Damage Detection in a Complex Truss Structure via EIT With Mixed Regularization

Abstract Electrical impedance tomography (EIT) is a modality for spatially mapping the internal conductivity distribution of a domain and has recently been explored for potential application in embedded sensing and nondestructive evaluation (NDE) of moderately conductive materials (e.g., carbon fiber composites). The underlying supposition of this approach is that damage represents a loss of conductivity that can be detected, localized, and roughly shaped via EIT. Mathematically, EIT is an ill-posed inverse problem that requires regularization. To date, there have been many studies showing that EIT can indeed work on carbon fiber composites. However, the state of the art suffers from, among others, three important limitations that this manuscript seeks to address. First, the vast majority of these studies make use of overly simple shapes such as flat plates that are not representative of the geometric complexity of real engineering components. For EIT to be established as a viable embedded sensing and NDE modality, work needs to be done to show that it can indeed perform on complex shapes. Second, the state of the art overwhelmingly uses simple regularization methods (e.g., Tikhonov regularization, the smoothness prior, etc.). This is problematic because regularization markedly affects the final image quality. And third, more sophisticated EIT formulations making use of different error norm terms are very seldom explored. Because of the ill-posedness of the EIT inverse problem, formulations that are more robust to outlier data, such as using the ℓ1-norm on the error term, are essential. In light of these limitations, we herein make three contributions: First, we apply EIT to a complexly shaped carbon fiber truss structure produced by a novel additive manufacturing process for the detection of notch damage. Second, we implement a mixed regularization scheme that combines a focal prior with a smoothness prior. These results are compared to images produced using only the smoothness prior. And third, we implement the ℓ1-norm on the error term via the primal-dual interior point method (PDIPM) in order to demonstrate the effect of different error norms (i.e., ℓ1 versus the pervasively used ℓ2-norm) on image quality. It is shown that EIT does indeed work well on this complex shape, that the mixed prior significantly improves image quality, and the ℓ1-norm adeptly localizes damage.