3D crack identification using the Nelder-Mead Simplex algorithm combined with a random generation of crack positions

Abstract

In this paper, we present a scheme for cracks identification in three-dimensional linear elastic mechanical components. The scheme uses a boundary element method for solving the forward problem and the Nelder-Mead simplex numerical optimization algorithm coupled with a low discrepancy sequence in order to identify an embedded crack. The crack detection process is achieved through minimizing an objective function defined as the difference between measured strains and computed ones, at some specific sensors on the domain boundaries. Through the optimization procedure, the crack surface is modelled by geometrical parameters, which serve as identity variables. Numerical simulations are conducted to determine the identity parameters of an embedded elliptical crack, with measures randomly perturbed and the residual norm regularized in order to provide an efficient and numerically stable solution to measurement noise. The accuracy of this method is investigated in the identification of cracks over two examples. Through the treated examples, we showed that the method exhibits good stability with respect to measurement noise and convergent results could be achieved without restrictions on the selected initial values of the crack parameters.