Abstract:

The identification of the boundary geometry is an important branch of the inverse heat conduction problem and is the theoretical basis for the development of thermographic non-destructive inspection technique from the qualitative to quantitative status. For the inverse geometry conduction problem, the boundary of the computational domain has to be updated during the iterative process, which will obviously increase the complexity of the algorithm and the computational time needed. This paper presents a new boundary identification algorithm based on the estimation of the effective thermal conductivity. The method, which converts the boundary estimation in an irregular-shaped computational domain to the identification of the effective thermal conductivity in a regular-shaped domain, can obviously reduce both the complexity and computational time needed for the inverse boundary identification problem. Numerical experiments have certified the effectiveness of the method. The initial boundary guess and the temperature measurement error have no obvious effect on the boundary identification result of the plate.

摘要：

基于表面测温的边界形状识别是导热反问题的重要研究内容，同时也是红外无损检测技术从定性到定量发展的重要理论基础。对于边界识别类导热反问题，由于需要在迭代过程中不断改变不规则的求解区域的形状，所以其计算复杂性较大，计算时间也相对比较长，直接影响到实际算法的应用。本文基于试件整体对传热的宏观影响规律提出了基于有效热导率评估的边界识别方法。该方法将不规则求解区域上的边界识别问题转化为一个规则求解区域上的有效热导率的识别问题，从而大大降低了边界形状迭代求解的复杂性和计算所需时间。数值算例证明了算法的有效性。边界的初始假设可以忽略。算法没有明显放大温度测量的误差。