Solving inverse heat conduction problems using trained POD-RBF network inverse method

    Authors

    Z. Ostrowski; R. A. Bialecki;A. J. Kassab

    Comments

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    Abbreviated Journal Title

    Inverse Probl. Sci. Eng.

    Keywords

    inverse problems; regularization; heat conduction; proper orthogonal; decomposition; PROPER ORTHOGONAL DECOMPOSITION; FLOWS; Engineering, Multidisciplinary; Mathematics, Interdisciplinary; Applications

    Abstract

    The article presents advances in the approach aiming to solve inverse problems of steady state and transient heat conduction. The regularization of ill-posed problem comes from the proper orthogonal decomposition (POD). The idea is to expand the direct problem solution into a sequence of orthonormal basis vectors, describing the most significant features of spatial and time variation of the temperature field. Due to the optimality of proposed expansion, the majority of the basis vectors can be discarded practically without accuracy loss. The amplitudes of this low-order expansion are expressed as a linear combination of radial basis functions (RBF) depending on both retrieved parameters and time. This approximation, further referred as trained POD-RBF network is then used to retrieve the sought-for parameters. This is done by resorting to least square fit of the network and measurements. Numerical examples show the robustness and numerical stability of the scheme.

    Journal Title

    Inverse Problems in Science and Engineering

    Volume

    16

    Issue/Number

    1

    Publication Date

    1-1-2008

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    39

    Last Page

    54

    WOS Identifier

    WOS:000252959000004

    ISSN

    1741-5977

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