Input estimation method including finite-element scheme for solving inverse heat conduction problems

This work presents an inverse method based on the input estimation method including the finite-element scheme to estimate unknown heat flux. The input estimation method is comprised of the Kalman filtering technique and a recursive least-squares estimator. This recursive least-squares estimator is weighted by the forgetting factor gamma. It is derived using the residual innovation sequence to compute the magnitude of the heat flux, and the discretization is carried out using the finite-element scheme. The superior capabilities of the proposed method are demonstrated in one-dimensional and two-dimensional time-varying estimate cases and by comparison of the proposed algorithm with the conjugate gradient method. Results show that this method has the advantages of stability and good accuracy.