中文摘要：

证明采用Hankel矩阵时奇异值分解（Singular value decomposition，SVD）可以将信号分解为一系列分量信号的简单线性叠加，为了确定其中的有用分量个数，提出奇异值差分谱的概念。差分谱可以有效地描述有用分量和噪声分量的奇异值性质差异，根据差分谱峰值位置可实现对有用分量个数的确定。研究结果表明，当差分谱最大峰值位于第一个坐标时，则表明原始信号存在较大的直流分量，此时根据第二最大峰值位置可以确定有用分量的个数，否则就根据最大峰值位置来确定分量个数。利用差分谱进一步研究Hankel矩阵的结构对SVD降噪效果的影响，指出矩阵列数和噪声去除量存在抛物线状的对称关系。利用基于差分谱的SVD方法对车削力信号进行处理，结果有效地分离出由于主轴箱故障齿轮的振动而引起的调制信号，并根据此信号可靠地定位了故障齿轮。

英文摘要：

It＇s proved that signal can be decomposed into the linear sum of a series of components by singular value decomposition （SVD） when Hankel matrix is used. In order to determine the proper number of useful components, the concept of difference spectrum of singular value is put forward. Difference spectrum can effectively reflect the difference of singular values of the useful components and noise ones, and the number of useful components can be determined according to the peak position in the difference spectrum. The research results show that if the maximum peak is in the first coordinate, it means that a major direct current component exists in the signal and under this circumstance the number of useful components will be determined by the second maximum peak position, otherwise the number of useful component is determined by the maximum peak position. The influence of Hankel matrix structure on noise reduction effect of SVD is studied by dint of difference spectrum and it＇s pointed out that there exits a parabolic symmetry relationship between matrix column and noise erasing amount. On these bases this method is applied to the processing of turning force signal and the modulated signal caused by the gear vibration in the headstock is isolated successfully, furthermore the fault gear is located reliably according to this isolated signal.