Detecting nonlinearity from a continuous dynamic system based on the delay vector variance method and its application to gear fault identification

Many natural time series and signals collected from engineered systems are continuous dynamical signals. In practice, it is necessary to study nonlinearities in such continuous dynamic systems under different sampling conditions. In this paper, nonlinearity tests based on the delay vector variance (DVV) and iterative amplitude adjusted Fourier transform (IAAFT) based surrogates are first applied to Lorenz time series under various sampling rates. Traditional nonlinearity measures, such as third-order autocovariance and asymmetry due to time reversal, are shown to be sensitive to different sampling conditions whereas the relative insensitivity of the DVV proves promising. This insensitivity makes DVV a desirable nonlinearity measure for describing continuous dynamic signals and herein it is shown to be a suitable nonlinear fault diagnostic method for use in the gearbox condition monitoring. Moreover, by applying the DVV rank test, faults in gears can be identified effectively.