Graph Laplacian-regularized pseudo-force sparse reconstruction imaging for damage in complex composite structures

Guided waves are promising tools for damage detection in composites due to their efficiency, large coverage, and sensitivity to various defects. However, imaging anomalies in composites with complex geometries, such as stiffened composite plates, is still challenging because of anisotropy and complex boundaries. This paper proposes a graph Laplacian-regularized pseudo-force sparse reconstruction (GL-PFSR) method for damage imaging in complex structures. Based on the first-order shear deformation theory (FSDT), it states that the scattered wave field produced by defects in a damaged composite structure is equivalent to that induced by pseudo-forces applied at the corresponding region of the intact structure. Thus, the damage imaging problem can be transformed into a force identification problem, in this paper, it is solved by optimizing a graph Laplacian regularized group LASSO problem. By adding a graph Laplacian regularization term, the inherent spatial continuity information can be leveraged, making the method better quantitatively evaluate defects. The method is validated on carbon fiber-reinforced plastics (CFRP) with omega stringers, and the results show that the method can image both simulated damage and real delamination induced by an impact. The results show that the method can not only localize damage but also evaluate the extent of the defects.