Detection of flaws in a two-dimensional body through measurement of surface temperatures and use of conjugate gradient method

Abstract

This paper aims to obtain parameters (i.e. location and dimensions) relevant to flaws in a two-dimensional body by measuring the temperature on its boundaries. In this endeavour, a steady-state heat conduction problem is formulated, and the geometry under study is subjected to a known heat load, resulting in a specific heat distribution in the body. By using a number of heat sensors, the temperature at selected points on the boundary of the body is obtained. Inverse heat conduction methods implement these temperature data, working toward estimating the flaw parameters. The objective function is optimized using conjugate gradients method, and in solving the direct problem, an FEM code is employed. To check the effectiveness of this method, sample cases with one or more circular, elliptical cavities or cracks in the body, and a case with unknown cavity shape is solved. Finally the ensuing results analyzed.