Iterative K-Singular Value Decomposition for Quantitative Fault Diagnosis of Bearings

Previous studies have shown that a step vibration response and an impulse vibration response are generated when a rolling element passes a fault zone on the outer or inner race. The time difference between the two fault-induced responses is referred to as the time-to-impact, which can be regarded as an indication of the fault size. However, step-impulse responses, especially step responses, are often contaminated by background noise, leading to difficult time-to-impact estimation. Therefore, an effective denoising method is required to reduce noise from step-impulse responses (especially step responses) in preparation for subsequent time-to-impact estimation. To this end, an iterative K-singular value decomposition (K-SVD) algorithm is proposed to extract fault-size-related responses. This algorithm works by iteratively alternating between a modified K-SVD algorithm and a global signal reconstruction. In the numerical and experimental studies, the iterative K-SVD algorithm, the original K-SVD algorithm, and the other two benchmark algorithms (i.e., wavelet shrinkage and spectral kurtosis) were conducted for comparative analysis. The results demonstrate that the proposed algorithm could be used as a promising signal pre-processing technique for the quantitative fault diagnosis of rolling element bearings.