An inverse patch transfer functions method based on a free field Green's function

Abstract

The inverse patch transfer functions (iPTF) method was proposed to reconstruct the normal velocity on the source surface in noisy environments. iPTF method is based on the measurements of the pressure and velocity on a surface surrounding the sound source and the Green's function of a virtual cavity satisfying Neumann boundary conditions. In the traditional way, the Green's function is obtained by using the modal superposition method, which involves the volume modeling and the modal analysis of the virtual cavity with the finite element method. In this work, an iPTF method based on Green's function in the free field is proposed. Consequently, the impedance matrix is obtained by using the boundary element method, which possesses higher computational efficiency and sufficient accuracy. Double-layer pressure measurements are adopted in this method to approximate the pressure and normal velocity on an intermediate hologram between the two conformal measurement surfaces. Two numerical examples with a sphere and a cubic radiator are given, and plane wave and point source are put aside as the disturbing source, respectively. Analytical and numerical solutions of the pressure and velocity on the hologram are used for these two radiators, respectively. The normal velocity and pressure on the structure radiated by the sound source in the free field could be reconstructed accurately even with a correlated signal to noise ratio (CSNR) at −20 dB. An experiment with a cubic radiator is also performed to confirm the validity of the proposed method.