Optimal hybrid parameter selection for stable sequential solution of inverse heat conduction problem

Abstract

To deal with the ill-posed 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.