Horizontal Reassigning Transform for Bearing Fault Impulses Characterizing

In current transient signals processing-related time-frequency analysis (TFA) algorithms, the group delay (GD) is primarily obtained by its definition, meanwhile, these TFA methods suffer from repeated assignment and nonreassigned point problems, which result in unsatisfactory time-frequency resolution. Hence, a novel TFA technique called horizontal reassigning transformation (HRT) is proposed for handling transient signals. In the developed technique, the Gaussian window function-based GD estimation criterion, which is fully different from traditional GD calculation methods, is defined, and the criterion contains three parts, namely, local maximum locating of the Gaussian window function, zeros searching of the first-order derivative of the Gaussian window function, and local minima locating of the absolute value of the first-order derivative of the Gaussian window function. With the estimated GD, the horizontal reassigning operator (HRO) is devised to adaptively extract the time-frequency coefficients along the GD trajectory and discard the coefficients that cause the time-frequency blurring. A simulation signal with nonlinear GDs is employed to illustrate the effectiveness of the HRT. Compared with the other seven typical TFA algorithms, the developed technique can accurately extract GD and eliminate repeated assignment and nonreassigned point problems. Analysis results of the bearing fault impact signals show that the proposed HRT can display the time when pulses occur while ensuring high time-frequency resolution, making it suitable for detecting the bearing fault.