Feature frequency extraction algorithm based on the singular value decomposition with changed matrix size and its application in fault diagnosis

Singular value decomposition (SVD) has an important application in signal analysis and feature extraction. In the existing SVD applications, the matrix size is generally invariant. The idea of changing the matrix size in SVD is proposed, and a new characteristic of SVD, viz. the frequency extraction characteristic under changed matrix size, is discovered, and a frequency extraction algorithm based on the SVD with changed matrix size (SVDWCMS) is proposed. For a signal with specific frequency structure, SVDWCMS can extract any individual frequency in this signal. The decomposition characteristics of the SVDWCMS are further investigated, and it is proved that the decomposition results obtained by the SVDWCMS are of the orthogonality and superposition. Two theorems are given to reasonably explain the frequency extraction characteristic of the SVDWCMS, and the frequency structure that can be decomposed by the SVDWCMS is analyzed. The application examples of the SVDWCMS are provided, the feature frequencies of rotor vi-bration and milling force are extracted, and the fault of the rotor and the stability of milling process are analyzed based on the feature frequencies extracted.