Inverse Material Identification in Coupled Acoustic-Structure Interaction using a Modified Error in Constitutive Equation Functional.


Journal Article

This work focuses on the identification of heterogeneous linear elastic moduli in the context of frequency-domain, coupled acoustic-structure interaction (ASI), using either solid displacement or fluid pressure measurement data. The approach postulates the inverse problem as an optimization problem where the solution is obtained by minimizing a modified error in constitutive equation (MECE) functional. The latter measures the discrepancy in the constitutive equations that connect kinematically admissible strains and dynamically admissible stresses, while incorporating the measurement data as additional quadratic error terms. We demonstrate two strategies for selecting the MECE weighting coefficient to produce regularized solutions to the ill-posed identification problem: 1) the discrepancy principle of Morozov, and 2) an error-balance approach that selects the weight parameter as the minimizer of another functional involving the ECE and the data misfit. Numerical results demonstrate that the proposed methodology can successfully recover elastic parameters in 2D and 3D ASI systems from response measurements taken in either the solid or fluid subdomains. Furthermore, both regularization strategies are shown to produce accurate reconstructions when the measurement data is polluted with noise. The discrepancy principle is shown to produce nearly optimal solutions, while the error-balance approach, although not optimal, remains effective and does not need a priori information on the noise level.

Full Text

Duke Authors

Cited Authors

  • Warner, JE; Diaz, MI; Aquino, W; Bonnet, M

Published Date

  • September 2014

Published In

Volume / Issue

  • 54 / 3

Start / End Page

  • 645 - 659

PubMed ID

  • 25339790

Pubmed Central ID

  • 25339790

Electronic International Standard Serial Number (EISSN)

  • 1432-0924

International Standard Serial Number (ISSN)

  • 0178-7675

Digital Object Identifier (DOI)

  • 10.1007/s00466-014-1018-0


  • eng