Estimation of Cyclic Cumulants of Machinery Vibration Signals in Non-stationary Operation

Abstract

Cyclic statistics have been proved to be a powerful tool for the study of rotating machinery vibration signals. Indeed, such signals usually exhibit cyclostationary features related to the shaft speed and to the geometry of the components. Cyclostationarity can be studied at order one (periodic deterministic components) or order 2 and more. Cyclic statistics at order N comprise a pure Nth order cyclostationary part and a contribution from orders 1 to N − 1. It may be interesting to study pure cyclostationarity at order N, i.e. to remove the influence of smaller orders. This can be done by computing cyclic cumulants instead of cyclic moments. In order to compute 2nd order cumulants of the vibration signal, one must remove from the signal the 1st order cyclostationary components, that is to say the deterministic periodic components. Some classical approaches have been proposed, based on synchronized averaging or Fourier transform. But some limitations appear when the vibration signal comprises components tied to different rotation frequencies (for instance in the case of gears) or under variable speed. The method that we propose in order to extract these periodic components is based on a biquad filter bank. Biquad filters have been extensively used in audio processing and allow building band-pass or notch filter banks at low computational cost. We show how such filters can be used to remove the 1st order cyclic components from the signal. An extension to variable speed operation is proposed by having the filters central frequency follow the variations of the rotation frequency. The technique is applied to simulated signals as well as real life signals.