Research On The Application Of A Real-Time Tracking Problem Based On Regularization Method

The moving boundary of a melting solid, which is named phase change interface, can be estimated from the temperature and flux measured on the fixed side of the solid. The lack of measurement in the liquid phase prevents the phase change interface to be recovered by straightforward use of the direct Stefan solution. The tracking of this phase change interface is an inverse problem that requires particular methods. An algorithm is presented, based on a regularized least square approach, that is extended to this case by a sliding horizon technique.First, to the question, this thesis presents a so-called reference model method, which is incorporated in the feedback control thoughtway, to identify and track the phase change interface. This method is base on a numerical simulation model of the phase change process. The model is based on a known phase change interface and the temperatures and heat fluxes collected at the fixed boundary. The governing equation is set up on the solid area to obtain the temperature distribution by finite element method. The accuracy of the model is verified through comparison with Neumann's exact solutions. The correlative parameters are chose suitably. We also compare our finite element numerical model with previous one, the simulation results are showed.Second, because this inverse problem is ill-posed, we use Tikhonov regularization method. In order to compress solution space and stabilize numerical solution, we add a regulative term in the criterion. Accordingly, the ill-posedness of this problem is resoled commendably.Third, the real-time tracking problem is solved by minimization of a penalized output least square criterion defined on a sliding time horizon. During the process of minimization, thinking of the instability and tardiness of the algorithms for multifunction, this study makes a linear hypothesis for the phase change because of its slow transformation. In this way, the multi-optimization is transformed an unitary problem and the performance is advanced.Lastly, aiming at several different phase change interface, we perform many experiments of simulation and investigate the effect of concerned parameters against the estimating results.