Title
An inverse POD-RBF network approach to parameter estimation in mechanics
Abbreviated Journal Title
Inverse Probl. Sci. Eng.
Keywords
proper orthogonal decomposition; inverse problem; parameter estimation; heat conduction; elasticity; fracture mechanics; PROPER ORTHOGONAL DECOMPOSITION; HEAT-CONDUCTION PROBLEMS; L-CURVE; EQUATIONS; Engineering, Multidisciplinary; Mathematics, Interdisciplinary; Applications
Abstract
An inverse approach is formulated using proper orthogonal decomposition (POD) integrated with a trained radial basis function (RBF) network to estimate various physical parameters of a specimen with little prior knowledge of the system. To generate the truncated POD-RBF network utilized in the inverse problem, a series of direct solutions based on the finite element method, the boundary element method or exact analytical solutions are used to generate a data set of temperatures or deformations within the system or body, each produced for a unique set of physical parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt algorithm to minimize the objective least-squares functional. While the POD-RBF inverse approach outlined in this article focuses primarily in application to conduction heat transfer, elasticity and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or relevant industrial problems.
Journal Title
Inverse Problems in Science and Engineering
Volume
20
Issue/Number
5
Publication Date
1-1-2012
Document Type
Article; Proceedings Paper
Language
English
First Page
749
Last Page
767
WOS Identifier
ISSN
1741-5977
Recommended Citation
"An inverse POD-RBF network approach to parameter estimation in mechanics" (2012). Faculty Bibliography 2010s. 3210.
https://stars.library.ucf.edu/facultybib2010/3210
Comments
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