The adaptive blind filtering: A unified framework for repetitive transient extraction linking blind deconvolution and narrowband envelope analysis

Blind deconvolution is a popular signal processing method in rotating machinery fault diagnosis to extract repetitive impulses induced by rotating component faults. However, blind deconvolution methods rooted in time domain convolution are limited by the filter length parameter and may behave unstably under varying operating conditions. To this end, a new paradigm for repetitive transient extraction, named adaptive blind filtering (ABF), is proposed in this paper and applied to the fault diagnosis of rotating machinery. ABF essentially deconvolves the measured signal from the frequency domain perspective to recover the original repetitive transients and novelly links blind deconvolution and another popular approach, i.e., narrowband envelope analysis. In this methodology, a cyclostationarity significance index-gram (CSIgram) is developed to estimate the differential distribution of repetitive transient information across the entire frequency band, enabling adaptive identification of one or multiple resonant frequency bands dominated by repetitive transients. The distribution of repetitive transient information within various frequency bands also allows a frequency-dependent weight function to be automatically constructed, which acts as the frequency-domain form of the inverse filter, enabling the measured signal to be adaptively filtered through frequency-domain blind deconvolution. ABF is a unified framework for blind deconvolution and narrowband envelope analysis and is able to automatically extract and fuse repetitive transient information in multiple resonant frequency bands while effectively removing multisource interference noise. It overcomes the limitations of blind deconvolution that requires filter length configuration and narrowband envelope analysis that struggles to accurately determine the resonant frequency and bandwidth and focuses only on one resonant frequency band. Validations on synthesized simulation signals and actual railway train bearing experimental signals, as well as comparisons with typical envelope analysis and blind deconvolution methods, demonstrate that ABF is an excellent and
promising repetitive transient extraction method in rolling element bearing fault diagnosis.