中文摘要：

运用多重分形理论，提出广义雏数最小二乘法的计算岔式，对实测的时域信号进行了广义堆数计算，得到广义维数序列值，并从广义堆数中获取盒雏数、信息雏数、关联堆数以厦敏感雏数。对故障样本进行功率谱分析、广义雏数计算分析，找出谱能量与分形维数的关系，对用分形维数分析故障的强度提供了依据。另外运用广义维数序列和数学方法相结合提出分形诊断分类方法。用广义雏数最大相关系数和广义雏数序列单值优化逼近原理方法。对待检信号的耦合故障分别进行了试验数据与理论响应模拟数据的诊断、识别分类。收到了良好的一致效果。通过对转子系统故障诊断的实例说明从广义维数中提取的各分形雏数都能较好地对故障状态进行诊断、识别；且耦合故障的分形诊断分类方法具有较好的实效性。

英文摘要：

The multi-fractal theory is applied to proposing the calculation formula of general dimension least square method, The general dimension of measured time domain signal is calculated, its sequence value is obtained, and from the general dimension the box dimension, information dimension, correlation dimension and sensitive dimension are gained. The power spectrum of a fault sample is analyzed, the general dimension of which is calculated. The relationship between spectrum energy and fractals is identified. These provide a basis for analyzing the fault strength by fractal dimension. In addition, with general dimension sequence value and mathematics method combined, the fractal diagnosis classification method is proposed. It achieves good results in diagnosing, identifying and classifying the coupled fault signals to be measured by utilizing the theorem of the general dimension maximum correlation coefficient and the general dimension sequence signal value. The instance of a rotor system＇s fault diagnosis indicates that all the fractal dimensions abstracted from the general dimension can better diagnose and identify a fault and its degree, The fractal diagnosis and classification method has better effectiveness.