Benchmark assessment of an improved regularization technique for generalized inverse beamforming

Thanks to their ability to deal with distributed and coherent acoustic sources, inverse beamforming methods have grown in popularity amongst the aeroacoustic community in the last few decades. This paper outlines the implementation of an improved version of the Generalized Inverse Beamforming (GIBF) with the purpose of ensuring an accurate source localization and a robust source strength reconstruction. In this respect, the development of a technique for the determination of the optimal regularization parameters at each iteration of the beamforming algorithm is of key importance. The regularization strategy is based on the Quasi-optimality criterion and on the L-curve method and, for its validation, GIBF code is applied to an experimental benchmark dataset labeled as NASA2. This test case concerns the analysis of a small-scale open-jet facility, the NASA Langley Quiet Flow Facility (QFF), for the characterization of airfoil self-noise. In order to evaluate the performances of the algorithm and to illustrate the potentialities and the benefits of its use for complex applications, a comparison with a Conventional Beamforming (CB) technique and with other array analysis methods applied to the same test case is performed. The analysis comprehends the qualitative evaluation of the source maps for several one-third octave frequency bands and the quantitative estimation of the integrated one-third octave band spectra of the leading edge and trailing edge regions of the model. The results show that, with a proper handling of the regularization strategy, GIBF can accurately resolve distributed acoustic sources. The source maps present improvements in terms of readability and reconstruction of the distributed nature of the source, whereas the integrated levels are in close agreement with the ones predicted by the other advanced methods.