Bayesian-driven cyclic-cross-spectral matrix completion: Non-synchronous measurements for cyclostationary acoustic sourcesa)

Accurate identification of cyclostationary acoustic sources, such as those generated by rotating machinery, is critical for noise control and fault diagnosis. Non-synchronous measurement (NSM) techniques using microphone arrays offer a cost-effective solution to overcome hardware limitations like insufficient aperture and spatial aliasing. However, existing methods, particularly fast iterative shrinkage-thresholding algorithm (FISTA)-based matrix completion algorithms, face two major challenges: (1) cumbersome parameter tuning due to reliance on empirical regularization and (2) lack of theoretical validation for cyclostationary scenarios where the low-rankness of cyclic-cross-spectral matrices (CCSMs) remains unproven. To address these issues, this paper proposes a Bayesian matrix completion framework tailored for cyclostationary NSM. The low-rank property of CCSM is rigorously established under cyclostationary conditions, and spatial continuity constraints are derived from frequency-shifted Green's function bases. A hierarchical Bayesian model is developed to automate parameter inference, eliminating manual tuning while integrating physical constraints. Numerical simulations demonstrate superior performance over FISTA, with lower matrix completion errors and source reconstruction errors under low signal-to-noise ratios and high-frequency regimes. Experimental validations, including loudspeaker localization and high-pressure pump noise mapping, confirm the method's ability to suppress aliasing artifacts, narrow main-lobewidth, and enhance spatial resolution.