Sparse damage detection via the elastic net method using modal data

The l₁ regularization technique has been developed for damage detection by utilizing the sparsity feature of structural damage. However, the sensitivity matrix in the damage identification exhibits a strong correlation structure, which does not suffice the independency criteria of the l₁ regularization technique. This study employs the elastic net method to solve the problem by combining the l₁ and l₂ regularization techniques. Moreover, the proposed method enables the grouped structural damage being identified simultaneously, whereas the l₁ regularization cannot. A numerical cantilever beam and an experimental three-story frame are utilized to demonstrate the effectiveness of the proposed method. The results showed that the proposed method is able to accurately locate and quantify the single and multiple damages, even when the number of measurement data is much less than the number of elements. In particular, the present elastic net technique can detect the grouped damaged elements accurately, whilst the l₁ regularization method cannot.