Solution of a multidimensional inverse radiation problem by means of mode reduction

The Karhunen–Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time‐varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three‐dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen–Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted. Copyright © 2004 John Wiley & Sons, Ltd.