Second-order Iterative Time-rearrangement Synchrosqueezing Transform and its application to rolling bearing fault diagnosis

Rolling bearings are key components in rotating machines, and their health condition is an important guarantee for the safety of the whole machine. In order to extract fault features of rolling bearings more accurately, a novel signal processing method named Second-order Iterative Time-rearrangement Synchrosqueezing Transform (2-ITSST) with a fast algorithm is proposed in this paper. Firstly, based on Time-reassigned SynchroSqueezing Transform (TSST), the approximation order is increased from the first order to the second order. Then, multiple iterations are conducted to calculate a more accurate group delay (GD) estimation operator. After that, the rearrangement operation is carried out to maximize the concentration of energy near the time-frequency (TF) ridgeline and obtain the result with higher TF aggregation. Lastly, the fast algorithm for 2-ITSST is introduced to overlap TF matrices into segments, which effectively reduced the computational complexity and ensured the TF aggregation of impact signal energy. Meanwhile, in order to make 2-ITSST more efficiently applied in bearing fault diagnosis, impulse extraction method is introduced to extract useful impulse features from the signal processed by 2-ITSST algorithm, and then the bearing fault frequency can be accurately extracted by envelope spectrum analysis. The effectiveness of the proposed method is verified by simulation and experimental studies.