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.

中文翻译：

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基于自适应匹配追踪的K-means奇异值分解新方法及其在滚动轴承弱故障诊断中的应用

稀疏分解在基于冗余和过完备字典描述任意复杂信号方面具有优良的适应性和高度的灵活性，从而具有不受正交基强加的小波和快速傅立叶变换等传统信号处理方法的限制的优点。稀疏分解为从旋转机械收集的复杂振动信号的特征提取提供了一种有效的方法。自学习过完备字典和预定义过完备字典是稀疏分解的两种字典构建模式。通常，前一种模式比后一种模式具有更加适应性和灵活性的优点，近年来出现了几种经典的自学习过完备词典方法。K-means奇异值分解是一种经典的自学习过完备字典方法，已应用于图像处理、语音处理和振动信号处理。然而，K-means奇异值分解的重建精度相对较低，稳定性较差，无法增强所需的特征。为了克服K-means奇异值分解的上述缺点，本文在传统K-means奇异值分解方法的基础上提出了一种新的K-means奇异值分解稀疏表示方法，该方法使用稀疏自适应匹配追踪算法一种基于原子结构最小相似度的迭代方法。通过仿真和实验验证了所提方法的有效性和优势。