Ph.D Student | Amitt Eyal |
---|---|

Subject | Improved Time-Reversal Methods for the Identification of Flaws in Aerospace Structures |

Department | Department of Aerospace Engineering |

Supervisor | Professor Dan Givoli |

Full Thesis text - in Hebrew |

Non-Destructive Testing (NDT) is one of the major requirements in
aerospace structural design. Appropriate use of NDT guarantees safety in
aerospace and is thus a subject of highest attention. Standard NDT has the
capability to **detect** damage but usually not to provide detailed
information on the damage parameters. Hence, in recent years computational
methods have been combined with physical NDT to yield better **identification**.
The mathematical problem of scatterer identification, and of identification of
other types of damage, falls into the category of inverse problems.

In standard experimental NDT, the response signals, measured by the
sensors, are compared with those of a healthy structure. When the difference
between the two sets of signals is larger than a certain threshold, this
indicates damage in the specimen. In a model-based NDT system, the measured
response signals are compared to those generated by a computational model which
assumes a candidate flaw. If the two sets of signals are close to each other
(in some specified norm), this indicates that the candidate flaw assumed by the
model is similar to the true one. However, if the signals differ greatly this
means that the candidate flaw has to be replaced by a better candidate. This
leads to an optimization problem: *Find the model’s damage parameters that
minimize the distance between the response signals measured and those computed
by the model*.

In this study, a new model-based NDT method is proposed for damage identification. The computational inverse problem of identifying a scatterer in a time-dependent wave field is considered. The wave speed of the background medium and the wave source are assumed to be known. Wave measurements, possibly noisy, are given at chosen discrete points in space (sensor locations) and time. The goal is to find scatterer parameters such as location, size and shape. The computational solution procedure consists of two steps. In the first step, a standard fast Arrival-Time Imaging (ATI) algorithm is employed. This results in a rough image which provides possible regions for the location of the scatterer. In the second step an optimization scheme based on Time Reversal (TR) is used to determine the location, size and shape of the scatterer. The combined scheme is called ATI-TR.

Relying on a computational model of the structure and on the measured signals, a TR solution is obtained for each assumed set of scatterer 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 scatterer which yields the best wave refocusing at the true source location. 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.

In addition, the ATI-TR scheme is compared to full waveform inversion based on the adjoint method, and conclusions are drawn regarding relative advantages of each technique.