Damage Identification of Euler–Bernoulli Beams Using Static Responses

The paper presents two computational procedures to reconstruct the stiffness distribution and to detect damage in Euler–Bernoulli beams. A novel methodology of damage identification is developed using static deflection measurements. The first formulation is based on the principle of the equilibrium gap along with a finite-element discretization, and leads to an overdeterminate linear system. The solution is obtained by minimizing a regularized functional using a Tikhonov total variation (TTV) scheme. The second proposed formulation is a minimization of a data-discrepancy functional between measured and model-based deflections. The optimal solution is obtained using a gradient-based minimization algorithm and the adjoint method to calculate the Jacobian. Also discussed is a simple procedure to measure the deflection of beams using a close-range photogrammetry technique. An edge detection-based algorithm is devised for quasi-continuous deflection measurement. The proposed identification methodology is validated using experimental data. Four beams with predefined damage scenarios are tested. In each case, the location and damage levels are reconstructed with good accuracy. However, results show that, in general, the equilibrium gap-based formulation has greater success than the data-discrepancy method. The proposed methodology has the potential to be used for long-term health monitoring and damage assessment of civil engineering structures.