Enhancing the reconstruction of in-duct sound sources using a spectral decomposition method.

The characterization of in-duct acoustic source parameters for their use at the design stage, in virtual prototyping of the noise induced by fans and obstacles, is of great engineering importance. Conventional inverse approaches, such as the equivalent source method, offer accurate reconstruction results, but they require a large number of virtual sources or a suitable location of a few number of them. This paper proposes an alternative method that provides a cross-sectional imaging of the amplitude distribution of ducted sources, which does not depend on a prior adequate placement of equivalent sources, or on the degree of correlation between the real ones. The method is based on a full spectral formulation of the inverse problem, from which a theoretical stopping criterion is derived that provides a stable reconstruction of the unknown source distribution. Accurate and well-resolved imaging results of the axial acoustic velocity generated by wall-mounted drivers are obtained from either in-duct or wall-pressure measurements, acquired respectively without or with flow. The accuracy and the resolution of the retrieved source strength are significantly enhanced from an iterative modal decomposition of the pressure field, when imaging from data acquired respectively at large or small standoff distances to the source plane.