Reconstructing damage geometry with computationally efficient algorithms is of primary importance in establishing a robust structural health monitoring system (SHMS). To this end, two linearized imaging algorithms, electromagnetic (EM) migration and Born imaging, are proposed for 3-D damage imaging of structures using EM waves. These algorithms are formulated in both differential equation (DE) and integral equation (IE) forms in time-domain for inhomogeneous anisotropic and lossy structures.When sensor data is collected in a common-shot experiment, the proposed imaging algorithms consist of three steps: 1) Back-propagation (migration) of the scattered field measured by the sensors; 2) Zero-lag cross-correlation of the back-propagated scattered field with the incident field in image area; and 3) Summation of partial images obtained from different actuator excitations. The computation of the back-propagated scattered field can be carried out based on either the differential equations or the integral equations associated with this field. In the first approach, the associated differential equations are discretized and solved by a finite difference time domain (FDTD) method. Mathematically, this approach is straightforward. However, its computational time may be very intensive for 3-D cases. In the second approach, the Green's functions of the healthy structure are required. For general 3-D cases, numerical solutions of these Green's functions may be computationally intensive if analytical solutions are not available. But, the numerical solutions of the Green's functions, if needed, are carried out only once before the monitoring stage is started. After calculating the Green's functions, the back-propagated scattered field is computed by performing simple integral (summation) operations during the monitoring stage. It is worth noting that target-oriented capability (i.e., a desired part of the complete image area can be imaged without having to consider the remaining parts) is another distinct advantage of employing the IE approach.To lower the computational cost of the zero-lag cross-correlation imaging condition, step (2), the incident field at each image point is approximated by a single-event model parameterized by a traveltime and an amplitude (modified excitation-time imaging condition). It is shown that by applying similar approximations to the fields associated with the Green's functions of the healthy structure in the IE form of the algorithms, real-time damage imaging algorithms suitable for SHM application can be realized.As another way of reducing the computational cost of the algorithms, the poststack concept, typically used in geophysical exploration, is utilized. This way, the incident field in image area is not involved in the imaging process at all but the sensor data should be collected in a zero-offset experiment.To show the effectiveness of the DE and IE forms of the imaging algorithms, numerical simulations in 2-D Transverse Magnetic case for a reinforced concrete slab and a fiberglass laminated plate with multiple damages are performed. All synthetic sensor data, incident field, back-propagated (migrated) field, and the Green's functions of the healthy structure are computed via a FDTD 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 form may be employed in a SHMS.
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Damage Imaging Algorithms For Structural Health Monitoring Using Electromagnetic Waves
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