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

To deal with the ill-posed nature of inverse heat conduction problem (IHCP), regularization parameter ? can be incorporated into a minimization problem, which is known as Tikhonov method, popular technique to obtain stable sequential solutions. Because penalty term, its excessive use may cause large bias errors. A ridge regression was developed an estimator optimal minimize magnitude gain coefficient matrix appropriately. However, sensitivity included in depends on time integrator; thus, certain parameters integrators should carefully considered handle instability. Based this motivation, we propose effective iterative hybrid selection algorithm We Euler integrator solve IHCP using finite element method. then ?, define Forward Backward integrators, ?. The error amplified by controlled first assuming ?=1. total classified and variance computed maximum flux change, calculated measurement noise generated prior information. Therefore, initially efficiently defined summation errors time-independent manner. Reducing for better stability solutions also available adjusting when spectral radius amplification less than one. Consequently, could updated new ? iteration process. proposed efficient essential implement engineering practice. possibility performance were evaluated well-constructed 1D 2D numerical examples.