Comparative Analysis of Structural Damage Identification Methods Based on Iterative Reweighted L1/2 Regularization and Three Optimization Functions

Previous vibration-based damage detection studies mostly focus on developing a more sensitive optimization function to promote the effectiveness of damage identification. However, a few studies have conducted comparative analyses on the detection performance of different optimization functions. In the study, changes in the frequency and mode shape are applied as the inputs to different optimization functions for damage identification. Three optimization functions are established using the frequency residuals, the combinations of frequency and mode shape residuals, and the modal flexibility residuals, respectively. Considering the sparsity of damage element distribution, an iterative reweighted $l_{1/2}$$(\mathrm{\text{IR}}{l}_{1/2})$ regularization is added as a norm penalty to the optimization function. A numerical model and an experimental example are applied to assess the performance of distinct optimization functions. The results show that the increase in modal data number cannot significantly improve the detection accuracy when the number meets the basic requirements for identifying damage. The detection error of the optimization function established by combining the frequency and mode shape residuals is 6.65% and 5.18% using the first four and fourteen-order noisy modal data, respectively. Furthermore, the optimization function constructed using the modal flexibility residuals requires more less modal data to identify damage than the other two functions.