Fractal Dimension-Based Damage Detection Method for Beams with a Uniform Cross-Section

For civil structures, damage usually occurs in localized areas. As fractal dimension (FD) analysis can provide insight to local complexity in geometry, a damage detection approach based on Katz's estimation of the FD measure of displacement mode shape for homogeneous, uniform cross-sectional beam structures is proposed in this study. An FD-based index for damage localization (FDIDL) is developed utilizing the difference of angles of sliding windows between two successive points, which is expressed in FD. To improve robustness against noise, FDIDL is calculated using multisliding windows. The influence of the spatial sampling interval length and the number of 2-sampling sliding windows on sensitivity to damage and robustness against noise is investigated. The relationship between the angle expressed in FD and the modal strain energy is established and thereby an FD-based index for the estimation of damage extent (FDIDE) is presented. The two damage indices are applied to a simply supported beam to detect the simulated damage in the beam. The results indicate that the proposed FDIDL can locate the single or multiple damages, and FDIDE can reliably quantify the damage extent. The optimal spatial sampling interval and the number of sliding windows are investigated. Furthermore, the simulation with measurement noise is carried out to demonstrate the effectiveness and robustness of the two defined FD-based damage indices. Finally, experiments are conducted on simply supported steel beams damaged at different locations. It is demonstrated that the proposed approach can locate the damages to a satisfactory precision.