Efficient frequency domain method for holographic localization of rotating sound sources with arbitrary array configurations

Owing to the widespread use of rotating machinery, the localization of rotating sources and the prediction of associated sound fields were extensively studied in the past decades. Most of the previous studies employed beamforming techniques for the localization of rotating sources. These methods usually rely on the use of a virtual rotating array (VRA), in which the Doppler effects caused by source rotation can be eliminated. In this study, compressive sensing (CS) near-field acoustic holography (NAH), which has been extended to the reconstruction of rotating sources using the frequency domain (FD) VRA method, can provide reconstruction capabilities that beamforming techniques cannot offer, such as predictions of the source amplitude and phase information. Furthermore, an improved resolution of spatial reconstructions at low frequencies was achieved. In addition to the direct combination of the FD-VRA method and recently developed stationary source CS acoustical holography techniques, a more efficient algorithm for FD-VRA was developed to address the shortcomings of the traditional approach, such as higher computational cost and the requirement of a circular array with equally spaced microphones. The proposed FD-VRA method only involves a direct summation of the rotating sidebands of signals measured on a stationary array, which effectively reduces the computational load. More importantly, an arbitrary array of optimized microphones can be used. The proposed algorithm works accurately for narrowband sources without overlapping frequency components in the rotating sidebands.