COMPARISON OF SENSITIVITY EQUATION AND ADJOINT EQUATION METHODS FOR PARAMETER-IDENTIFICATION PROBLEMS

This paper deals with the inverse analysis of a thermal conduction pro blem, in which the thermal conductivity is identified as an unknown pa rameter, which is determined so as to minimize the cost function repre sented by the square of the difference between the computed and observ ed temperatures at pre-assigned observation points. To minimize the co st function, both sensitivity equation and adjoint equation methods ca n be adopted. The sensitivity equation can be introduced by differenti ating the governing equation directly. The sensitivity coefficient is obtained by the sensitivity equation. The adjoint equation is introduc ed via a variational approach using a Lagrange multiplier. The Lagrang e multiplier is solution to an adjoint equation. Both sensitivity coef ficient and Lagrange multiplier are used to calculate the gradient of the cost function. The purpose of this paper is to compare the sensiti vity equation and adjoint equation methods from the convergence and co mputational efficiency points of view.