Fast computation of the kurtogram for the detection of transient faults

• Published in: Mechanical systems and signal processing Vol. 21; no. 1; pp. 108 - 124
• Main Author: Antoni, Jérôme
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2007; Elsevier
• Subjects: Acoustics; Kurtogram; Mechanics; Physics; Spectral kurtosis; Time–frequency; Transient detection; Vibration surveillance and diagnostics; Wavelet analysis; Transient detection; Vibration surveillance and diagnostics; Kurtogram; Wavelet analysis; Spectral kurtosis; Time–frequency
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2005.12.002

The kurtogram is a fourth-order spectral analysis tool recently introduced for detecting and characterising non-stationarities in a signal. The paradigm relies on the assertion that each type of transient is associated with an optimal (frequency/frequency resolution) dyad {
f
,
Δ
f
} which maximises its kurtosis, and hence its detection. However, the complete exploration of the whole plane (
f
,
Δ
f
) is a formidable task hardly amenable to on-line industrial applications. In this communication we describe a fast algorithm for computing the kurtogram over a grid that finely samples the (
f
,
Δ
f
) plane. Its complexity is on the order of
N
log
N
, similarly to the FFT. The efficiency of the algorithm is then illustrated on several industrial cases concerned with the detection of incipient transient faults.