Damage tomography as a state estimation problem : crack detection using conductive area sensors

Typically, structural damage tomography (SDT) approaches aim to reconstruct a parameter field containing damage information from distributed data by solving an iterative inverse problem. Often, there are two shortcomings in adopting such an approach: (a) the high computational expense and (b) temporal information is inadequately used. In principle, both issues may be alleviated by approaching SDT as a state-estimation problem – i.e. treating the reconstruction problem as a temporally-evolving stochastic process. In this letter, we study the feasibility of state estimates in SDT. For this, we use an extended Kalman filter (EKF) for electrical resistance tomography (ERT) imaging of progressive cracking on an experimentally-tested reinforced concrete beam with an applied surface area sensing skin. In the investigation, we quantitatively analyze the effect of including multiple temporal data sets and corroborate EKF-ERT reconstructions with standard and advanced ERT approaches. It is shown that increasing the amount of temporal data significantly improves the quality of EKF-ERT reconstructions, which compare favorably with the standard and advanced ERT approaches. In addition, for the data sets used herein, the EKF-ERT regime computed seven reconstructions approximately 50-100 times faster than the standard and stacked approaches required to reconstruct one image, respectively.