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Estimation of acoustic source strength by inverse methods: Part I, Conditioning of the inverse problem; Part II, experimental investigation of methods for choosing regularisation parameters

Estimation of acoustic source strength by inverse methods: Part I, Conditioning of the inverse problem; Part II, experimental investigation of methods for choosing regularisation parameters
Estimation of acoustic source strength by inverse methods: Part I, Conditioning of the inverse problem; Part II, experimental investigation of methods for choosing regularisation parameters
This paper deals with the discrete inverse problem in acoustics. It is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field. The transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known. In principle, the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions. The accuracy of source strength reconstruction (in the presence of noise which contaminates the measured pressures) is crucially dependent on the conditioning of the matrix to be inverted. This paper examines the conditioning of this inverse problem, particularly with regard to the geometry and number of sources and measurement positions and the non-dimensional frequency. A preliminary investigation is also presented of methods such as Tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases. Results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time-stationary random processes and the spectra and cross-spectra are measured at a number of positions in the radiated field. The paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements.
0022-460X
639-701
Nelson, P.A.
41f7a079-1d7d-4d97-8fec-ffd5c271b26c
Yoon, S.H.
15886fe3-f4d5-41b5-9119-7806cdcfed0a
Nelson, P.A.
41f7a079-1d7d-4d97-8fec-ffd5c271b26c
Yoon, S.H.
15886fe3-f4d5-41b5-9119-7806cdcfed0a

Nelson, P.A. and Yoon, S.H. (2000) Estimation of acoustic source strength by inverse methods: Part I, Conditioning of the inverse problem; Part II, experimental investigation of methods for choosing regularisation parameters. Journal of Sound and Vibration, 233 (4), 639-701. (doi:10.1006/jsvi.1999.2837).

Record type: Article

Abstract

This paper deals with the discrete inverse problem in acoustics. It is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field. The transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known. In principle, the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions. The accuracy of source strength reconstruction (in the presence of noise which contaminates the measured pressures) is crucially dependent on the conditioning of the matrix to be inverted. This paper examines the conditioning of this inverse problem, particularly with regard to the geometry and number of sources and measurement positions and the non-dimensional frequency. A preliminary investigation is also presented of methods such as Tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases. Results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time-stationary random processes and the spectra and cross-spectra are measured at a number of positions in the radiated field. The paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements.

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Published date: 2000

Identifiers

Local EPrints ID: 10186
URI: http://eprints.soton.ac.uk/id/eprint/10186
ISSN: 0022-460X
PURE UUID: 52aec9eb-1818-40f5-9131-628460562c99

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Date deposited: 19 Jan 2005
Last modified: 15 Mar 2024 04:58

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Contributors

Author: P.A. Nelson
Author: S.H. Yoon

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