Title
Solving Inverse Heat Conduction Problems Using Trained Pod-Rbf Network Inverse Method
Keywords
Heat conduction; Inverse problems; Proper orthogonal decomposition; Regularization
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.
Publication Date
1-1-2008
Publication Title
Inverse Problems in Science and Engineering
Volume
16
Issue
1
Number of Pages
39-54
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1080/17415970701198290
Copyright Status
Unknown
Socpus ID
38949107968 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/38949107968
STARS Citation
Ostrowski, Z.; Białecki, R. A.; and Kassab, A. J., "Solving Inverse Heat Conduction Problems Using Trained Pod-Rbf Network Inverse Method" (2008). Scopus Export 2000s. 10644.
https://stars.library.ucf.edu/scopus2000/10644