Inverse Aeroacoustic Problem for a Rectangular Wing

Abstract

An investigation is made of the feasibility of aeroacoustic inversion, where the pressure on a thin, flat, rigid rectangular wing undergoing rigid oscillations or interacting with unsteady, subsonic flow is to be predicted from the far-field acoustic signal. This problem is ill-posed because small pressure fluctuations in the far field are larger in the near field by a factor equal to the reciprocal of the distance from the wing. In the inverse model, this ill-posedness manifests itself in the kernel of a two-dimensional Fredholm integral equation of the first kind. Discretization of this integral equation using a physically meaningful collocation series results in an ill-conditioned system of equations which is solved using the singular value decomposition (SVD). The SVD generally requires regularization techniques to discard redundant or unphysical information. An algorithm is developed for optimally determining the near-field pressure without relying on a user-specified regularization parameter. Tests using numerically generated input data show the inversion is feasible and accurate for accurate input data. The inversion remains feasible when errors are introduced in the far-field measurements and the measurable parameters of the flow.