Axisymmetric and two-dimensional crack identification using boundary elements and coupled quasi-random downhill simplex algorithms

In this paper, a crack identification method is developed for axisymmetric and two-dimensional structures. The dual boundary element method is coupled with a quasi-random sequence and the downhill simplex algorithm to minimize the error function, which is expressed as the difference between strains at the boundary sensor points in the guessed crack shape and ones measured in the actual crack identity. The measures are randomly perturbed and the residual norm is regularized to provide an efficient and numerically stable algorithm that leads to stabilized solutions. The accuracy of this method is investigated in the identification of single two-dimensional and axisymmetric cracks on several cases. Through the treated examples, we showed that the quasi-random sequence presents a solid tool, allowing the choice of the optimal initial solution necessary to the convergence of the downhill simplex algorithm.