Abstract:

 To accurately identify the thermal conductivity of a hypersonic vehicle’s heat shield material, the constrained functional minimization problem for the heat conduction partial differential equation system is developed and effectively solved. Based on the Weierstrass theorem, the Lagrange polynomial is used to parameterize the thermal conductivity to obtain the finite-dimensional nonlinear programming (NLP) problem from the original infinite-dimensional problem. With the dynamic optimization equation (DOE) based method, the NLP is transformed to the initial-value problem (IVP) to be solved. In order to accurately learn the thermal conductivity from the limited measurement data, the adaptive mesh refinement method that prevents the over-fitting is proposed to enhance the identification accuracy. The research suggests that the identification approach and the optimization method are effective, and the identified results may accurately simulate the true thermal conductivity.

Key words:  Hypersonic vehicle, Thermal conductivity identification, Constrained functional minimization, Nonlinear programming, Dynamic optimization equation, Over-fitting test