Singular value decomposition (SVD) is an effective tool, which is a non-parametric signal analysis method free from phase shift and waveform distortion, for analyzing signals of mechanical systems and fault diagnosis. In the SVD, the embedding dimension of the Hankel matrix is an important parameter and directly influences the effectiveness of the SVD. However, the embedding dimension is usually determined by the experience which is quite subjective and limits the applicability of the SVD. As such, a novel SVD method, named adaptive SVD (ASVD), is proposed in this paper. In the ASVD, the novel criterions are defined to obtain the specific embedding dimensions for difference mechanical signals using the means of numerical simulation. Namely, the novel phenomenon, which is that the singular value pairs (SVP) changes periodically with the step size of half-cycle sampling points, is found and it can be used to calculate specific embedding dimension instead of selecting it from a range using experience. Meanwhile, the envelope spectral amplitude ratio (ESAR) index is developed for addressing the issue of the excessive decomposition in classic SVD. Lastly, the ASVD-based bearing fault diagnosis method is proposed for adaptively select useful sub-signals and detect fault. Both simulated signal and experiment signals, which collected from different bearing test rigs are used to verify the effectiveness of the proposed method. The results show that the proposed method has satisfactory ability to eliminate interference noise and detect bearing fault.
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