Quantitative fault analysis of roller bearings based on a novel matching pursuit method with a new step-impulse dictionary

A novel matching pursuit method based on a new step-impulse dictionary to measure the size of a bearing׳s spall-like fault is presented in this study. Based on the seemingly double-impact theory and the rolling bearing fault mechanism, a theoretical model for the bearing fault with different spall-like fault sizes is developed and analyzed, and the seemingly double-impact characteristic of the bearing faults is explained. The first action that causes a bearing fault is due to the entry of the roller element into the spall-like fault which can be described as a step-like response. The second action is the exit of the roller element from the spall-like fault, which can be described as an impulse-like response. Based on the quantitative relationship between the time interval of the seemingly double-impact actions and the fault size, a novel matching pursuit method is proposed based on a new step-impulse dictionary. In addition, the quantitative matching pursuit algorithm is proposed for bearing fault diagnosis based on the new dictionary model. Finally, an atomic selection mechanism is proposed to improve the measurement accuracy of bearing fault size. The simulation results of this study indicate that the new matching pursuit method based on the new step-impulse dictionary can be reliably used to measure the sizes of bearing spall-like faults. The applications of this method to the fault signals of bearing outer-races measured at different speeds have shown that the proposed method can effectively measure a bearing׳s spall-like fault size.