中文摘要：

根据外壁面的温度分布计算内壁面的几何边界是一类不适定的导热反问题。在建立具有不规则内壁缺陷的管道二维稳态传热模型的基础上，将反问题转化成正问题和最优化问题。采用有限元方法求解导热正问题，利用外壁面温度分布，从目标函数的泛函变分出发，根据共轭梯度法，实现了内壁几何边界的识别。通过对几种典型缺陷的数值计算，分析了初值选取、测量误差和传热边界条件等对反演结果的影响，验证了方法的有效性和稳定性。

英文摘要：

It is a typical ill-posed inverse heat conduction problem to estimate the geometry boundary of the inner surface of pipe by the temperature of outer surface. With the establishment of a two-dimensional steady model for pipe with irregular inner surface, the inverse problem is transformed into a direct problem and an optimization problem. Based on the temperature at the outer surface obtained from the infrared thermography and the variation of the object function, the conjugate gradient method （CGM） is introduced into the geometry problem. With the numerical analysis of three typical defects, the effects of the measurement errors, choice of the initial value, boundary conditions and number of discrete temperature points are discussed and the proposed methodology is approved.