A new K-means singular value decomposition method based on self-adaptive matching pursuit and its application in fault diagnosis of rolling bearing weak fault

Abstract

Sparse decomposition has excellent adaptability and high flexibility in describing arbitrary complex signals based on redundant and over-complete dictionary, thus having the advantage of being free from the limitations of traditional signal processing methods such as wavelet and fast Fourier transform being imposed by orthogonal basis. Sparse decomposition provides an effective approach for feature extraction of intricate vibration signals collected from rotating machinery. Self-learning over-complete dictionary and pre-defined over-complete dictionary are the two dictionary construction modes of sparse decomposition. Normally, the former mode owns the virtues of much more adaptive and flexible than the latter one, and several kinds of classical self-learning over-complete dictionary methods have been arising in recent years. K-means singular value decomposition is a classical self-learning over-complete dictionary method and has been used in image processing, speech processing, and vibration signal processing. However, K-means singular value decomposition has relative low reconstruction accuracy and poor stability to enhance the desired features. To overcome the above-mentioned shortcomings of K-means singular value decomposition, a new K-means singular value decomposition sparse representation method based on traditional K-means singular value decomposition method was proposed in this article, which uses the sparse adaptive matching pursuit algorithm and an iterative method based on the minimum similarity of atomic structure. The effectiveness and advantage of the proposed method were verified through simulation and experiment.