Vibrations of rotating machinery primarily originate from two sources, both of which are distorted by the machine's transfer function on their way to the sensor: the dominant gear-related vibrations and a low-energy signal linked to bearing faults. The proposed method facilitates the blind separation of vibration sources, eliminating the need for any information about the monitored equipment or external measurements. This method estimates both sources in two stages: initially, the gear signal is isolated using a dilated CNN, followed by the estimation of the bearing fault signal using the squared log envelope of the residual. The effect of the transfer function is removed from both sources using a novel whitening-based deconvolution method (WBD). Both simulation and experimental results demonstrate the method's ability to detect bearing failures early when no additional information is available. This study considers both local and distributed bearing faults, assuming that the vibrations are recorded under stable operating conditions.

Specifically, in wide-sense second-order cyclo-stationary (CS2) signals, the first two moments change periodically [1]. These signals are prevalent in numerous domains, including telecommunications, telemetry, radar, sonar, mechanics, radio astronomy, econometrics, and atmospheric science [2]. In the field of mechanics, the rotation of machinery is a significant source of such periodicity. Early signs of faults in gears, bearings, or components of internal combustion engines are represented by CS2 signals, typically detected using vibration, acoustic, or pressure sensors [3]. In telecommunications, telemetry, radar, and sonar, the periodicity in statistics stems from processes such as modulation, sampling, multiplexing, and coding. In radio astronomy, periodicity is observed due to phenomena like planetary revolution, rotation, and star pulsations. Econometrics encounters periodicity induced by seasonality, while atmospheric science studies periodic variations resulting from the Earth's rotation and revolution [4]. In the literature, two types of CS2 detectors are distinguished: one that identifies the presence of a CS2 signal amidst noise [5], and another that estimates CS2 signals, assuming prior knowledge about the cycle period or signal's sparsity [6]. However, in real-world situations, this information might not be available.