Nonlinearity Detection For Condition Monitoring Using Higher-Order Statistics

this paper are the bicoherence and tricoherence. These are polyspectral measures at third- and fourth-orders, and represent normalised versions of the bispectrum and trispectrum resepectively. The reason for normalising is related to variance issues outside the scope of this paper (see [8] for a review). If it is assumed that the signal is stationary, then these quantities can be estimated using simple segment-averaging, identical in approach to the Welch periodogram technique for estimating the power spectrum [9]. In fact the power spectrum is needed as part of the normalisation, so this is estimated too. The validity of this assumption of stationarity is difficult to gauge, and some recent work has investigated the bicoherence in non-stationary noise environments [10]. Without the assumption it is practically impossible to estimate polyspectral measures