Identifying the Thermal-Conductivity Tensor of a Nitrogen Thermal Protection by the Iterative Regularization Method

Consideration is given to the method of parametric identification of a symmetric thermal-conductivity tensor for a cryogenic nitrogen thermal protection thermostatting an aluminum skeleton of a cylindrical nitrogen-filled vessel. This problem is solved as the problem of seeking the global minimum of the root-mean-square residual functional between the theoretical field of temperatures and the registered maximum thermal-protection temperature. To this end, it is necessary to solve the “primal” problem of heat transfer between the thermal protective coating with a selected initial approximation of components of the thermal-conductivity vector and their basis functions taking account of their dependence on temperature. The method of conjugate directions has been selected as the most accurate optimization method of first order of convergence. To implement this method, it is necessary to find components of the gradient of the residual functional under study. The descent step in this method is sought from the minimum of the target functional at each computational iteration, which corresponds to the iterative regularization method. A criterion for the cessation of the iterative process is the superposition of errors that introduce ill-posedness into the formulation of the problem under study.