Kalman Smoothing Technique Applied to the Inverse Heat Conduction Problem

The time-dependent surface heat flux at one boundary of a one-dimensional system is reconstructed by using the Kalman smoothing technique, given the initial temperature distribution and the time-temperature history at an interior location. The study makes a parametric investigation and analyzes the behavior of two finite-difference schemes. The numerical results show the very good performance of the proposed technique, which provides a comprehensive way for using future temperature measurements. Although in this study attention is devoted to the one-dimensional linear problem, the algorithm can be generalized for the stochastic nonlinear multidimensional case.