Improved DLV Method For Structural Damage Detection Using L1Norm

In recent years, the damaged identification methods based on vibration of the structures have been expanding rapidly, and those based on flexibility matrix changes before and after damage is one of the methods being considered promising in the future. The Damage Locating Vector (DLVs) method is one of the methods based on the flexibility matrix changes. In the DLVs method, a set of vectors, i.e., DLVs is computed, and when the vectors are applied to the undamaged structures as loads, they induce stress fields whose magnitude is zero or very small in the damaged elements. The DLVs is the null space of the change in measured flexibility. The DLVs method is not structure type dependent and can be applied to single or multiple damage scenario, therefore it is advantage over many other methods. However, the DLVs method requires that the structure is linear in pre-and postdamage states.In this paper, the Damage Locating Vector method is revisited by looking at the sparsity of the damage locating vectors (DLVs). We first analyze the desired property of DLVs, and focused on the sparsity of the DLVs. We measure the sparsity of the DLVs by the newly developed lp norm (p<2), and find that less sparse DLVs perform better than those opposite ones. We propose a new method for selecting DLVs for damage localization. The damage location results by the DLVs selected using the new method and DLVs selected by strain energy criterion are compared. We find that the new method is superior to the original ones. We also expect that DLVs by the new method reduce the false-alarms in a noisy environment.We then propose an algorithm to compute the DLVs using sparse recovery theory, instead of using SVD in the original DLVs method. We then locate damages using the computed most non-sparse DLVs by an appropriate criteria based on the desired property of the DLVs. The performance of the new method is numerically validated by detecting damage elements of a truss and experimentally validated on a frame structure. The results validate the effectiveness of the new method and expectation of the DLVs. The new method for selecting DLVs is also more efficient and easy implemente as it avoids the reanalysis performed on the intact structure loaded with each DLV.