Sparse regularization-based damage detection in a bridge subjected to unknown moving forces

Output-only structural damage detection (SDD) is an important issue in the field of structural health monitoring (SHM). As an attempt, this study aims to propose a sparse regularization-based method for detecting the structural damage using structural responses caused by unknown moving forces. First, a transmissibility matrix between two sensor sets is constructed using a known bridge model and least square-based moving force identification algorithm. Second, the measured responses are used as inputs to estimate the reconstructed responses with the help of the transmissibility matrix. Then, the damage detection procedure can be regarded as an optimization problem trying to find a possible damage vector, which makes the difference between the measured and reconstructed responses minimum. L-p-norm (0 < p <= 1) sparse regularization is adopted to improve the ill-conditioned SDD problem. To assess the feasibility of the proposed method, damaged bridges subjected to moving forces are taken as examples for numerical simulations. Differences between finite element model (FEM) used for model updating and the one applied to simulate the true damage conditions are considered. The illustrated results show that the proposed method can identify structural damages with a strong robustness. Some related issues, such as regularization parameters, finite element models, L-p-norm (0 < p <= 1) penalty terms, noise levels and damage patterns, are discussed as well.