An effective computational approach based on XFEM and a novel three-step detection algorithm for multiple complex flaw clusters

•An effective computational approach for detecting multiple complex flaw clusters is presented.•Forward problem is solved by XFEM to avoid re-meshing as changing the flaw geometry.•A novel three-step strategy is developed for solving inverse problem.•“Queue and Kill” method is proposed to identify and eliminate the improper candidate.•The three-step strategy can save computational time and reduce the sensor number. This paper presents an effective computational approach comprised of forward and inverse analyses for detection of multiple complex flaw clusters in elastic solids. A three-step detection strategy is introduced for inverse analysis, whereas extended finite element method (XFEM) is adopted for forward analysis. The use of XFEM is to avoid re-meshing during the change of flaw geometries. The three-step detection strategy involves: firstly, an optimization method that couples an improved discrete artificial bee colony algorithm and hierarchical clustering analysis (IDABC-HCA) is used to capture subdomains containing flaws with limited measure points in the global domain; secondly, additional measure points are introduced locally within each captured subdomain, where the number of flaws and the rough geometry of each flaw are quickly determined with the IDABC-HCA; finally, true geometries of flaws are obtained on the basis of the rough geometries by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. To save computational time, “Queue and Kill” method is proposed to actively identify and eliminate the improper candidate flaws and/or flaw clusters. Three numerical examples of multiple flaw detection that include simple and complex flaw geometries are analyzed. The results demonstrate that the proposed approach can effectively detect multiple complex flaw clusters without prior information of the flaw number.