导热反问题的空间状态分析——单个边界条件的确定

State-space approach to inverse problem of heat conduction for single condition on boundaries

本文以现代控制理论为基础,引用线性控制系统的空间状态表达式来描述和探讨单个边界条件的确定问题。采用现有较为完善的空间离散方法——有限单元法或有限差分法,通过数值计算以获得较为准确的解。最后,由数值实验的例子来表明所采用方法的合理性和可靠性。

According to theory of modern control, a State-Space Approach to linear control system is tried to be used to find exact solutions to an inverse problem of heat conduction for single condition on boundaries with time-dependent input foreing functions, and the inverse heat conduction problem must be linear is required. The inverse problem of heat conduction is spatially discretized by finite elements or by finite differences to be computational calculated economically. The method is verified to be applicable and effective by a two-dimensional illustrative example.