Optimal demodulation-band selection for envelope-based diagnostics: A comparative study of traditional and novel tools

•Traditional band-selection methods focus on impulsiveness or cyclostationarity.•The two properties are often entangled in fault signals, giving misleading results.•The properties can be separated, and cyclostationarity appears most important.•Log-cycligram proposed to capture cyclostationarity separately from impulsiveness.•Performance of new method validated against existing tools on multiple datasets. The demodulation of machine signals is a key step for the diagnostics and prognostics of components such as rolling element bearings. Whereas diagnostic approaches could perform a cyclostationary analysis over the full spectral band (i.e. using cyclic-spectral maps), in order to extract time domain and statistical features for prognostics, a pre-processing filtering step is required to extract the often-weak fault-symptomatic signal components. A series of techniques derived from the original idea of the kurtogram have been proposed in previous studies for the selection of this optimal demodulation band. All of these methodologies have been designed to identify signal components with high impulsiveness (non-Gaussianity) or strong second-order cyclostationarity, both assumed to be typical characteristics of bearing fault signals. However, a recent series of theoretical works has shown how non-Gaussianity and non-stationarity (in its cyclic form), despite being clearly distinct properties, are practically entangled in bearing signals, and can be easily confused by indices such as kurtosis (implicitly assuming stationarity) or second-order cyclostationary (CS2) indicators (implicitly assuming Gaussianity). In addition, it has been shown that generalised Gaussian cyclostationary models are effective tools to describe and separate these two properties in bearing signals. Partial evidence seems to show that the cyclostationary property is dominant and more clearly indicative of a bearing fault, whereas impulsiveness is potentially misleading and not uniquely attributable to the bearing component of the signal. In this paper, we therefore propose a new statistically robust band selection tool which can capture cyclostationarity separately from non-Gaussianity. The tool, coined the log-cycligram (LC), is based on the strength of target cyclic frequency components in the spectrum of the log envelope (LES), and so potential fault frequencies must be known in advance. The effectiveness of the method is validated against the traditional kurtogram and a range of other