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

Abstract

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.

Electrical tomography for characterizing transport properties in cement-based materials: A review

“…As a response, researchers have recently begun implementing constrained optimization regimes to ensure parameters are within physically-realistic bounds [47,56]. These days, there are numerous regimes available for optimizing, constraining, and regularizing the LS ET problems; for these and references to many others, the reader is referred to [88][89][90][91].…”

Failure prediction in self-sensing nanocomposites via genetic algorithm-enabled piezoresistive inversion

“…In this study we make use of an interior-point algorithm implemented via the “lsqlin” function in MATLAB to solve equation (12). More advanced approaches such as those discussed by Smyl et al 39 have shown great potential in previous work but have not been implemented here for simplicity. These include the Bayesian approach 40 which involves a probabilistic treatment of the conductivity distribution and the Kalman filter technique 41,42 which involves a state estimation-type treatment of the EIT problem and is especially good for imaging fast conductivity changes.…”

Damage Tomography as a State Estimation Problem: Crack Detection Using Conductive Area Sensors

“…To investigate this query, we apply the EKF described in the previous section to ERT imaging of a lightly reinforced concrete beam with an applied silver sensing skin. In the testing regime, thoroughly detailed in [1], [5], a 15.2×50.8×15.2 cm beam was loaded in three-point bending with a maximum load of approximately 120 kN. On the beam's surface, a sensing skin with 28 copper boundary electrodes was utilized in the ERT experimental program.…”

“…To investigate this, we compare EKF reconstructions to (a) an estimate obtained using a positively constrained standard iterative approach equipped with a TV regularizer and (b) a stacked approach. For the stacked approach (details in [1]), we use a smoothness prior in computing the (non-cracked) background conductivity σ 1 and TV for the change in conductivity (∆σ) yielding the final estimate σ 2 = σ 1 + ∆σ. In order to quantitatively and equitably corroborate the results from all approaches, we first normalize the reconstructions and compare them to the true crack geometries extracted from the Damage Level 4 photograph by generating a binary image using a simple thresholding technique and interpolating the assumed binary distribution (0 for a crack, 1 for the background) onto the inversion grid.…”

“…Structural damage tomography (SDT) is an emerging field where users aim to image structural damage processes. Specifically, in SDT users aim to estimate a particular two-or three-dimensional parameter field using distributed measurements -usually by solving an inverse problem [1]. In turn, by interpreting the reconstructions, an assessment of structural damage can be made.…”