Interval inverse analysis of hyperbolic heat conduction problem

A general numerical model was presented to analyze the interval inverse hyperbolic heat conduction problem, with Bregman distances and weighted Bregman distances as regularization terms. By using the interval finite element method and interval extension theory, the direct and inverse models were established for uncertainties. The eight-point isoparametric elements were applied for the discretization in the space domain, and the Precise algorithm in time domain was empolyed. The inverse problems were implicitly formulated as optimization problems, using squared residues between the calculated and measured quantities as the objective function of the inverse identification. Results show that the proposed numerical models can identify single and combined interval thermal parameters and boundary conditions for hyperbolic heat transfer problems accurately and efficiently.