Although the Spectral Correlation is one of the most versatile spectral tools to analyze cyclostationary signals (i.e. signals comprising hidden periodicities or repetitive patterns), its use in condition monitoring has so far been hindered by its high computational cost. The Cyclic Modulation Spectrum (the Fourier transform of the spectrogram) stands as a much faster alternative, yet it suffers from the uncertainty principle and is thus limited to detect relatively slow periodic modulations. This paper fixes the situation by proposing a new fast estimator of the spectral correlation, the Fast Spectral Correlation, based on the short-time Fourier transform (STFT). It proceeds from the property that, for a cyclostationary signal, the STFT evidences periodic flows of energy in and across its frequency bins. The Fourier transform of the interactions of the STFT coefficients then returns a quantity which scans the Spectral Correlation along its cyclic frequency axis. The gain in computational cost as compared to the conventional estimator is like the ratio of the signal length to the STFT window length and can therefore be considerable. The validity of the proposed estimator is demonstrated on non trivial vibration signals (very weak bearing signatures and speed varying cases) and its computational advantage is used to compute a new quantity, the Enhanced Envelope Spectrum.

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Due to its practical importance, the diagnosis of rolling element bearing has attracted constant interest in the scientific community. At the incipient stage of a failure, the measured vibration signal typically consists of a series of repetitive transients immerged in background noise. Although they are usually carried in high frequency bands due to the high stiffness of bearings, they are fairly weak compared with surrounding noise and other interfering signals. In addition, taking random slips and fluctuations into account, the transients produced by impacts are not strictly periodic but rather tend to be random cyclostationary. This makes the diagnosis of rolling element bearing quite challenging and, consequently, various signal processing techniques have been developed for either the detection, the identification or the extraction of the fault, whose combination asks for a high level of expertise of the user. The aim of this paper is to address all these objectives at once, in the same algorithm, by proposing a semi-automated method that requires the setting of only one parameter. It is rooted on a probabilistic model, in the form of a mixture of Gaussians, endowed with a hidden variable that indicates the occurrence of impacts. The method is shown to be optimal for detection in the Neyman-Pearson sense, it returns an envelope spectrum comparable to the best that can be obtained by other meanswhich often require a careful pre-filtering stepfrom which fault frequencies can be identified, and it eventually returns the fault signal from which subsequent severity/health indicators can be computed. There is almost no demand on the user's expertise (apart from setting the frequency resolution), even though the method does not address the decision part. The performance is investigated on synthetic signals and its robustness is also verified on several vibration signals measured on test-rigs. Results are found superior or at least equivalent to those of the conventional semi-automated method based on the fast kurtogram in combination with the envelope analysis.