Dictionary-based Equivalent Source Method for Near-Field Acoustic Holography

Abstract

In this paper, we propose a modification of the standard Equivalent Source Method (ESM) for Near-Field Acoustic Holography (NAH). As in EMS, we aim at modeling the acoustic pressure radiated from a vibrating object, and its surface velocity, as the joint effect of a set of equivalent sources located within or dose to the object itself. The estimation of the equivalent source strengths (weigths) comes from the solution of a highly ill-conditioned problem. Rather than solving this problem in the least-squares sense, we exploit the 3D model of the vibrating object, along with a rough estimate of its physical parameters, to restrict the space of the solutions. More specifically, we make use of Finite Element Analysis for populating a compressed dictionary of possible equivalent source weights. NAH is then approached by seeking a sparse linear combination of the entries of the dictionary. Experiments carried on a public database prove the effectiveness of the proposed technique, especially when the number of available microphones is limited, and in the presence of a significant level of measurement noise.

A Physics-Informed Neural Network Approach for Nearfield Acoustic Holography

“…To the authors knowledge, only rules of thumb are proposed, which are not, however, applicable in some contexts. In order to deal with this problem, ESM techniques based on CS [ 20 , 21 , 22 ] have been proposed with the aim of finding small and sparse subsets of equivalent sources.…”

“…For example, Canclini et al [ 22 ] proposed building a dictionary of equivalent sources in order to solve NAH. This technique, called dictionary-based esm (DESM), exploits synthetic data for finding the equivalent sources.…”

“…Recently, a new approach to NAH based on deep learning [ 23 ] has been proposed in [ 24 ]. The authors, inspired by the effectiveness of learned features for NAH [ 22 ] and the well-known feature learning capabilities of deep neural networks (DNN) in the context of acoustics [ 25 , 26 , 27 , 28 , 29 ], proposed a convolutional neural network (CNN) [ 30 ] for performing NAH. The promising approach of [ 24 ] provides accurate results, but the evaluation is limited to rectangular plates of isotropic material only.…”

Near field Acoustic Holography on arbitrary shapes using Convolutional Neural Network

“…The main problem of ESM is the computation of the optimal set (in terms of number and location) of equivalent sources. In order to deal with this problem, ESM techniques based on CS [15]- [17] have been proposed with the aim of finding small and sparse subsets of equivalent sources.…”

“…In [17] a dictionary-based ESM (DESM) is proposed in order to consider a sparse domain for solving ESM limitations. The ESM solution space is restricted to a suitable compressed dictionary whose components are retrieved from several sets of equivalent sources.…”