Application of KF-RLSE algorithm for on-line estimating the time-dependent melting thickness and input heat flux in participating media

This study proposes an inverse heat transfer process to estimate the time-dependent melting thickness and input heat flux in participating media. The inversion algorithm comprises Kalman filter technique and recursive least squares estimator (KF-RLSE) for on-line and real time predict the input heat flux and position of the solid–liquid phase front from the temperature history by using a sensor mounted on the surface. The KF technique is employed to generate a regression equation between the biased residual innovation and the unknown thermal coefficient. The recursive least squares estimator is utilized in the regression equation to predict time-varying phase front position and input heat flux. Based on simulation results, the proposed algorithm exhibits good reconstruction capability. The influences of forgetting factor, process noise, measurement noise, and absorption coefficient on the stability and precision of the retrieval results are also analyzed. The accuracy of the estimation increases with decrease of the distance between the acting surface of input heat flux and the sensor location. Furthermore, the present algorithm cannot accurately determine the abrupt heat flux with large time step.