PSI - Issue 77

Douaa Benhaddouche et al. / Procedia Structural Integrity 77 (2026) 152–160 Author name / Structural Integrity Procedia 00 (2026) 000 – 000

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to predict, likely due to reduced external influences such as traffic or temperature fluctuations. These results show that the GCN-LSTM model can capture the spatio-temporal patterns from acceleration data efficiently, as demonstrated by the high correlation and low MSE values. The CDI values corresponding to the undamaged and damaged states are presented in Figure 5. The CDI of the undamaged state remains close to zero, confirming the structural system’s stability in the baseline condition. In contrast, the CDI values exhibit a progressive increase during 19/03, 10/04 and 06/06, with a pronounced acceleration in June. This temporal evolution provides strong evidence for the onset of damage and its subsequent propagation within the structure.

(a) (c) Fig. 6. Forecasting errors in undamaged and damaged states for morning (a), afternoon (b) and evening (c). (b)

A less pronounced growth of the CDI is observed during the nighttime intervals of 19/03 and 10/04, suggesting that deviations from the undamaged state are comparatively weaker under these conditions. This behavior may be attributed to the reduced dynamic loads and lower environmental disturbances at night, which render the structural response more predictable and thereby limit the accumulation of damage-sensitive errors. Accordingly, the CDI proves to be an effective indicator for detecting the emergence of anomalies and tracking the progression of structural degradation over time.

(a) (c) Fig. 7. Empirical CDFs of forecast errors for morning (a), afternoon (b) and evening (c). (b)

The empirical CDFs of the log-transformed MSE errors shown in figure 6 provide a clear comparison between the undamaged and damaged structural states. In the three plots, the reference undamaged state (blue curve) exhibits the lowest error distribution, while the damaged states show a progressive rightward shift, indicating increasing forecast errors. In the three daytimes of 19/03/2008 (orange, KS=0.055, KS=0.007, KS=0.059) and 10/04/2008 (green, KS = 0.128, KS=0.011, KS=0.129) only slight deviations from the undamaged distribution are observed, suggesting early signs of degradation. In contrast, the state on 06/06/2008 (red, KS=0.4148, KS=0.463, KS=0.535) displays a pronounced displacement with a much higher error distribution, evidencing a significant departure from the undamaged baseline.