An overview of 38 least squares–based frameworks for structural damage tomography

The ability to reliably detect damage and intercept deleterious processes, such as cracking, corrosion, and plasticity are central themes in structural health monitoring. The importance of detecting such processes early on lies in the realization that delays may decrease safety, increase long-term repair/retrofit costs, and degrade the overall user experience of civil infrastructure. Since real structures exist in more than one dimension, the detection of distributed damage processes also generally requires input data from more than one dimension. Often, however, interpretation of distributed data—alone—offers insufficient information. For this reason, engineers and researchers have become interested in stationary inverse methods, for example, utilizing distributed data from stationary or quasi-stationary measurements for tomographic imaging structures. Presently, however, there are barriers in implementing stationary inverse methods at the scale of built civil structures. Of these barriers, a lack of available straightforward inverse algorithms is at the forefront. To address this, we provide 38 least-squares frameworks encompassing single-state, two-state, and joint tomographic imaging of structural damage. These regimes are then applied to two emerging structural health monitoring imaging modalities: Electrical Resistance Tomography and Quasi-Static Elasticity Imaging. The feasibility of the regimes are then demonstrated using simulated and experimental data.