Rolling element bearings are one of the key elements used in rotating machines. Their failure will result in system breakdowns and cause unexpected accidents. The health condition monitoring of bearings is, therefore, an emerging discipline to scientifically manage machine lifetime. Instantaneous frequency (IF) extraction and IF-based resampling consist of the major tasks used in conventional approaches for bearing fault diagnosis under variable speeds, where it is often desirable for the IF to be extracted based on the time-frequency analysis (TFA) of the vibration signal, instead of using a tachometer. However, an accurate IF extraction based on vibration signals from incipient bearing faults is often undermined by poor energy concentration and the weak readability of the TFA. Furthermore, the resampling procedure for bearing fault diagnosis is error-prone and vulnerable to noise. An approach based on multiple IF ridge integration is, therefore, proposed to address such problems. The proposed approach is dedicated to an accurate IF estimation and bearing fault diagnosis without tachometer utilization and resampling involvement. It is mainly comprised of four steps: (1) acquire multiple pre-IF ridges via a regional peak search algorithm (RPSA) from time frequency representations (TFRs); (2) integrate pre-IF ridges based on the probability density function (PDF) to gain an accurate IF estimation; (3) rectify the multiple pre-IF ridges; (4) diagnose bearing health condition according to the average ratios of any two rectified IF ridges, i.e. fault characteristic coefficient (FCC) or FCC-related numbers. Then, the IF can be accurately estimated based only on the collected vibration signals, and bearing fault diagnosis under variable speed conditions can be implemented. Numerical simulations and experimental signal analyses validate the effectiveness of the proposed method.
