A regularized solution for the inverse two-order transient heat conduction problems with multi-variables

In the present work, Tikhonov's regularization approachhas been used to solve inverse two-order transient heat conduction problemswith multi-variables, using Bregman distances and weighted Bregman distancesin the construction of regularization terms for the Tikhonov's function. Theinverse problem is formulated implicitly as an optimization problem with thecost functional of squared residues between calculated and measuredquantities.The eight-point finite element is used for the discretization inthe space system and a time stepping scheme is used for transient analysis.A finite element model is given, facilitating to sensitivity analysis fordirect and inverse problems, and taking account of inhomogeneity andparameters distribution. Combined identifications can be carried out forthermal parameters and boundary conditions etc. Satisfactory numericalvalidation is given including a preliminary investigation of effect of noisedata on the results and the computational efficiency for differentregularization terms. Results show that the proposed method can identifysingle and combined thermal parameters and boundary conditions for two-ordertransient heat conduction problems with precision.