Solution of inverse radiation problems using the Karhunen-Loeve Galerkin procedure

The low-dimensional model obtained by the Karhunen-Loeve Galerkin procedure is employed to solve the inverse radiation problem of estimating radiative parameters from the temperature measurement in three-dimensional participa ting media, where radiation and conduction occur simultaneously. The invers e radiation problem is solved through the minimization of a performance fun ction, which is expressed by the sum of square residuals between calculated and observed temperature, utilizing the conjugate gradient method. The low -dimensional model based on the Karhunen-Loeve Galerkin procedure can repre sent a given system with a minimum degree of freedom, and consequently the number of equations to be solved in the estimation of parameters is minimiz ed when the present technique is used. It is shown that the present techniq ue of solving inverse radiation problems employing the Karhunen-Loeve Galer kin procedure yields results as accurate as those using the S-4 method at a drastically reduced computational cost. (C) 2001 Elsevier Science Ltd. All rights reserved.