Sorted L1 regularization method for damage detection based on electrical impedance tomography

Carbon fiber reinforced polymers (CFRPs) are composite materials in which carbon provides strength and stiffness, whereas polymers provide cohesiveness and toughness. The electrical impedance of CFRP laminates is changed due to different kinds of damages. Electrical impedance tomography (EIT) has significant advantages such as non-intrusion, portability, low cost, and quick response and has widely been used as a nondestructive testing method. Therefore, EIT has great potential in structural health monitoring of CFRPs. Regularization can solve the ill-posed inverse problem of EIT. However, conventional regularization algorithms have their own limitations, such as over-smoothness of reconstructed edges and unstable solution caused by measurement noise. In addition, the anisotropic property of CFRPs also affects the image quality based on traditional methods. In this paper, the sorted L1-norm regularization is proposed. It promotes grouping highly correlated variables while encouraging sparsity by using more effective penalty terms. The sharp edges between different materials can be obtained, and the obtained solution is more stable. The image quality of different objects, especially the image quality of multi-targets, can be significantly improved with this new method. In addition, the sorted L1 norm can generate adaptive regularization parameters without empirical selection. The new regularization problem is solved by the alternating direction method of multipliers. Both experimental and simulation results demonstrate that the sorted L1 norm improves the quality of reconstructed images under various noise levels. The proposed method is comprehensively evaluated with three image quality criteria by numerical simulation quantitatively.