IRLS based inverse methods tailored to volumetric acoustic source mapping

Planar microphone arrays are of common use in acoustic source identification methods, as well as the use of planar calculation grids. Indeed, the assumption is that the planar grid contains all sources of interest. However, this assumption may not be true in several applications and hence return misleading results. One tentative to overcome this issue is to consider three-dimensional surface adhering on the target. Unfortunately, also this choice may not be enough to obtain accurate results in challenging applications like aeroacoustic source mapping, since noise sources are not necessarily located on the surface of the target. This paper aims to analyze the issues and the benefits arising when the calculation grid turns into a volume. Two inverse methods based on Iterative Re-weighted Least Squares (IRLS) and Bayesian Regularization (BR) are formulated: Equivalent Source Method (ESM-IRLS) and Covariance Matrix Fitting (CMF-IRLS). Even though these methods are based on concepts already known in literature, the focus of this paper is on theoretical and algorithmic aspects that make them able to produce accurate volumetric acoustic maps. The methods proposed are applied both on a simulated and an experimental test case. The former is reported to highlight the difference between standard surface mapping and volumetric mapping. The latter reports an application on an airfoil in an open jet. A comparison with the CLEAN-SC approach is reported in both cases to show the performance of the proposed methods with respect to a well-known state of the art algorithm.