TIME REVERSAL IN ELASTODYNAMICS AND APPLICATIONS TO STRUCTURAL HEALTH MONITORING

Abstract eng:
In structural health monitoring, detection of localized damage can be achieved by exploiting recorded signals at a limited number of sensors within the structure. Here we propose the localization of damage using an array of sensors as a computational time-reversal mirror (TRM). Time reversal (TR) is a physical process that exploits the time reversibility of wave equations and achieves re-focusing of the wave on the source of its origin by sending back, reversed in time, the signals recorded on an array of transducers. TR was originally introduced by Mathias Fink and his group and has several applications ranging from medical imaging to telecommunications [14]. In the present work, we perform time reversal numerically in order to effectively detect and localize defects in a bounded two-dimensional elastic domain. This is a generalization of a respective time-reversal implementation in an acoustic medium [12]. The solid contains a number of Nr sensors which can act as sources as well. Our data is the response matrix of the scattered field, that is, the difference between the total field obtained in the damaged structure and the incident field corresponding to the response in the healthy structure. Numerical solution of the wave propagation problem is performed using a mixed finite element formulation in terms of the velocity and stress fields [6]. In order to dissociate the response caused by Nd different defects, we apply the singular value decomposition (SVD) of the response matrix, while back-propagation of the projection of each singular vector corresponding to a non-zero singular value is performed in order to highlight each defect separately.

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