Defects detection in the inner surface of pipes based on inverse heat conduction problem

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.