Abstract

Dictionary design is a primary challenge for sparsity-assisted fault diagnosis techniques. The dictionary can either be specified through signal priors or learned from data samples. In this paper, we propose a singular vector-inspired dictionary learning (SVDL) method, combining signal priors and data samples for sparse decomposition of machinery vibration signal. The SVDL is a data driven scheme for learning dictionary atoms and simultaneously exploring the prior information. It is achieved by alternating between atom design and dictionary update steps. First, we introduce the singular vector as vibration signal priors to atom design procedure. Through singular value decomposition on the Hankel matrix of the vibration signal, the inherent signal features corresponding to mechanical fault can be expressed with some singular vectors. These vectors, closely related to fault features, are extracted as basis vectors to constitute atoms. Second, the vector quantization method is used for atom design, by clustering the extracted basis vectors for the purpose of learning representative atoms. As to the dictionary update step, a strategy including sparse coding and dictionary optimization is adopted to simplify and update atoms. The results of the numerical simulation and experimental application show that the proposed SVDL method outperforms the classical K-SVD method for vibration signal denoising and fault feature extraction.

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