Automated algorithm for the nondestructive detection of subsurface cavities by the IR-CAT method

Abstract

An algorithm is presented to automate the detection of irregular-shaped subsurface cavities within irregular shaped bodies by the IR-CAT method. The algorithm is based on the solution of an inverse geometric steady state heat conduction problem. Cauchy boundary conditions are prescribed at the exposed surface. An inverse heat conduction problem is 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 using the Newton Raphson method with a Broyden update to drive the error between the imposed boundary conditions and 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 AGP is introduced in the Traveling Hole Method to adaptively refine the detection of inner cavities. The proposed algorithm is general and can be used to detect multiple cavities. Results are presented for the detection of single and multiple irregular shaped cavities. Convergence under grid refinement is demonstrated.