Crack Detection in 2D Domains Using Extended Finite Element Method and Particle Swarm Optimization

Damage detection of structures is an important issue for maintaining structural safety and integrity. In order to evaluate the condition of structures, many structural health monitoring (SHM) techniques have been proposed over the last decades. Major approaches of SHM are non-destructive in nature and are widely used for damage detection in engineering structures such as aerospace, civil and marine structures. The existence of damage in a structure may be traced by comparing the response of time-domain wave traveling in the structure at its present state with a base-line response. A difference from the base-line response is correlated to the damage location through estimation of time of arrival of the new peaks (scattered waves). Thus, by employing the wave based methods, presence of damage in a structure is detected by inspecting at the wave parameters affected by the damage. The wave parameters that are commonly used for damage detection are the parameters representing attenuation, reflection and mode conversion of waves due to damage. Although detection of flaws is extremely important for many industrial applications, current approaches are severely restricted to specific flaws, simple geometries and homogeneous materials. In addition, the computational burden is very large due to the inverse nature of the problems where one solves many forward and backward problems. For instance, conventional ultrasonic methods measure the time difference of returning waves reflected from a crack; however, for laminated composite plates, the ultrasonic wave would be partially reflected at the interface of two layers where no crack actually exists, and partially continues to propagate further where it eventually is reflected back by the true crack. Numerical methods employed in crack detection algorithms require the solution of inverse problems in which the spatial problem is often discretized in space using finite elements in association with an optimization scheme. The solution of these problems is not unique, and sometimes the optimization algorithm may converge to local minima which are not the real optimal solution. Moreover, they often require hundreds of iterations to converge considering the algorithm used in the process. On the other hand, an accurate detection of cracks requires the re-meshing of the finite element domain at each iteration of the optimization. This is a severe limitation to any numerical approach when the conventional finite element method is employed for crack modeling, as the re-meshing of a domain is often not a trivial task. This paper investigates crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with particle swarm optimization (PSO) algorithm. The XFEM is utilized to model the cracked structure as a forward problem, while the PSO is employed for finding crack location as an optimization scheme. The XFEM is a robust tool for analysis of structures having discontinuities without re-meshing. Therefore, it is an efficient tool for an iterative process. Also, the PSO is a well-known non-gradient based method which is suitable for this inverse problem. The problem is formulated such that the PSO algorithm searches crack coordinates in order to detect the existing crack by minimizing an error function based upon sensor measurements. This problem is a non-destructive evaluation of a structure. Three benchmark numerical examples are solved to demonstrate capability and accuracy of the XFEM and the PSO for crack detection of 2D domains.