Method of Multi-resolution and Effective Singular Value Decomposition in Under-determined Blind Source Separation and Its Application to the Fault Diagnosis of Roller Bearing

Considering the background of the roller bearing´s compound fault with strong noise, it is difficult to determine the actual fault when the machine has something wrong. In this paper, we propose a method which is called as multi-resolution and effective singularity value decomposition in under-determined blind source separation. Firstly, we put the one-channel compound fault signal into several components through the method of multi-resolution singular value decomposition. By improving the signal´s dimension, we solve the limitation of the classical blind source separation method in under-determined case. That is to say the observed signal numbers are less than source numbers. Then we use the effective singularity value decomposition about the track matrix of attractor reconstructed by every component´s phase space to detect abrupt information. After that, we apply the method of envelope spectrum analysis to the reconstructed signals to pick out the active ingredients, which include the fault characteristic frequency, to get the new mixed matrix. By this way, we have realized the noise reduction. Finally, we use the method of blind source separation based on kurtosis which is called as Robust Independent Component Analysis to make the new mixed matrix separate. Besides, the application to the roller bearing´ compound fault shows that the method we proposed can extract the weak faults from the severe conditions and make accurate judgment for the types of fault.