Time-frequency (TF) rearrangement methods represented by synchrosqueezing transform (SST) and synchroextracting transform (SET) have recently been considered efficient tools for obtaining time-varying features of nonstationary signals. However, so far improving concentration and accuracy is still an open problem, especially for the signal with strongly time-varying instantaneous frequency (IF), due to the fact that they cannot achieve an accurate and generalized IF estimation. In order to address this problem, we introduce a new TF analysis method termed as generalized synchroextracting transform (GSET) by constructing a general signal model. Our first contribution in this study is proposing a new computational framework to derive the generalized explicit formula of Nth-order IF estimation, which can realize the programming of any order IF. By extracting the energy of the TF representation (TFR) on the estimated IF, a more concentrated and accurate TFR can be obtained. Our second contribution is giving a more accurate signal reconstruction method of the TFR from a new perspective. It solves the problem that the reconstruction method of the synchroextracting transform cannot be extended to the Nth-order. Numerical analysis of multicomponent simulated signal demonstrates that the GSET can effectively improve the TF readability of strongly time-varying signal and accurately reconstruct the signal from the TFR. Moreover, experiment and application results verify that the proposed method can be used for fault diagnosis of rotating machinery.

中文翻译：

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广义同步提取变换：算法和应用


以同步压缩变换 （SST） 和同步提取变换 （SET） 为代表的时频重排方法最近被认为是获得非平稳信号时变特征的有效工具。然而，到目前为止，提高浓度和准确度仍然是一个悬而未决的问题，特别是对于具有强时变瞬时频率 （IF） 的信号，因为它们无法实现准确和广义的 IF 估计。为了解决这个问题，我们通过构建通用信号模型，引入了一种新的 TF 分析方法，称为广义同步提取变换 （GSET）。我们在这项研究中的第一个贡献是提出了一个新的计算框架来推导 N 阶 IF 估计的广义显式公式，可以实现任意阶 IF 的编程。通过提取 TF 表示 （TFR） 在估计的 IF 上的能量，可以获得更集中和准确的 TFR。我们的第二个贡献是从新的角度给出了更准确的 TFR 信号重建方法。它解决了同步提取变换的重建方法不能扩展到 N 阶的问题。对多分量模拟信号的数值分析表明，GSET 可以有效提高强时变信号的 TF 可读性，并准确地从 TFR 重建信号。此外，实验和应用结果验证了所提方法可用于旋转机械的故障诊断。