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Investigation of regularization parameters and error estimating in inverse elasticity problems
Author(s) -
Maniatty Antoinette M.,
Zabaras Nicholas J.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370610
Subject(s) - regularization (linguistics) , inverse problem , backus–gilbert method , mathematics , inverse , bayesian probability , gaussian , tikhonov regularization , regularization perspectives on support vector machines , mathematical optimization , algorithm , computer science , statistics , mathematical analysis , artificial intelligence , physics , geometry , quantum mechanics
The method of Tarantola 1 based on Bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in Schnur and Zabaras. 2 It is shown that when normal Gaussian distributions are assumed and the error in the data is uncorrelated, the Bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in Schnur and Zabaras, 2 As such, the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem. Examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution.