High-order iterative rearrangement transform for time–frequency characterization of bearing fault impact

Time–frequency analysis (TFA) can effectively characterize features of non-stationary signals. Traditional TFA algorithms construct signal models in the time domain and make the assumption that the instantaneous characteristics of each component are continuous. However, the instantaneous frequency (IF) of the transient signal is discontinuous in the time domain and exhibits a multifaceted relationship with time, such as shock, vibration wave, damped sound wave, etc. Additionally, in most existing TFA methods, low-order group delay (GD) is used to describe transient signals, which leads to unsatisfactory energy concentration and calculation accuracy. To address about issues, a novel TFA technique, termed high-order iterative rearrangement transform (HOIRT), is developed in this research. First, the signal model is defined within the frequency domain, and the frequency ridge of the transient signal is described by a high-order GD (HOGD), which is similar to the IF. Second, a HOGD-based iterative synchrosqueezing operator is defined to reassign time–frequency coefficients into the GD trajectories along the time direction. Finally, the HOGD-based frequency extraction operator is constructed to only retain the target time–frequency information of the transient signal from the rearranged results, such that the noise interference is eliminated and the energy-concentrated TFR is obtained. A simulation signal with nonlinear GDs is employed to illustrate the effectiveness of the HOIRT. Compared with the other seven typical TFA algorithms, the developed technique has the smallest calculation error and Rényi entropy, showing that the HOIRT has the highest accuracy and energy concentration. Analysis result of the bearing fault impact signal shows that the proposed HOIRT can display the time when pulses occur while ensuring high time–frequency resolution, making it suitable for detecting bearing faults.