The deterministic bispectrum of coupled harmonic random signals and its application to rotor faults diagnosis considering noise immunity

This paper considers the properties of a bispectrum estimate when applied to a system with quadratic nonlinearity excited by the superposition of harmonics in the presence of additive Gaussian noise. This is compared using signal-to-noise ratios, to the power spectrum. Numerical examples were included to verify the results. In addition, an application of the use of the bispectrum to detect rotor faults in rotating machinery through detection of quadratic phase coupling is presented. The paper aims to clarify the use of the bispectrum to detect non-linearity in time series and presents the background theory on the bispectrum and in its application. Further, we show how patterns in the bispectrum are useful for identifying the frequency (or bifrequency) components involved in the non-linear interaction. The properties of interest are insensitivity to Gaussian noise and it's ability to detect quadratic phase coupling. The study aims to expand the domain of induction machines faults diagnosis. To verify the theoretical development, stator currents which were collected from a test bed based on a 18.5 kW three-phase squirrel cage induction machine have been used in a steady-state condition.