Traditional sound source localization methods encounter significant challenges in simultaneously locating rotating and static sources. These challenges arise from the different motion patterns of these two types of sound sources, and they are typically not situated on the same plane. To address this issue, a method based on Modal Composition Beamforming (MCB) and the equivalent source method is proposed for separating rotating and static sound sources, which fully utilizes the prior knowledge of the spatiotemporal properties of these sources. The proposed approach involves establishing a Rotating-Static Sources Power Propagation (R-S2P) model, utilizing the relationship between the equivalent source strength and the actual beamforming output. By employing this forward model and applying an appropriate inversion method, it is possible to separate the components of rotating and static sources. Simulations for three cases with different source strengths are presented, and the R-S2P inversion problem is resolved using the Least Absolute Shrinkage and Selection Operator (LASSO) method. We showed that this method enables accurate separation and localization of rotating and static sources on different planes with varying relative intensities, even if the background noise is strong.

Rotating source beamforming techniques have been effective means of noise localization on rotary machines. In this letter, we derive an alternative expression for modal composition beamforming (MCB) and subsequently consider the equivalent source assumption and cyclostationarity of the constant angular-speed rotating sound source so that a rotating sound source power (RSP) propagation model is derived. By estimating a suitable solution for the RSP model using the subspace variational Bayesian (SVB) technique with sparsity and total variation (TV) priors, the validity of the RSP model was established. According to the simulation results, the proposed RSP-SVB method leads to a significantly higher resolution than the MCB method. It can localize multiple fast-rotating sound sources accurately, rapidly, and effectively in environments with strong background noise interference. Therefore, our proposed RSP-SVB can offer a reliable solution for identifying fast-rotating blade noise.

The non-synchronous measurement (NSM) technology has been significantly developed. NSM at the coprime position (CP-NSM) is a measurement principle in two-dimensional (2D) acoustic imaging, wherein a planar array is moved to a coprime position for measurements. However, there are certain drawbacks to the measurement principles of spherical arrays in three-dimensional (3D) acoustic imaging. A measurement principle of 3D acoustic imaging has been investigated using 3D Non-Synchronous Measurements with a Central Reference based on Revolution and Autorotation (CR-NSM). The primary contributions of this CR-NSM are as follows: (1) A measurement principle for 3D non-synchronous measurements with a central reference based on revolution and autorotation is proposed. (2) The spatial resolution is primarily determined by the revolution in CR-NSM, and the side lobe is reduced by autorotation in CR-NSM. In the simulation results, the spatial resolution is obtained using CR-NSM for good imaging at low signal-to-noise ratios (SNR). Moreover, the cross-spectral matrix (CSM) completion error is enhanced by adding the phase relations between consecutive positions. The CR-NSM algorithm was developed according to the measurement principles of 3D acoustic imaging.

In this letter, an acoustic imaging method is proposed to improve conventional non-synchronous measurements (NSM) by carrying out the NSM at coprime positions (CP-NSM). The pattern of the NSM movement is guided by a set of coprime positions. A virtual domain signal is then constructed by vectorizing the covariance matrix of the NSM. Similarly, a virtual array is constructed using the Kronecker product of the Green's function of the CP-NSM. Therefore, the synthetic aperture of the proposed CP-NSM is first expanded by the NSM, and further enlarged by the virtual array. The simulation results demonstrate that the proposed CP-NSM achieves higher spatial resolution at lower frequencies and a lower signal-to-noise ratio than the conventional NSM.