INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2013; 95:871–900 Published online 16 July 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.4529 Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm Hao Sun, Haim Waisman * ,† and Raimondo Betti Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA SUMMARY We present a novel algorithm based on the extended finite element method (XFEM) and an enhanced artifi- cial bee colony (EABC) algorithm to detect and quantify multiple flaws in structures. The concept is based on recent work that have shown the excellent synergy between XFEM, used to model the forward prob- lem, and a genetic-type algorithm to solve an inverse identification problem and converge to the ‘best’ flaw parameters. In this paper, an adaptive algorithm that can detect multiple flaws without any knowledge on the number of flaws beforehand is proposed. The algorithm is based on the introduction of topological variables into the search space, used to adaptively activate/deactivate flaws during run time until convergence is reached. The identification is based on a limited number of strain sensors assumed to be attached to the structure surface boundaries. Each flaw is approximated by a circular void with the following three variables: center coordinates .x c , y c / and radius .r c /, within the XFEM framework. In addition, the proposed EABC scheme is improved by a guided-to-best solution updating strategy and a local search (LS) operator of the Nelder– Mead simplex type that show fast convergence and superior global/LS abilities compared with the standard ABC or classic genetic algorithms. Several numerical examples, with increasing level of difficulty, are studied in order to evaluate the pro- posed algorithm. In particular, we consider identification of multiple flaws with unknown a priori information on the number of flaws (which makes the inverse problem harder), the proximity of flaws, flaws having irreg- ular shapes (similar to artificial noise), and the effect of structured/unstructured meshes. The results show that the proposed XFEM–EABC algorithm is able to converge on all test problems and accurately iden- tify flaws. Hence, this methodology is found to be robust and efficient for nondestructive detection and quantification of multiple flaws in structures. Copyright © 2013 John Wiley & Sons, Ltd. Received 1 November 2012; Revised 28 February 2013; Accepted 22 April 2013 KEY WORDS: flaw detection; inverse problem; topological variable; extended finite element method (XFEM); enhanced artificial bee colony (EABC) algorithm, genetic algorithm (GA) 1. INTRODUCTION Detection of flaws in structures, formulated as an inverse problem or a problem of system identifi- cation, is an important subfield of structural health monitoring that has drawn significant attention during the past few decades [1–13]. Clearly, flaw detection is extremely important for assessment of the reliability and durability of structures, determination of the appropriate maintenance pro- cedures, and prediction of its remaining service life. Nondestructive evaluation (NDE) of damage is an attractive methodology to assess flaws without disassembling or damaging the structure in the process. However, traditional NDE techniques are usually limited in their ability to provide *Correspondence to: Haim Waisman, Department of Civil Engineering and Engineering Mechanics, Columbia Univer- sity, New York, NY 10027, USA. † E-mail: waisman@civil.columbia.edu Copyright © 2013 John Wiley & Sons, Ltd.