Testing second order cyclostationarity in the squared envelope spectrum of non-white vibration signals

•Statistical properties of the squared envelope spectrum of a coloured noise signal.•Derivation of a statistical test (thresholds) for the identification of CS2 components.•Analytical evaluation of the effect of CS1 and CS2 components on SES distribution.•Validation on numerically generated signals.•Experimental application of the new threshold to rolling element bearing signals.

Cyclostationary models for the diagnostic signals measured on faulty rotating machineries have proved to be successful in many laboratory tests and industrial applications. The squared envelope spectrum has been pointed out as the most efficient indicator for the assessment of second order cyclostationary symptoms of damages, which are typical, for instance, of rolling element bearing faults. In an attempt to foster the spread of rotating machinery diagnostics, the current trend in the field is to reach higher levels of automation of the condition monitoring systems. For this purpose, statistical tests for the presence of cyclostationarity have been proposed during the last years. The statistical thresholds proposed in the past for the identification of cyclostationary components have been obtained under the hypothesis of having a white noise signal when the component is healthy. This need, coupled with the non-white nature of the real signals implies the necessity of pre-whitening or filtering the signal in optimal narrow-bands, increasing the complexity of the algorithm and the risk of losing diagnostic information or introducing biases on the result. In this paper, the authors introduce an original analytical derivation of the statistical tests for cyclostationarity in the squared envelope spectrum, dropping the hypothesis of white noise from the beginning. The effect of first order and second order cyclostationary components on the distribution of the squared envelope spectrum will be quantified and the effectiveness of the newly proposed threshold verified, providing a sound theoretical basis and a practical starting point for efficient automated diagnostics of machine components such as rolling element bearings. The analytical results will be verified by means of numerical simulations and by using experimental vibration data of rolling element bearings.