针对轴承传动本身具有非线性而在传统故障诊断中又被忽略掉的问题，提出了基于分形和混沌等非线性几何不变量的轴承故障诊断方法。该方法对测得的轴承振动时间序列去噪以后进行相空间重构，然后计算重构信号的分形维数、Lypunove指数、K熵、关联距离熵等多个几何不变量，并以此作为轴承故障诊断特征量，输入到径向基神经网络，对轴承故障进行模式识别。实验结果表明该方法能有效区别轴承各种故障状态，且为旋转机械的故障诊断提供了一种新方法。

Aiming at the non-linearity which exits in the bearing transmission but ignores in the fault diagnosis traditionally, a method of fault diagnosis of bearing based on non-linear time series geometry invariant applying the theory of chaos and fractal is put forward. This method reduced noise by using wavelet transform and re-constructed the phase space of bearing vibrating time serial, after that , the non-linear geometry invariant such as correlation dimension, max Lyapunov exponent, K entropy and relative correlation distance entropy were calculated and were import the nerve network regarded as the character values of fault of bearing. The results of experiments show that the method can implement the fault diagnosis of bearing, otherwise, this method provides a new approach for the fault diagnosis of rotating machinery.