Cyclostationary analysis with logarithmic variance stabilisation

Highlight
• Logarithmic variance stabilisation in CS2 indicators.
• Unbiased test for multiple CS2 sources.
• Automated damage diagnostics in complex machines.

Second order cyclostationary (CS2) components in vibration or acoustic emission signals are typical symptoms of a wide variety of faults in rotating and alternating mechanical systems. The square envelope spectrum (SES), obtained via Hilbert transform of the original signal, is at the basis of the most common indicators used for detection of CS2 components. It has been shown that the SES is equivalent to an autocorrelation of the signal׳s discrete Fourier transform, and that CS2 components are a cause of high correlations in the frequency domain of the signal, thus resulting in peaks in the SES. Statistical tests have been proposed to determine if peaks in the SES are likely to belong to a normal variability in the signal or if they are proper symptoms of CS2 components. Despite the need for automated fault recognition and the theoretical soundness of these tests, this approach to machine diagnostics has been mostly neglected in industrial applications. In fact, in a series of experimental applications, even with proper pre-whitening steps, it has been found that healthy machines might produce high spectral correlations and therefore result in a highly biased SES distribution which might cause a series of false positives. In this paper a new envelope spectrum is defined, with the theoretical intent of rendering the hypothesis test variance-free. This newly proposed indicator will prove unbiased in case of multiple CS2 sources of spectral correlation, thus reducing the risk of false alarms.