A Bayesian Framework of Non-Synchronous Measurements at Coprime Positions for Sound Source Localization With High Resolution

The noise distribution in the mechanical system is tightly connected to the structure design and particular operating conditions. The noise source localization can effectively assist with the operating condition monitoring and noise reduction design of the mechanical device. The performance limitation of the array aperture for lower frequency acoustic localization is broken up by the non-synchronous measurement at coprime positions (CP-NSM), while this method has high uncertainty and requires an efficient adaptive regularization method to solve its corresponding acoustic inverse problem. The algorithms under the Bayesian framework with Student-t priors (variational Bayesian approximation and subspace variational Bayesian) are derived and deployed to solve the acoustic inverse problem in the CP-NSM method, and the results are compared with those obtained by the interior-point method and the alternating direction method of the multipliers algorithm. The proposed Bayesian methods have the advantages of adaptive regularization parameter estimation, which can reduce the influence of various interferences in CP-NSM. At the same time, in addition to using simulations and experiments in the anechoic chambers, the proposed Bayesian algorithms are validated further in real industrial applications. The proposed method is applied to improve the noise reduction design of the centrifugal fan, a mechanical device containing more information from noise sources.