Overlapping Group Sparse Regularization Technique for Vibration-Based Regional Damage Detection of Structures

In structural damage detection (SDD) studies, regularization techniques have shown potential for improving ill-posedness. However, existing methods based on regularization techniques cannot yield satisfactory results for the SDD problem involving regional damages. Based on the sparse distribution characteristics of regional damages in the finite element (FE) model, this study proposes a novel SDD method that integrates sensitivity analysis of modal parameters with overlapping group sparse regularization. First, the relationship between modal parameters and structural damages is established based on sensitivity analysis. Then, the overlapping group sparsity of regional damages is analyzed and the objective function for SDD can be defined. Finally, a grouping matrix is introduced to transform the objective function from overlapping to non-overlapping group sparse regularization. To evaluate the effectiveness of the proposed method, both numerical simulations and experimental studies are employed, and comparative studies are conducted with the SDD method based on the l1-norm regularization. The identification results indicate that the proposed method can handle regional damages in the FE model and identify both single and multiple damages well.