Abstract: A new method of blind source separation (BSS) in under-determined mixtures is presented, which is based on the reconstruction of phase space and singular value decomposition to increase dimensions. The first step is to obtain the track matrix of the attractor by reconstruction of phase space based on appropriate time delay and embedded dimension, and apply singular value decomposition to this matrix. Then the inverse transform is applied to the revised signal matrix and a new linear combination of the source signals can be obtained, so that the signal dimensions are increased. Moreover the connection of the new linear combination, obtained, of the source signals and the original one is discussed, and the relativity of these two signals is analyzed so as to verify the feasibility of this new method. This method is used to research the under-determined BSS composed of some common signals, such as sine signal, frequency modulation signal, amplitude modulation signal mixed with white noise based on the different distribution features of the singular values, and then applied in the fault diagnosis of the experimental gear bench to diagnose the typical faults of gear.

Key words: Blind source separation, Fault diagnosis, Singular value decomposition, Under-determined mixtures