Fast computation of the kurtogram for the detection of transient faults

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,Δff,Δf} which maximises its kurtosis, and hence its detection. However, the complete exploration of the whole plane (f,Δff,Δf) 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,Δff,Δf) plane. Its complexity is on the order of NlogN, similarly to the FFT. The efficiency of the algorithm is then illustrated on several industrial cases concerned with the detection of incipient transient faults.