Stochastic inverse heat conduction using a spectral approach

An adjoint-based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill-posed stochastic inverse problem is restated as a conditionally well-posed L2 optimization problem. The gradient of the objective function is obtained in a distributional sense by defining an appropriate stochastic adjoint field. The L2 optimization problem is solved using a conjugate-gradient approach. Accuracy and effectiveness of the proposed approach is appraised with the solution of several stochastic inverse heat conduction problems