Boundary Condition Estimation of Ablating Material Using Modified Sequential Function Specification Method

An inverse analysis is applied in a one-dimensional ablation problem for simultaneous estimation of unknown time-dependent boundary conditions including the applied heat flux and the Biot number at the two end surfaces of the ablating material. The sequential function specification method is employed to minimize the least-square objective function. Due to the ablation process, a moving boundary is created at the heated surface. The estimated boundary conditions along with the direct equations are used to calculate the front position of the moving surface. To deal with the high nonlinearity caused by the moving boundary and to treat the ill posedness associated with deeply embedded sensors of the current inverse problem, a small number of future time steps are used as the regularizing parameters to stabilize the inverse problem. Furthermore, to fasten the solution of the inverse problem, a new adaptive overrelaxation factor is developed that increases the speed of convergence significantly. The simulated temperature measurements at specific sensor positions inside the ablating materials are used to evaluate the objective function. The accuracy of an applied inverse analysis is examined by the step and triangular boundary condition profiles containing discontinuities and sharp corners, respectively. In spite of high nonlinearity, an appropriate consistency between the estimated values and the exact ones are obtained.