Rotating machines (i.e. gear-box) are always assembly of many associated parts, such as gears and bearings. Commonly, high rate of fault isolation for such machines need enough test points. Since the machines are always too compact to fix enough sensors, it is significative to study on how to use fewer sensors for machine monitoring and fault diagnosis by vibration analysis of rotating machine groups.Based on these conditions, this thesis describes the methods for the blind source separation of noisy harmonic signals from rotating machine when the underlying system is underdetermined (i.e. separation of n sources from m mixtures, when m |