Application of Kalman Filtering with Input Estimation Technique to On-Line Cylindrical Inverse Heat Conduction Problems

Abstract

An on-line methodology to solve the inverse heat conduction problems of a hollow cylinder is presented. A new input estimation technique based on the concept of Kalman filtering is developed for estimating unknowns in real time, such as the what of the heat source or the heat flux on the boundary of the hollow cylinder. A recursive relation between the observed value of the residual sequence with unknown heat flux and the theoretical residual sequence of the Kalman filter that assumes known heat flux is formulated. A real time least squares algorithm is derived that uses the residual innovation sequence to compute the magnitude of heat flux. This recursive approach facilitates practical implementation and its capabilities are demonstrated in several typical cases with discontinuous and time-varying heat flux inputs.