When the rotary machinery is running, the vibration signals measured with sensors are mixed with all vibration sources and contain very strong noises. It is difficult to separate mixed signals with conventional methods of signal processing, so there are difficulties in machine health monitoring and fault diagnosis. The principle and method of blind source separation were introduced, and it was pointed out that the blind source separation algorithm was invalid in strong pulse noise environment. In these environments, the vibration signals are first denoised with the synchronous cumulative average noise reduction (SCA) method, and the denoised signals were separated with the improved fast independent component analysis (FastICA) algorithm. The results of simulation test and rotor fault experiments demonstrate that the novel method can effectively extract fault features, certifying its superiority in comparison with previous methods. Therefore, it is likely to be useful and practical in the fault detection area, especially under the condition of strong noise and vibration interferences.