Estimating the location and shape of a scatterer by using its representative point for three-dimensional acoustic inverse problems

Abstract

We investigate a method to estimate the location and shape of an acoustic scatterer inversely from the profile (waveform) of sound pressure observed at designated observation points. Basically, the scatterer is represented using Non-Uniform Rational B-Splines (NURBS) patches, allowing the deformation of the scatterers by treating the control points (CPs) of the NURBS patches as design variables. However, large movements of the CPs can lead to self-intersections and collisions of the scatterers. So, we develop a new expression of the locations of the CPs with the representative points so that they can determine the approximate locations of the scatterers independently from their shapes. Upon the new expression, sensitivities with respect to the representative points and the local-position vectors of the CPs are derived from the shape derivative for the unsteady acoustic problem. Those sensitivities are integrated into a quasi-Newton method to solve the present inverse problem. The numerical experiments access the proposed method, focusing on the usefulness of representative point.