Deconvolution model for the cyclostationary acoustic source beamforming with high spatial resolution

Given the cyclostationarity inherent in the noise emitted by rotating machinery, cyclostationary conventional beamforming (CSCBF) emerges as an effective tool for visually pinpointing noise sources. However, CSCBF faces challenges similar to those of conventional beamforming (CBF), notably poor spatial resolution at lower frequencies and the manifestation of ghost sources at higher frequencies. To address these limitations, this paper introduces a novel deconvolution model that incorporates a non-convex sparse penalty, termed Cyclo-GMCP. Initially, the acoustic map generated by CSCBF is obtained, and subsequently, the point spread function (PSF) within CSCBF is derived to establish the deconvolution model. To ensure high spatial resolution in localization results, a generalized minimax-concave penalty (GMCP) is imposed on the acoustic map. Numerical examples and real-data experiments validate the efficacy of the proposed Cyclo-GMCP method, demonstrating its ability to address the aforementioned issues by distinguishing acoustic sources with different cyclic frequencies, displaying narrower main lobes, and reducing side lobes compared to CSCBF.