A combination of extended finite element method and the Kriging model based crack identification method

Abstract

In this paper, we proposed a crack identification method in which the extended finite element method (XFEM) and a surrogate model are employed. The XFEM is used for accurate modeling of fractures, while the employment of Latin hypercube sampling (LHS) ensures a representative sample space for the input parameters. Then, we use a Kriging surrogate model to establish the response surface between the input and output data and to verify the accuracy of the model predictions. The Kriging model is based on a Gaussian process that models the correlation between the sample points, and it provides an efficient way to interpolate between known data points. To find the optimal solution, we combine the Kriging surrogate model with the particle swarm optimization (PSO) algorithm. From the numerical examples, it can be found that the optimal solutions are in good agreement with the exact solutions.