Identification of isolated structural damage from incomplete spectrum information using l1-norm minimization

•Localization and quantification of damage based on eigenvalue sensitivity.•Proposes the use of ℓ1-normℓ1-norm regularization for damage detection.•The algorithm allows for the examination of a significantly larger number of potentially damaged elements with respect to identified eigenvalue shifts.•The algorithm finds sparse solutions.•The results are verified in detecting localized damage in a non-uniform shear building and in a thin rectangular plate.

The objective of this paper is to provide a new theoretical basis to identify localized damage in structures using incomplete modal information, such as a subset of the spectrum. The paper expands upon well-established ideas from sensitivity-based model updating and offers a new perspective on the problem by using l1 norm minimization to solve the inverse problem. It is shown that in contrast with the more traditional l2 (Euclidean) norm minimization, the proposed l1 norm minimization approach enables accurate examination of a set of potentially damaged locations significantly larger than the subset of the spectrum used in the formulation of the sensitivity matrix. The main prerequisite is that the damage must be sparse, i.e. occur in a small portion of the domain, no other information regarding the damage is required. The computational effort necessary to solve the l1 optimization is larger than in traditional Euclidean norm minimization and requires the use of convex optimization methods. However, given the results that can be obtained, the computational effort is justified.