Optimal Weighted Envelope Spectrum: An enhanced demodulation method for extracting specific characteristic frequency of rotating machinery

Envelope spectrum plays a crucial role in fault diagnosis of rotating machinery. Narrowband demodulation and cyclostationary analysis are two mainstream methods to construct this kind of spectral quantity. However, the former is prone to fail in the cases of low Signal-to-Noise Ratio (SNR) or with non-Gaussian noise, while the latter is sensitive to cyclostationary noise such as electromagnetic interferences. It is noted that specific tasks determine the characteristic frequencies expected to be detected by envelope spectrum. Stated more precisely, the target component and the noise interference are decided by the mechanical part of concern. Therefore, the classical envelope spectrums constructed by narrowband demodulation and cyclostationary analysis always show inadequacies when facing complicated monitoring signals from rotating machinery. To deal with this dilemma, this paper proposes the Optimal Weighted Envelope Spectrum (OWES) to realize the enhanced extraction of specific characteristic frequency. First, a cyclostationary model of rotating machinery is established, and it is defined that only the cyclostationary signal caused by the mechanical part of concern is the target component to be extracted. Second, the optimal weighting function is constructed by evaluating the Carrier-to-Noise Ratio (CNR) from Spectral Correlation (SC), and the OWES is proposed as the integrated quantity of the Optimal Weighted Spectral Correlation (OWSC) along the spectral frequency axis. After that, the indicators Harmonics Characterization Coefficient (HCC) and Harmonics Characterization Ratio (HCR) are designed to measure the demodulation performance of different spectral quantities. Finally, the effectiveness of OWES is validated by simulation signals and actual data from rolling bearing and centrifugal pump, and the comparison with several classical methods also verifies its superiority.