Three-dimensional gridless imaging of aeroacoustical fields with sonons based on a hierarchical Bayesian framework

Abstract

The imaging of aeroacoustic fields by means of microphone arrays is a complex task due to the 3D nature of volumetric sources in turbulent flow. Rather than meshing the full space for the identification of aeroacoustical source distributions, the aim of this work is to reconstruct the acoustic sound fields generated by an equivalent set of point sources with free coordinates, called "acoustic sonons". Their radiation is expected to reproduce the same acoustical properties as the measured acoustical field, such as its pressure level, its directivity, and its spatial coherence by retrieving phase information. It is shown that the proposed concept of sonons, while being very flexible, effectively provides equivalent representations for a large variety of source distributions, whether they are initially composed of monopoles, dipoles, or quadrupoles, and whether these are spatially coherent or not. Additionally, source position priors can be taken into account in sonons generation, which improves localization ability. The problem is solved within a probabilistic framework, by means of a hierarchical Bayesian model inferred witha dedicated Markov chain Monte Carlo algorithm. The performance of the method is evaluated on two analytical test cases composed of the radiation of elementary sources and of a trailing edge.