Near on-line reconstruction of time-varying surface heat flux and internal temperature field of graded-index medium by Kalman smoothing technique

The time-resolved surface heat flux (q(t)) and internal temperature field (Tfield(t)) of graded index medium are concurrently retrieved in virtually real time without any priori information about the expression of q(t). The coupled conductive and radiative heat transfer issue in graded index medium is addressed by finite volume method (FVM). The Kalman filter algorithm combined with R-T-S smoother technique (Kalman smoother) is exploited for solving the aforementioned estimation problem. The temperature of rear face of medium is utilized as input signal for inverse problem so as to achieve non-destructive detection of the medium. The influence of model state parameters (such as measurement error covariance, process error covariance and future time step) and measurement errors on estimation results is thoroughly researched. It is found that the q(t) and Tfield(t) of graded index medium can be accurately and stably reconstructed by Kalman smoothing technique. A larger future time step should be used to obtain more accurate and stable prediction results when the measurement error is large in practical engineering applications.