A recursive algorithm for multidimensional inverse heat conduction problems by means of mode reduction

A recursive algorithm is developed to solve the inverse heat conduction problem of estimating time-varying strength of a heat source from the knowledge of temperature readings taken inside the domain. It is based on the Kalman filtering technique. Although the recursive nature of the Kalman filter algorithm allows the possibility of on-line estimation in place of batch form off-line estimation, the straightforward implementation of this algorithm to multidimensional partial differential equations has not been feasible due to the tremendous requirement of computer time and memory. In the present investigation we overcome this difficulty by employing the Karbunen–Loeve Galerkin procedure which reduces the governing partial differential equation to a minimum number of ordinary differential equations. The performance of the present technique of inverse analysis is evaluated by several numerical experiments, and is found to be very accurate as well as efficient.