CS2 analysis in presence of non-Gaussian background noise – Effect on traditional estimators and resilience of log-envelope indicators

Abstract

Second-order cyclostationary (CS2) analysis has become popular in the field of machine diagnostics and a series of digital signal processing techniques have been developed to extract CS2 components from the background noise. Among those techniques, squared envelope spectrum (SES) and cyclic modulation spectrum (CMS) have gained popularity thanks to their high computational efficiency and simple implementation. The effectiveness of CMS and SES has been previously quantified based on the hypothesis of Gaussian background noise and has led to statistical tests for the presence of CS2 peaks in squared envelope spectra and cyclic modulation spectra. However a recently established link of CMS with SES and of SES with kurtosis has exposed a potential weakness of those indicators in the case of highly leptokurtic background noise. This case is often present in practice when the machine is subjected to highly impulsive phenomena, either due to harsh operating conditions or to electric noise generated by power electronics and captured by the sensor. This study investigates and quantifies for the first time the effect of leptokurtic noise on the capabilities of SES and CMS, by analysing three progressively harsh situations: high kurtosis, infinite kurtosis and alpha-stable background noise (for which even first and second-order moments are not defined). Then the resilience of a recently proposed family of CS2 indicators, based on the log-envelope, is verified analytically, numerically and experimentally in the case of highly leptokurtic noise.