Simultaneous Retrieval of Parameters in a Transient Conduction-Radiation Problem Using a Differential Evolution Algorithm

Abstract

This article deals with the application of the differential evolution (DE) algorithm for the inverse analysis of a transient conduction-radiation heat transfer problem. Thermophysical properties and/or optical properties of the medium are simultaneously retrieved with a known temperature field. The conducting-radiating planar enclosed medium bounded by diffuse-gray boundaries is absorbing, emitting, and scattering. In both the direct and inverse methods, the energy equations are solved using the lattice Boltzmann method (LBM), and the finite volume method (FVM) is used to compute the radiative information. In the inverse method, the objective function is minimized using the DE algorithm. Any two sets of parameters, viz., the extinction coefficient, the scattering albedo, emissivity and conduction-radiation parameter, are simultaneously retrieved. The effects of key DE algorithm parameters, such as the weighting factor and the crossover constant on the quality of solutions, are studied. Measurement errors are accounted. The accuracy of the DE algorithm is compared with the genetic algorithm. The DE algorithm is significantly faster, and it yields the global optimum for a wide range of parameters.

Notes

Numbers of generations = 50; exact parameter values (β, ω: 1.0, 0.5).

Numbers of vectors (N _V ) = 20.; exact parameter values (β, ω: 1.0, 0.5).

Exact parameter values (β, ω)= (1.0, 0.5); (N _V  = 20, N _G  = 50).