Krylov subspace iterative methods for time domain equivalent sources method based nearfield acoustical holography

Abstract

This paper studies the acoustic field reconstruction on an arbitrarily shaped vibrating surface using the time-domain equivalent source method (ESM) based near-field acoustic holography (NAH) from measurements of the pressure field on a nearby conformal surface. For the classical frequency-dependent ESM, we represent the acoustic field by a set of frequency-dependent monopole sources strategically distributed over a close and conformal surface to the vibrating structure. We demonstrated that in this setup, the ESM representation approximates the classical integral representations, which justifies the ESM as an extension to the classical integral theory. For time-domain ESM in a similar manner, we demonstrate that a set of time-dependent monopole sources approximates the single layer retarded potential and then characterize the acoustic field. The discretization of time-domain ESM produces a matrix system with a particular sparse structure that can be efficiently solved using Krylov subspace iterative methods. The iterative methods that will be of our interest are Conjugate Gradients Normal equation Residual, Conjugate Gradients Normal equation Error and Least Squares QR. To reduce the amplification of measurement in the numerical reconstructions, we combine the proposed iterative methods with heuristic stopping rules like L-curve, Quasi-Optimality, Hanke–Raus, Brezinski–Rodriguez–Seatzu and a posteriori stopping rule. To determine the best combination of reconstruction technique, iteration and stopping rule, we develop a statistical study that uses multiple samples of numerically generated data by Gaussian pulses over a sphere. We produce these samples using a random source position and different noise levels. Finally, we validate our proposed methodology using scattering data from an elastic spherical shell.