The factorization method and Capon's method for random source identification in experimental aeroacoustics

TL;DR

This paper explores the use of the factorization method and Capon's method for identifying uncorrelated aeroacoustic sources from microphone array data, providing a novel connection between inverse scattering and beamforming techniques.

Contribution

It introduces a variant of the factorization method for source support recovery and reveals a surprising relation to Capon's beamforming method in aeroacoustics.

Findings

The factorization method can effectively recover source support.

A connection between the factorization method and Capon's method is established.

Numerical examples validate the theoretical insights.

Abstract

Experimental aeroacoustics is concerned with the estimation of acoustic source power distributions, which are for instance caused by fluid structure interactions on scaled aircraft models inside a wind tunnel, from microphone array measurements of associated sound pressure fluctuations. In the frequency domain aeroacoustic sound propagation can be modelled as a random source problem for a convected Helmholtz equation. This article is concerned with the inverse random source problem to recover the support of an uncorrelated aeroacoustic source from correlations of observed pressure signals. We show that a variant of the factorization method from inverse scattering theory can be used for this purpose. We also discuss a surprising relation between the factorization method and a commonly used beamforming algorithm from experimental aeroacoustics, which is known as Capon's method or as the minimum variance method. Numerical examples illustrate our theoretical findings.