Sparse Green’s Functions Estimation Using Orthogonal Matching Pursuit: Application to Aeroacoustic Beamforming

Abstract

The Paper presents a new methodology for the numerical estimation of the Green’s functions in complex external aeroacoustic configurations. Computational aeroacoustics is used to propagate multifrequency signals from focus points to microphones. The method takes advantage of the sparsity of the Green’s functions in the time domain to minimize the simulation time. It leads to a complex sparse linear regression problem. To solve it, the orthogonal matching pursuit algorithm is adapted. The method is first applied on the case of the diffraction by a rigid sphere. Results are studied both in terms of Green’s function estimation and aeroacoustic beamforming. They show that the Green’s functions are obtained with a good accuracy and enable localization of acoustic sources placed behind the diffracting object. The methodology is then applied on a NACA0012 two-dimensional wing in a potential flow for which the Green’s function is not known analytically. The use of the reverse-flow reciprocity principle enables reduction of the complexity of the estimation problem when there are more scan points than microphones. It is shown that it is possible to take advantage of the presence of diffracting objects to improve the capability of detection of a sensor array.