Application of a Particle Swarm Algorithm for Parameter Retrieval in a Transient Conduction-Radiation Problem

Abstract

This article addresses the application the particle swarm optimization (PSO) algorithm as an optimization tool for retrieval of parameters in a combined mode 1-D transient conduction-radiation heat transfer problem. In the chosen problem, the participating medium is absorbing, emitting, and scattering. The boundaries are taken to be diffuse gray. In both direct and inverse methods, the energy equation is 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 PSO algorithm. The objective function considered in the inverse formulation is an error function evaluated with the exact and inverse temperature fields for the simultaneous retrieval of the extinction coefficient and the scattering albedo. The inverse analysis constituted the effect of measurement errors on solution efficacies. In addition, the effect of important PSO parameters such as swarm size, inertia factor and constriction factor on the parameter retrieval is considered. For the chosen problem, it is found that the PSO with 20 discrete particles and 50 iterations is adequate for accurate parameter retrieval. The PSO has been found to provide a better accuracy than the genetic algorithm.

Notes

Numbers of iterations = 50, and Exact parameter values (β, ω: 1.0, 0.5).

Number of particles (n _P ) = 20, and exact parameter values (β, ω: 1.0, 0.5).

Number of particles (n _p ) = 20, number of iterations = 50, and exact parameter values (β, ω: 1.0, 0.5).

Number of particles (n _P ) = 20, number of iterations = 50.

Number of particles (n _P ) = 20, exact parameter values (β, ω: 1.0, 0.5), and measurement error = 0%.