The application of inverse methods to spatially-distributed acoustic sources

Acoustic inverse methods, based on the output of an array of microphones, can be readily applied to the characterisation of acoustic sources that can be adequately modelled as a number of discrete monopoles. However, there are many situations, particularly in the fields of vibroacoustics and aeroacoustics, where the sources are distributed continuously in space over a finite area (or volume). This paper is concerned with the practical problem of applying inverse methods to such distributed source regions via the process of spatial sampling. The problem is first tackled using computer simulations of the errors associated with the application of spatial sampling to a wide range of source distributions. It is found that the spatial sampling criterion for minimising the errors in the radiated far-field reconstructed from the discretised source distributions is strongly dependent on acoustic wavelength but is only weakly dependent on the details of the source field itself. The results of the computer simulations are verified experimentally through the application of the inverse method to the sound field radiated by a ducted fan. The un-baffled fan source with the associated flow field is modelled as a set of equivalent monopole sources positioned on the baffled duct exit along with a matrix of complimentary non-flow Green functions. Successful application of the spatial sampling criterion involves careful frequency-dependent selection of source spacing, and results in the accurate reconstruction of the radiated sound field. Discussions of the conditioning of the Green function matrix which is inverted are included and it is shown that the spatial sampling criterion may be relaxed if conditioning techniques, such as regularisation, are applied to this matrix prior to inversion.