Inverse determination of temperature-dependent thermophysical parameters using multiobjective optimization methods

Multiobjective optimization is employed for solving the inverse steady-state heat transfer for temperature dependent thermophysical properties. On the basis of the proposed method, the thermophysical properties are denoted as a linear combination of a set of basis functions, which are formulated from the measured temperature. Taking the undetermined coefficients as estimation variables, the problem of inverse determination of thermophysical properties can be turned into a multiobjective optimization problem by constructing the temperature distributions in a structure with different forms. Then, the metamodeling, radial basis functions, is introduced to improve the efficiency of optimization, and the solution can be determined by comparing the Pareto set, which is gained by Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II), based on screening criteria. Finally, the proposed method has been demonstrated firstly on a one-dimensional problem with exact analytical solution and then tested on a 2-D heat conduction problem simulated by FEA. Numerical results demonstrate that the multiobjective estimation method is high efficient in treating this type of problem, meanwhile, it can solve the ill-post problem which is caused by approximate error of metamodeling and measurement noise.