Reconstruction of the surface normal acoustic intensity from noisy pressure data by regularized Helmholtz equation least squares method

Abstract

Reconstructing the normal acoustic intensity on a source surface from the field pressure measurements is critical in identifying the noise sources and their transmission paths. In this paper, we consider the reconstruction of time-averaged normal acoustic intensities from noisy pressure data using the Helmholtz equation least squares (HELS) method with regularization by truncated singular value decomposition or the method of Tikhonov. The regularization parameter is calculated by generalized cross validation, L-curve, and quasioptimality criterion and the best solution is chosen. Numerical results show that the normal velocity reconstruction is more sensitive to noise in the input data than the pressure reconstruction, and depends critically on the choice of the regularization parameter. It is found that the HELS-based Dirichlet-to-Neumann (DtN) map has a similar accuracy as compared to the Green’s formula-based DtN map with Tikhonov regularization for 1% noise or larger in the input data, provided that HELS converges sufficiently fast. Moreover, determining the surface normal velocity from the reconstructed surface pressure is more stable than reconstructing it directly from the field pressure data. It is concluded that a regularized HELS, when it converges fast enough, can be an easy-to-use and cost-effective tool for intensity reconstruction [Work supported by NSF.]