A variable future-time-steps method for solving nonlinear unsteady inverse heat conduction problems

Abstract

In some non-linear unsteady inverse problems, the inverse solution will oscillate violently in the whole time domain due to the sharp change of the sensitivity coefficients. To deal with this problem, a new sequential function specification method with variable future time steps is proposed in this paper. The future time steps are adjusted by the error amplification coefficients which are defined as the reciprocal of the square sum of the sensitivity coefficients. When the error amplification coefficients are small, a small number of future time steps is used to reduce the deterministic error. While in the period with large error amplification coefficient, a large number of future time steps is used to reduce stochastic error. Finally, the total error of estimated heat flux is reduced. Avoid the sharp fluctuation of estimated heat flux in time domain due to the sharp change of sensitivity coefficients. The variable future-time-steps method is applied to the estimation of 1-D non-linear unsteady heat flux without and with ablation through numerical experiments. Numerical experiments show that the proposed method can not only estimate various forms of heat flux, but also its inversion results are significantly better than those of the fixed future time steps method based on the discrepancy principle, and also better than those of the fixed future time step method based on the minimum relative error of heat flux.