Automated hybrid singularity superposition and anchored grid pattern BEM algorithm for the solution of inverse geometric problems

Abstract

A method for solving an inverse geometric problem is presented by reconstructing the unknown subsurface cavity geometry with the boundary element method (BEM) and a genetic algorithm in combination with the Nelder-Mead non-linear simplex optimization method. The heat conduction problem is solved by the BEM which calculates the difference between the measured temperature at the exposed surface and the computed temperature under the current update of the unknown subsurface flaws and cavities. In a first step, clusters of singularities are utilized to solve the inverse problem and to identify the location of the centroid(s) of the subsurface cavity(ies)/flaw(s). In a second step, the reconstruction of the estimated cavity(ies)/flaw(s) geometry(ies) is accomplished by utilizing an anchored grid pattern upon which cubic spline knots are restricted to move in the search for the unknown geometry. The solution is achieved using a genetic algorithm accelerated with the Nelder-Mead non-linear simplex method. The automated algorithm successfully reconstructs single and multiple subsurface cavities within two dimensional mediums. The cavity detection was enhanced by applying multiple boundary condition sets (MBCS) to the same geometry. This extra information supplied on the boundary made the subsurface cavity easily detectable despite its low heat signature effect on the boundaries.