The University of Southampton
University of Southampton Institutional Repository

The Quantification of Structure-Borne Transmission Paths by Inverse Methods - Part 2: Use of Regularization Techniques

The Quantification of Structure-Borne Transmission Paths by Inverse Methods - Part 2: Use of Regularization Techniques
The Quantification of Structure-Borne Transmission Paths by Inverse Methods - Part 2: Use of Regularization Techniques
The inversion of an ill-conditioned matrix of measured data lies at the heart of procedures for the quantification of structure-borne sources and transmission paths. In an earlier paper the use of over-determination, singular value decomposition and the rejection of small singular values was discussed. In the present paper alternative techniques for regularizing the matrix inversion are considered. Such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography. The application to structure-borne sound transmission involves matrices, which vary much more with frequency and from one element to another. In this study Tikhonov regularization is used with the ordinary cross-validation method for selecting the regularization parameter. An iterative inversion technique is also studied. Here a form of cross-validation is developed allowing an optimum value of the iteration parameter to be selected. Simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques. Experiments are also performed to validate the results. Both techniques are found to give considerably improved results compared to singular value rejection.
0022-460X
433-451
Thite, A.N.
c3db753e-656c-4efe-9195-398ac5e7f6eb
Thompson, D.J.
bca37fd3-d692-4779-b663-5916b01edae5
Thite, A.N.
c3db753e-656c-4efe-9195-398ac5e7f6eb
Thompson, D.J.
bca37fd3-d692-4779-b663-5916b01edae5

Thite, A.N. and Thompson, D.J. (2003) The Quantification of Structure-Borne Transmission Paths by Inverse Methods - Part 2: Use of Regularization Techniques. Journal of Sound and Vibration, 264 (2), 433-451. (doi:10.1016/S0022-460X(02)01203-8).

Record type: Article

Abstract

The inversion of an ill-conditioned matrix of measured data lies at the heart of procedures for the quantification of structure-borne sources and transmission paths. In an earlier paper the use of over-determination, singular value decomposition and the rejection of small singular values was discussed. In the present paper alternative techniques for regularizing the matrix inversion are considered. Such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography. The application to structure-borne sound transmission involves matrices, which vary much more with frequency and from one element to another. In this study Tikhonov regularization is used with the ordinary cross-validation method for selecting the regularization parameter. An iterative inversion technique is also studied. Here a form of cross-validation is developed allowing an optimum value of the iteration parameter to be selected. Simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques. Experiments are also performed to validate the results. Both techniques are found to give considerably improved results compared to singular value rejection.

This record has no associated files available for download.

More information

Published date: 2003

Identifiers

Local EPrints ID: 10114
URI: http://eprints.soton.ac.uk/id/eprint/10114
ISSN: 0022-460X
PURE UUID: b5d0a662-d6ed-4053-a2d7-8a4273985cc4
ORCID for D.J. Thompson: ORCID iD orcid.org/0000-0002-7964-5906

Catalogue record

Date deposited: 16 Feb 2005
Last modified: 16 Mar 2024 02:54

Export record

Altmetrics

Contributors

Author: A.N. Thite
Author: D.J. Thompson ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×