CUBIC SPLINE ANCHORED GRID PATTERN ALGORITHM FOR HIGH-RESOLUTION DETECTION OF SUBSURFACE CAVITIES BY THE IR-CAT METHOD

An algorithm is presented for the high-resolution detection of irregular-shaped subsurface cavities within irregular-shaped bodies by the IR-CAT method. The theoretical basis of the algorithm is rooted in the solution of an inverse geometric steady-state heat conduction problem. A Cauchy boundary condition is prescribed at the exposed surface, and the inverse geometric heat conduction problem is formulated by specifying the thermal condition at the inner cavities wa.Us, whose unknown geometries are to be detected. The location of the inner cavities is initially estimated, and the domain boundaries are discretized. Linear boundary elements are used in conjunction with cubic splines for high resolution of the cavity walls. An anchored grid pattern (AGP) is established to constrain the cubic spline knots that control the inner cavity geometry to evolve along the AGP al each iterative step. A residual is defined measuring the difference between imposed and computed boundary conditions. A Newton-Raphson method with a Broyden update is used to automate the detection of inner cavity walls. During the iterative procedure, the movement of the inner cavity walls is restricted to physically realistic intermediate solutions. The proposed cubic spline algorithm is general and can be extended to detect multiple cavities. Numerical simulation demonstrates the superior resolution of the cubic spline AGP algorithm over the linear spline-based AGP in the detection of an irregular-shaped cavity. Numerical simulation is also used to test the sensitivity of the linear and cubic spline AGP algorithms by simulating bias and random error in measured surface temperatures. The proposed AGP algorithm is shown to satisfactorily detect cavities with these simulated data.