Synchrosqueezing transform (SST) is a high resolution time frequency representation technology for nonstationary signal analysis. The short time Fourier transform-based synchrosqueezing transform (FSST) and the S transform-based synchrosqueezing transform (SSST) time frequency methods are effective tools for bearing fault signal analysis. The fault signals belong to a non-Gaussian and nonstationary alpha () stable distribution with and even the noises being also stable distribution. The conventional FSST and SSST methods degenerate and even fail under stable distribution noisy environment. Motivated by the fact that fractional low order STFT and fractional low order S-transform work better than the traditional STFT and S-transform methods under α stable distribution noise environment, we propose in this paper the fractional lower order FSST (FLOFSST) and the fractional lower order SSST (FLOSSST). In addition, we derive the corresponding inverse FLOSST and inverse FLOSSST. The simulation results show that both FLOFSST and FLOSSST perform better than the conventional FSSST and SSST under stable distribution noise in instantaneous frequency estimation and signal reconstruction. Finally, FLOFSST and FLOSSST are applied to analyze the time frequency distribution of the outer race fault signal. Our results show that FLOFSST and FLOSSST extract the fault features well under symmetric stable (SS) distribution noise.

中文翻译：

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分数阶低阶同步压缩时频技术在机械故障诊断中的应用

同步压缩变换（SST）是用于非平稳信号分析的高分辨率时频表示技术。基于短时傅立叶变换的同步压缩变换（FSST）和基于S变换的同步压缩变换（SSST）时频方法是进行轴承故障信号分析的有效工具。故障信号属于具有以下特征的非高斯和非平稳alpha（）稳定分布：甚至噪音也稳定分布。常规的FSST和SSST方法在稳定的分布噪声环境下会退化甚至失效。由于在α稳定分布噪声环境下，分数低阶STFT和分数低阶S变换比传统的STFT和S变换方法更好地工作，本文提出分数低阶FSST（FLOFSST）和分数低阶FSST。低阶SSST（FLOSSST）。此外，我们推导了相应的反FLOSST和反FLOSSST。仿真结果表明，FLOFSST和FLOSSST的性能优于传统的FSSST和SSST。瞬时频率估计和信号重建中的稳定分布噪声。最后，利用FLOFSST和FLOSSST分析外圈故障信号的时频分布。我们的结果表明，在对称稳定（S S）分布噪声下，FLOFSST和FLOSSST能够很好地提取故障特征。