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Selection of response measurement locations to improve inverse force determination

Selection of response measurement locations to improve inverse force determination
Selection of response measurement locations to improve inverse force determination
The forces obtained by inverse methods are prone to errors. These arise due to a combination of errors in the measurements and high condition numbers in the matrix of transfer functions to be inverted. Ill-conditioning of the frequency response function matrix causes measurement errors to be magnified significantly. When the condition numbers are small, the measurement errors simply propagate without much amplification. Due to modal behaviour of the structure, the condition numbers can vary significantly over the frequency range and with the spatial location of the response measurements.
The spatial variation can be quite considerable across the structure. The potential for using this characteristic to improve force determination is explored in this paper as an alternative to matrix regularization methods. The aim is to reduce error magnification in inverse methods by an ‘optimal’ spatial distribution of response locations. A method is proposed which is based on the minimization of the average condition number across the frequency range. If many possible locations are available, however, this can involve excessive calculation. An approximate method is therefore proposed which results in consistently good location selection for use in inverse force determination but involves much less computational effort. The error reduction in reconstructed forces is found to be significant in numerical simulations on a simply supported plate and in validation experiments.
inverse force determination, sensor location selection, condition numbers, structure-borne noise, transfer path analysis, inverse problems
0003-682X
797-818
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. (2006) Selection of response measurement locations to improve inverse force determination. Applied Acoustics, 67 (8), 797-818. (doi:10.1016/j.apacoust.2006.01.001).

Record type: Article

Abstract

The forces obtained by inverse methods are prone to errors. These arise due to a combination of errors in the measurements and high condition numbers in the matrix of transfer functions to be inverted. Ill-conditioning of the frequency response function matrix causes measurement errors to be magnified significantly. When the condition numbers are small, the measurement errors simply propagate without much amplification. Due to modal behaviour of the structure, the condition numbers can vary significantly over the frequency range and with the spatial location of the response measurements.
The spatial variation can be quite considerable across the structure. The potential for using this characteristic to improve force determination is explored in this paper as an alternative to matrix regularization methods. The aim is to reduce error magnification in inverse methods by an ‘optimal’ spatial distribution of response locations. A method is proposed which is based on the minimization of the average condition number across the frequency range. If many possible locations are available, however, this can involve excessive calculation. An approximate method is therefore proposed which results in consistently good location selection for use in inverse force determination but involves much less computational effort. The error reduction in reconstructed forces is found to be significant in numerical simulations on a simply supported plate and in validation experiments.

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More information

Published date: 2006
Keywords: inverse force determination, sensor location selection, condition numbers, structure-borne noise, transfer path analysis, inverse problems

Identifiers

Local EPrints ID: 28432
URI: http://eprints.soton.ac.uk/id/eprint/28432
ISSN: 0003-682X
PURE UUID: 7ae47a79-245a-45c9-96f4-02861dd75e72
ORCID for D.J. Thompson: ORCID iD orcid.org/0000-0002-7964-5906

Catalogue record

Date deposited: 02 May 2006
Last modified: 16 Mar 2024 02:54

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Contributors

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

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