Estimation of heat transfer parameters by using trained POD-RBF and Grey Wolf Optimizer

Abstract

The article presents a numerical model for estimation of heat transfer parameters, e.g. thermal conductivity and convective coefficient, in two-dimensional solid bodies under steady-state conduction. This inverse problem is stated as an optimization problem, in which input is reference temperature data and the output is the design variables, i.e. the thermal properties to be identified. The search for optimum design variables is conducted by using a recent heuristic method, namely Grey Wolf Optimizer. During the heuristic search, direct heat conduction problem has to be solved several times. The set of heat transfer parameters that lead to smallest error rate between computed temperature field and reference one is the optimum output of the inverse problem. In order to accelerate the process, the model order reduction technique Proper-Orthogonal-Decomposition (POD) is used. The idea is to express the direct solution (temperature field) as a linear combination of orthogonal basis vectors. Practically, a majority of the basis vectors can be truncated, without losing much accuracy. The amplitude of this reduced-order approximation is then further interpolated by Radial Basis Functions (RBF). The whole scheme, named as trained POD-RBF, is then used as a surrogate model to retrieve the heat transfer parameters.