Hilbert versus Concordia transform for three-phase machine stator current time-frequency monitoring

This paper deals with mechanical fault diagnosis in three-phase induction machines from stator current measurements. According to machine models, mechanical faults lead to amplitude and/or phase modulations of the measured stator current with possibly time varying carrier frequency. The modulation diagnosis requires a univocal definition of the instantaneous phase and amplitude. This is performed by associating a complex signal to the real measured one. For a convenient separate modulation diagnosis, the complex signal instantaneous phase and amplitude are expected to carry, respectively, information about the phase and amplitude modulations. The complex signal is classically obtained through the Hilbert transform. Under Bedrosian conditions, the so-called analytic signal allows a separate modulation diagnosis. However, mechanical faults may also produce fast modulations violating the Bedrosian conditions. This study proposes an alternative complex signal representation which takes advantage of the three stator current measurements available in a three-phase machine. From two stator current measurements, the Concordia transform builds a complex vector, the so-called space vector, which unconditionally allows separate modulation diagnosis. This paper applies and compares the Hilbert and Concordia transforms, theoretically and in case of simulated and experimental signals with various modulation frequency ranges.