Bi-spectrum analysis of coupled harmonics and its application to rotor faults diagnosis

The paper aims to clarify the use of the bi-spectrum to detect non-linearity in time series. Further we show how patterns in the bi-spectrum are useful for identifying the frequency (or bi-frequency) components involved in the nonlinear interaction. The bi-spectrum, a third-order spectrum, has properties that lend themselves to the measurement of nonlinearities in systems. The properties of interest are insensitivity to Gaussian noise and ability to detect quadratic phase coupling. This paper considers the properties of a bi-spectrum 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. The study aims to expand the domain of induction machines faults diagnosis. Therefore, to verify the theoretical development, an experimental test bed has been used in a steady-state condition.