Optimal hybrid parameter selection for stable sequential solution of inverse heat conduction problem
Abstract
To deal with the illposed nature of the inverse heat conduction problem (IHCP), the regularization parameter alpha can be incorporated into a minimization problem, which is known as Tikhonov regularization method, a popular technique to obtain stable sequential solutions. Because alpha is a penalty term, its excessive use may cause large bias errors. Ridge regression was developed as an estimator of the optimal alpha to minimize the magnitude of a gain coefficient matrix appropriately. However, the sensitivity coefficient matrix included in the gain coefficient matrix depends on the time integrator; thus, certain parameters of the time integrators should be carefully considered with alpha to handle instability. Based on this motivation, we propose an effective iterative hybrid parameter selection algorithm to obtain stable inverse solutions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.01297
 Bibcode:
 2021arXiv211001297A
 Keywords:

 Mathematics  Numerical Analysis;
 65F22;
 G.1.6
 EPrint:
 25 pages, 13 figures, 4 tables