Acoustic field reconstruction for aircraft engine fans is essential for effective noise reduction. However, the use of a limited number of far-field measurement points in the reconstruction process exacerbates the ill-posedness issues, which necessitates the adoption of regularization techniques. The hierarchical Bayesian-based regularisation method has recently been applied to solve the equivalent source intensity distribution and reconstruct the sound field. However, previous methods have failed to accurately obtain the acoustic modal coefficients of the sound source, which are essential for determining the radiation type and directivity. This paper proposes a sound field reconstruction method that applies the hierarchical Bayesian algorithm to the source modal coefficient solution. Firstly, the deconvolution beamforming method obtains the sound source position. Subsequently, the hierarchical Bayesian algorithm is employed to obtain the source modal coefficients of the sound field, thereby completing the reconstruction of the sound field in the far-field region. Experimental results indicate that the proposed algorithm is highly effective in reconstructing far-field sound fields. Under free-field conditions and in mid-high frequency ranges, the average reconstruction error can be significantly reduced by using a few far-field microphones compared to traditional methods.
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