62 J. Zeng et al. Fig. 1 Percentage Difference Matrix for the damaged state: Bridge-4-SS. In the case of Bridge-4-SS (Figure 1), the PDM exhibits pronounced differences, with values reaching as high as 23.14%. This indicates significant structural changes, particularly when comparing Bridge-4-SS with other bridges in the system. These elevated values reflect the localized damage and the limited ability of the single-span structure to redistribute the effects of the damage, making the changes more concentrated around the affected bridge. The high percentage difference clearly signals that the single-span structure is vulnerable to localized damage, and the signal-level comparison method is effective in detecting these changes. Conversely, the PDM for Bridge-17-TS (Figure 2) shows much lower percentage differences, even though the same level of damage (30% stiffness reduction) was applied. The largest percentage differences remain below 4%, indicating a more subdued response to the damage. The lower PDM values suggest that the multi-span structure, with its more complex geometry and additional support at mid-span, is able to distribute the effects of the damage across multiple spans, thereby reducing the severity of localized structural responses[15, 16]. This highlights a key difference between single-span and multi-span bridges, where the structural complexity in the latter allows for better redistribution of stresses, leading to less pronounced changes in correlation coefficients. While these visual insights from the PDMs provide an initial understanding of the changes in structural behavior, they are limited in detecting more subtle deviations that may occur across the bridge network. To address this, the RDI offers a more comprehensive, quantitative measure for assessing structural health.
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