Method of harmonic retrieval based on time averaged three-order cumulant and its application in engineering

For the purpose of identifying harmonic components in vibration signals with strong Gaussian colored noise, by using an estimation algorithm of time averaged three-order cumulant, a method of harmonic retrieval from the vibration signals is presented in the paper. Time averaged three-order cumulant is one of the estimation values of three-order cumulant. Theoretical derivation indicates that time averaged three-order cumulant of signals, which are from random phase harmonic processes, is nonzero and its one-dimension slice is also a harmonic process. Consequently, the harmonic components of the signals with strong Gaussian colored noise can be identified by the spectrum of the time averaged three-order cumulant. The method is very effective to restrain Gaussian noise and to identify harmonic components from vibration signals. Experiments and analog signals indicate that the method is feasible and right.