Title

An inverse POD-RBF network approach to parameter estimation in mechanics

Authors

Authors

C. A. Rogers; A. J. Kassab; E. A. Divo; Z. Ostrowski;R. A. Bialecki

Comments

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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

WOS:000306833100012

ISSN

1741-5977

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