Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition

    Authors

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

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Comput. Mech.

    Keywords

    inverse problems; Proper Orthogonal; decomposition; regularization; heat; transfer; heat conductivity; EQUATIONS; Mathematics, Interdisciplinary Applications; Mechanics

    Abstract

    An inverse approach is developed to estimate the unknown heat conductivity and the convective heat transfer coefficient. The method relies on proper orthogonal decomposition (POD) in order to filter out the higher frequency error. The idea is to solve a sequence of direct problems within the body under consideration. The solution of each problem is sampled at a predefined set of points. Each sampled temperature field, known in POD parlance as a snapshot, is obtained for an assumed value of the retrieved parameters. POD analysis, as an efficient mean of detecting correlation between the snapshots, yields a small set of orthogonal vectors (POD basis), constituting an optimal set of approximation functions. The temperature field is then expressed as a linear combination of the POD vectors. In standard applications, the coefficients of this combination are assumed to be constant. In the proposed approach, the coefficients are allowed to be a nonlinear function of the retrieved parameters. The result is a trained POD base, which is then used in inverse analysis, resorting to a condition of minimization of the discrepancy between the measured temperatures and values calculated from the model. Several numerical examples show the robustness and numerical stability of the scheme.

    Journal Title

    Computational Mechanics

    Volume

    37

    Issue/Number

    1

    Publication Date

    1-1-2005

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    52

    Last Page

    59

    WOS Identifier

    WOS:000232819300007

    ISSN

    0178-7675

    Share

    COinS