Sound source reconstruction using inverse boundary element calculations

Abstract

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation ͑GCV͒ approach for the present tire noise studies.

An alternating iterative procedure for the Cauchy problem for the Helmholtz equation

“…Cauchy problem (1) has physical applications in optoelectronics [3] and characterization of sound sources [4,5]. The Cauchy problem is an ill-posed problem: its solution is unique but does not depend continuously on the Cauchy data; see [6][7][8][9].…”

Experimental feasibility of in-duct sound source reconstruction

“…Depending on the choice of the integral representation of the radiated pressure field, model-based reconstruction techniques include the Inverse Boundary Element Method (IBEM) and the Equivalent Source Method (ESM). The IBEM assumes an interpolation of the unknown surface velocity distribution at the nodes of each discretized boundary element [4]. The ESM assumes a distribution of volume velocity monopole-type [5] or pressure dipole-type sources which respectively discretize, the single and double layer potential densities in an indirect integral representation of the radiated pressure field.…”

Numerical Methods for Near-Field Acoustic Holography over Arbitrarily Shaped Surfaces

“…The indirect formulations are based on representations to the solution of Equation 1 like the single source or double source representation found in Augusztinovicz (1999); Delillo et al (2000); DeLillo et al (2001;; Raveendra et al (1998);Schuhmacher et al (2003); Tekatlian et al (1996); Vlahopoulos & Raveerdra (1998);Williams et al (2000); Zhang et al (2001;2000). Using the notation of the previous subsection the single source representation is defined as…”