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A modified dolphin monitoring (MDM) is used to augment the efficiency of particle swarm optimization (PSO) and enhanced vibrating particle system (EVPS) for the numerical crack identification problems in plate structures. The extended finite element method (XFEM) is employed for modeling the fracture. The forward problem is untangled by some cycle loading phase via dynamic XFEM. Furthermore, the inverse problem is solved and compared via two PSO and EVPS algorithms. All the problems are also dissolved by means of fine and coarse meshing. The results illustrate that the function of XFEM-PSO-MDM and XFEM-EVPS-MDM is superior to XFEM-PSO and XFEM-EVPS methods. The algorithms coupled via MDM offer a higher convergence rate with more reliable results. The MDM is found to be a suitable tool which can promotes the ability of the algorithms in achieving the optimum solutions.

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The contourlet transform as an extension of the wavelet transform in two dimensions uses the multiscale and directional filter banks, and has a more adequate performance in comparison with the classical multi-scale representations. In this study, the efficiency of the contourlet transform is assessed for identifying the damage of plate structures in various conditions. The conditions include single damage and multi–damages with different shapes and severities, the different supports (i.e., boundary conditions), and the higher mode shapes,. For achieving this purpose, the process of the damage detection of plate structures using contourlet transform is implemented in the three steps. In the first step, the first mode shapes of a damaged plate and a reference state as the intact plate are obtained using the finite element method. In the second step, the damage indices are achieved by applying the contourlet transform to the responses of the first mode shapes for the damaged and intact plates. Finally, the location and the approximate shape of the damage are identified by plotting the damage indices. The obtained results indicate that the various conditions influence the performance of the contourlet transform for identifying the location and approximate shape of damages in plate structures.