The University of Southampton
University of Southampton Institutional Repository

Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination

Choi, H.G., Thite, A.N. and Thompson, D.J. (2007) Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination Journal of Sound and Vibration, 304, (3-5), pp. 894-917. (doi:10.1016/j.jsv.2007.03.040).

Record type: Article

Abstract

In performing transfer path analysis of structure-borne sound transmission, the operational forces at the excitation points and/or at the connections within the structure-borne paths are required. These forces can be obtained by using inverse techniques but the measured data used will contain some unknown errors. Therefore the reconstructed forces may include large errors due to the inversion of an ill-conditioned matrix of these measured data. In this study, Tikhonov regularization is used in order to improve the conditioning of the matrix inversion. Several methods are available to select the optimal regularization parameter. The purpose of this paper is to compare the performance of the ordinary and generalized cross validation methods and the L-curve criterion. Simulations are carried out, representing measurements on a rectangular plate, for different noise levels in measured data. Also, the robustness of the conclusions is investigated by varying the shape of the plates, the force positions, and the noise levels included in the measured data. The L-curve method is found to perform better than OCV or GCV, particularly for high noise levels in the operational responses, but less well when these noise levels are low. It is therefore found to be less susceptible to producing large reconstruction errors but it tends to over-regularize the solution in the presence of low noise, leading to under-estimates of the forces. In practice, measurements of operational responses may be susceptible to noise contamination which suggests that the L-curve method is likely to be the most appropriate method in practical situations. Nevertheless, it is important to obtain good estimates of the likely noise in the signals before determining the most appropriate regularization technique. Ordinary cross validation method is generally found to have a better performance than generalized cross validation method if the matrix condition numbers are high. Since the need for regularization is greater with high condition numbers, it is consequently found that the ordinary cross validation method gives more reliable results overall than the generalized cross validation method.

Full text not available from this repository.

More information

Published date: 24 July 2007

Identifiers

Local EPrints ID: 49587
URI: http://eprints.soton.ac.uk/id/eprint/49587
ISSN: 0022-460X
PURE UUID: d6bc0675-0e4c-43d2-96c9-c273d59660a6
ORCID for D.J. Thompson: ORCID iD orcid.org/0000-0002-7964-5906

Catalogue record

Date deposited: 20 Nov 2007
Last modified: 17 Jul 2017 14:55

Export record

Altmetrics

Contributors

Author: H.G. Choi
Author: A.N. Thite
Author: D.J. Thompson ORCID iD

University divisions

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.

×