| Reconstructing damage geometry with computationally efficient and effective algorithms is of primary importance in establishing a robust structural health monitoring (SHM) system. To this end, two linearized imaging algorithms, electromagnetic (EM) migration and Born imaging, are formulated for 3-D damage imaging of structures using EM waves. These algorithms are derived in both differential equation (DE) and integral equation (IE) formalisms in time-domain for inhomogeneous anisotropic and lossy structures. In the DE approach, the back-propagation (migration) of the scattered field data derived from measured sensor data, which is the first step of the imaging process, is carried out by numerical solution of the associated DEs. Although mathematically this approach is straightforward, it may be computationally intensive for 3-D cases. In the IE approach, however, the Green's functions of the pristine structure are required. Fortunately, numerical solutions of these Green's functions (when analytical solutions are not available) can be performed prior to the monitoring stage. It is shown that by applying proper approximations on the incident field and Green's functions, real-time damage imaging algorithms suitable for SHM application may be realized.;To show the effectiveness of the DE and IE formalisms of the proposed imaging algorithms, numerical simulations in 2-D transverse magnetic (TM) case for a reinforced concrete slab and a glass/epoxy composite plate with multiple damages are performed. In this simulated study, all sensor data, incident field, back-propagated (migrated) field, and the Green's functions of the pristine structure are generated via a finite difference time-domain method with second-order of accuracy in time and space.;It is concluded that the proposed imaging algorithms are capable of efficiently identifying the damages geometries, are robust against measurement noise, and in their IE formalism may be employed in a SHM system. |
