Sound source identification in a noisy environment based on inverse patch transfer functions with evanescent Green's functions

A modified inverse patch transfer function (iPTF) method is used to reconstruct the normal velocities of the target source in a noisy environment. The iPTF method simplifies the Helmholtz integral equation to one term by constructing a Green's function satisfying Neumann boundary conditions for an enclosure, which is generally constructed by slowly convergent modal expansions. The main objective of the present work is to provide an evanescent Green's function to improve the convergence of calculations. A brief description of the iPTF method and two sets of Green's functions for a rectangular cavity are presented firstly. In simulations, both the Green's functions are used to calculate the condition numbers of impedance matrices describing the relation between source and measurement patches, and the time cost of calculation based on the two sets of Green's functions at 450 Hz is compared. Double pressure measurements are then employed as the input data instead of pressure and velocity measurements. The normal velocities of two baffled loudspeakers are reconstructed by the combination of a measurement method and a Green's function in the presence of a disturbing source in the frequency range of 50–1000 Hz. In addition, the double pressure measurements are examined by an experiment. The precise identification of the sources indicates that the double pressure measurements are capable of localizing sources in a noisy environment. It is also found that the reconstruction with the evanescent Green's functions is slightly better than that with the modal expansions.