Automated Solution of an Inverse Heat Conduction Problem for the Nondestructive Detection of Subsurface Cavities Using Boundary Elements

Abstract

An automatic procedure for the detection of irregular-shaped subsurface cavities within irregular shaped bodies is presented. The temperature profile at the exposed surface of an irregular shaped body is provided by an Infrared Scanner. Cauchy thermal boundary conditions are then prescribed at the external boundary. An inverse heat transfer problem is then formulated by specifying the thermal boundary condition along the inner cavities whose unknown geometries are to be determined. An initial guess is made for the location of the inner cavities, the domain boundaries are discretized, and an Anchored Grid Pattern(AGP) is established. The nodes of the inner cavities are constrained to move along the AGP at each iterative step. The location of inner cavities is determined by successively solving the heat transfer problem so as to drive the error between the imposed boundary conditions and BEM computed boundary conditions to zero. During the iterative procedure, the movement of the inner cavity walls is restricted to physically realistic intermediate solutions. A dynamic relocation of the grid is then introduced in the Traveling Hole Method to adaptively refine the detection of the inner cavities. Results are presented for the detection of single and multiple irregular shaped cavities.