Invisibility and indistinguishability in structural damage tomography

Structural damage tomography (SDT) uses full-field or distributed measurements collected from sensors or self-sensing materials to reconstruct quantitative images of potential damage in structures, such as civil structures, automobiles, aircraft, etc. In approximately the past ten years, SDT has increased in popularity due to significant gains in computing power, improvements in sensor quality, and increases in measurement device sensitivity. Nonetheless, from a mathematical standpoint, SDT remains challenging because the reconstruction problems are usually nonlinear and ill-posed. Inasmuch, the ability to reliably reconstruct or detect damage using SDT is seldom guaranteed due to factors such as noise, modeling errors, low sensor quality, and more. As such, damage processes may be rendered invisible due to data indistinguishability. In this paper we identify and address key physical, mathematical, and practical factors that may result in invisible structural damage. Demonstrations of damage invisibility and data indistinguishability in SDT are provided using experimental data generated from a damaged reinforced concrete beam.