The Role of Regularization on Impact Damage Imaging in a Carbon Fiber/Epoxy Airfoil via Electrical Impedance Tomography

Abstract Electrical impedance tomography (EIT) is the process of estimating the spatially varying electrical conductivity distribution of a domain based on voltage-current measurements collected at the boundary of the domain. Because EIT is minimally invasive (i.e., needing only externally mounted electrodes), requires only simple voltage and current measurements, can potentially be used in nearly real time, and damage events generally cause conductivity losses, it has attracted attention for embedded or on-board sensing and nondestructive evaluation (NDE). However, EIT is mathematically an ill-posed inverse problem that requires regularization to achieve a physically meaningful solution. The effect of regularization type and norm has been widely explored by biomedical and mathematical practitioners of EIT, but comparatively little work in this area has been done by the materials imaging and NDE communities. This is an important gap in the state of the art because regularization, which is essentially the process of imposing some assumption on the conductivity solution, profoundly impacts EIT image quality. That is, imposing a poor assumption on the conductivity solution can misrepresent or altogether miss the damage. We herein address this gap in the state of the art by exploring the role of regularization type on impact damage detection in a carbon fiber/epoxy laminate shaped as a NACA airfoil, a shape of representative complexity and relevant to aerospace applications. More specifically, we consider regularization by the identity matrix, the discrete Laplace operator, the total variation operator, and a mixed prior developed previously by the authors. We also demonstrate the impact of regularization norm for total variation regularization. Our results clearly show the keen importance of judicious regularization selection for effective damage detection via EIT.