将矩阵变结构思想引入到奇异值分解(SVD)中来，提出变结构SVD的概念，在SVD中将矩阵结构可调性和递推分解相结合，利用信号成分对矩阵结构敏感，通过变化的矩阵结构形成对信号不同成分的适应性，克服以往SVD中矩阵结构固定不变这一不足，利用SVD实现对复杂信号不同成分由强到弱的多层次适应性分解，获得一系列反映原信号主要能量构成的主分量和占小能量比例的副分量。提出三种具体的矩阵变结构方式，研究解决相应变结构SVD的分解和重构算法，并通过对各层主、副向量空间关系和性质的研究，明确变结构SVD的信号分解特性。提出对副分量做进一步细分，以实现对复杂背景信号中弱故障特征信息的提取。最后将变结构SVD应用到工程实践，研究它对复杂信号不同成分的分离效果、对弱信号的提取效果、消噪效果以及它在特征提取和设备早期微弱故障诊断中的应用，形成一种较为完备的变结构SVD理论和应用体系，为SVD开拓一个新的应用研究领域。

The idea of variable structure of matrix is introduced into singular value decomposition (SVD) and the concept of variable structure SVD is put forward. It is proposed that the adjustment of matrix structure and recursive decomposition be combined together in this variable structure SVD, and the characteristic that the components of signal are sensitive to the structure of matrix in the SVD based signal processing is utilized, so the adaptation for the different components of the complicated signal can be formed via the variable structure of matrix, and the defect of fixed structure of matrix in the usual SVD based signal processing is overcome, and a multi-gradation adaptive decomposition of the complicated signal can be implemented with SVD. By this adaptive decomposition way the different components can be isolated gradually from strong to weak from the original signal, a series of principal components, which reflect the main energy of the original signal, and a series of subsidiary components, which only occupy the small energy proportion of the original signal, will be got. In total three variable structure ways of matrix are proposed in this project, and decomposition and reconstruction algorithms of the corresponding variable structure SVD will be solved theoretically. The signal decomposition essence and performance of the variable structure SVD will be ascertained by the study on the relationship and property of the principal and subsidiary vector spaces of the different gradations. Moreover, it is proposed that subsidiary components be further decomposed so that the weak fault feature information can be extracted from the original complicated signal. Finally the variable structure SVD is applied to the engineering practice, and its separation effect for the different components of the complicated signal, extraction effect for the faint signal, noise reduction effect and its application to fault feature extraction and diagnosis of the weak inchoate fault of mechanical devices will be studied systematically. The object of this project is to establish a complete theory and application system of the variable structure SVD, and a new research and application field of SVD can be developed.