A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

We present a sweeping window method in elastodynamics for detection of multiple flaws embedded in a large structure. The key idea is to measure the elastic wave propagation generated by a dynamic load within a smaller substructural detecting window domain, given a sufficient number of sensors. Hence, rather than solving the full structure, one solves a set of smaller dynamic problems quickly and efficiently. To this end, an explicit dynamic extended FEM with circular/elliptical void enrichments is implemented to model the propagation of elastic waves in the detecting window domain. To avoid wave reflections, we consider the window as an unbounded domain with the option of full-infinite/semi-infinite/quarter-infinite domains and employ a simple multi-dimensional absorbing boundary layer technique. A spatially varying Rayleigh damping is proposed to eliminate spurious wave reflections at the artificial model boundaries. In the process of flaw detection, two phases are proposed: (i) pre-analysis-identification of rough damage regions through a data-driven approach, and (ii) post-analysis-identification of the true flaw parameters by a two-stage optimization technique. The 'pre-analysis' phase considers the information contained in the 'pseudo' healthy structure and the scattered wave signals, providing an admissible initial guess for the optimization process. Then a two-stage optimization approach (the simplex method and a damped Gauss-Newton algorithm) is carried out in the 'post-analysis' phase for convergence to the true flaw parameters. A weighted sum of the least squares, of the residuals between the measured and simulated waves, is used to construct the objective function for optimization. Several benchmark examples are numerically illustrated to test the performance of the proposed sweeping methodology for detection of multiple flaws in an unbounded elastic domain. Copyright (C) 2015 John Wiley & Sons, Ltd.