Time reversal for crack identification

A general computational methodology is proposed for identifying cracks in structures. It is based on a time reversal (TR) technique and on the notion of refocusing. In the proposed procedure, a known source generates waves in the structure, and the time-varying response of the structure is measured only at certain points and times. In an industrial application this step is performed experimentally, but in the present study it is emulated numerically. Relying on a computational model of the structure and on the measured signals, a TR solution is obtained for each assumed set of crack parameters. This amounts to evolving the solution backward in time, till the initiation time of the original source. The crack identification is based on seeking, among all crack candidates, the crack which yields the best wave refocusing at the true source location. To test the proposed methodology, a simple rectangular membrane model governed by the 2D time-dependent scalar wave equation is employed. Finite element discretization of the structure and an explicit time-stepping scheme are used. The performance of the method is tested under various conditions and with various amounts of partial information. Its sensitivity to noise and to perturbations in the material properties is also investigated.