【摘要】 为准确辨识高超声速飞行器防热材料热传导系数,构造了针对热传导偏微分方程系统的约束泛函极值问题,基于表征多项式逼近性能的Weierstrass定理,采用Lagrange多项式对热传导系数进行参数化建模,进而将无穷维的约束泛函极值问题转化为有限维的非线性规划问题,再利用基于动态优化方程的优化方法将此非线性规划问题转化为常微分方程初值问题进行求解。为从较有限的测量数据中准确地"学习"热传导系数,建立采用"过拟合"判别准则的网格自适应迭代算法改善辨识精度。研究表明本文采用的辨识策略与优化方法有效,辨识结果可以较准确地反映材料热传导系数的变化规律。更多还原

【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.更多还原