基于预报误差法的边界热流反演方法研究

Inversion of Boundary Heat Flux of Unsteady Heat Transfer System by Prediction Error Method

在热传导领域科学研究中,当边界条件、材料特性和未知热源等难以获得时,需要通过温度测量和反问题算法来获取一些未知条件和参数的具体信息。基于预报误差准则的渐进收敛性、弱正则化性和对随机系统的抗不适定性,对非稳态传热系统的边界热流设计了反演方法。方法根据传热系统的特点,将顺序函数的原理同预报误差法以及阶跃响应系数概念结合确定准则函数,并利用牛顿-莱弗森法求解了准则函数的极小值,最终得到了不同测量误差、不同测点个数和不同测点位置影响下的边界热流值,证明了所设计方法具有较好的稳定性以及准确性。

In the scientific field of heat conduction,when boundary conditions,material characteristics,and unknown heat sources are difficult to obtain,some specific information about unknown conditions and parameters could be obtained by temperature measurement and inverse problem algorithms.Based on the gradual convergence,weak regularization and qualitative discomfort resistance of the prediction error criterion,an inversion method for the boundary heat flux of unsteady heat transfer systems is designed in the paper.According to the characteristics of the heat transfer system,the principle of the sequence function is combined with the prediction error method and the concept of step response coefficient to determine the standard function.By utilizing the Newton-Raphson method,the minimum value of the standard function is solved.Finally,the boundary heat flux value of different measurement errors,different measurement points and different positions of different measurement points is obtained,which could prove that the design method has good stability and accuracy.