-component signal. Once the boundaries are found, a zero-phase filter bank and the Fourier transform are used to accomplish frequency spectrum segmentation of the mono-component signal. Finally, each mono-component signal is reconstructed by employing the inverse Fourier transform to each segment, which realizes the mode decomposition of a time-varying structure. The feasibility of the proposed method has been verified against a numerical 2DOF mass-spring-damper system, a numerical three-story frame structure and an experimental twelve-story reinforced concrete frame structure. The analysis results show that the proposed method provides better precision than the empirical Fourier transform in the aspect of time-varying mode decomposition. Moreover, the proposed method has higher decomposition accuracy in the presence of high interference between adjacent frequency bands.

中文翻译：

---

基于经验多重同步提取分解的时变结构振动信号分解方法


为了提高时变结构的经验傅里叶变换的模态分解能力，提出了一种经验多同步提取分解方法，并将其应用于时变结构的模态分析。引入多重同步提取变换以获得响应信号的时频系数和时频谱。然后，通过对整个时间历程的时频系数求和来获得任意频率线的时频能量。由于特征频带内的总时频能量大于频带外相邻区域内的能量，因此构建了能量分割算子来确定每个单分量信号的能谱边界。找到边界后，使用零相位滤波器组和傅里叶变换来完成单分量信号的频谱分割。最后，通过对每个分段采用逆傅里叶变换来重构每个单分量信号，从而实现时变结构的模式分解。该方法的可行性在数值二自由度质量-弹簧-阻尼器系统、数值三层框架结构和实验性十二层钢筋混凝土框架结构中得到了验证。分析结果表明，所提方法在时变模态分解方面提供了比经验傅里叶变换更好的精度。此外，在相邻频段之间存在高干扰的情况下，所提方法具有更高的分解精度。