Time-frequency analysis (TFA) is one of the most critical tools to process nonstationary signals for a long time. However, classical TFA methods is invalid for the transient signal with sharply frequency-varying features. This paper proposes a new TFA method termed as the generalized horizontal multi-synchrosqueezing transform (GHMST) to deal with the transient signal. Firstly, a frequency-domain signal model is constructed and expanded to a high-order Taylor expression. Then, based on this expression, the explicit formula of the high-order group delay (GD) is derived with a concise manner. Finally, the time-frequency energy is reassigned to this estimated GD through an iterative procedure. Meanwhile, the corresponding algorithm implementation is programmed to demonstrate the feasibility of the GHMST. The numerical validation shows the superiority of the proposed method in analysing impulse-like signal compared with other advanced TFA methods. The experimental data verifies the effectiveness of the GHMST in impact fault diagnosis of mechanical system.

Nonstationary signal; Time-frequency analysis (TFA); Synchrosqueezing transform (SST); Fault diagnosis