Abstract: The multi-fractals theory is applied for proposing the calculation formula of general dimension least square method. The general dimension of measured time domain signal is calculated, the sequence value of general dimension is obtained, and the box dimension, the information dimension, the correlation dimension and the sensitive dimension are got from general dimension. The general dimension of the fault sample is calculated. And the relationship between fault and fractal is found out. These provide the basis of analyzing the fault strength by fractal dimension. In addition, combined general dimension sequence value and mathematics method, the fractal diagnosis classification is proposed. It achieves good results to diagnose, identify and classify the measuring and modal coupling fault signal by the utilizing theorem of the general dimension maximum correlation coefficient and the general dimension sequence signal value. Through the example of the rotor system fault diagnosis, it explains that the fractal dimensions abstracted from the general dimension can better diagnose, identify the fault and its degree. The method of fractal diagnosis and classification has better actual effective property.

Key words: Modal fractal characteristic, Coupling fault diagnosis, Fault sensitive dimension, Fractal diagnosis and classify, Multi-fractal theory