PSI - Issue 78

Francesco Mariani et al. / Procedia Structural Integrity 78 (2026) 875–882

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Fig. 4. Test results for the pier damage parameters: a) elastic modulus of the base segment of pier n.1; b) elastic modulus of the base segment of pier n.3; c) elastic modulus of the base segment of pier n.5; d) elastic modulus of the base segment of pier n.7

Fig. 5. Damage detection on girder scenario

the location and severity of damage, the median of each predicted distribution was compared against the observed (deterministic) elastic modulus for each element. Representative results are shown in Figure 5 and Figure 6. These figures demonstrate the model’s capability to accurately detect both the location and magnitude of multiple damage cases. Specifically, Figure 5 illustrates a plausible scenario in which elements of the superstructure exhibit residual damage following a seismic event, primarily due to the vertical seismic response. In this case, the network correctly identifies the damaged segments, with elastic modulus reductions ranging from 5% to 10%. Conversely, Figure 6 presents a potential real-world scenario where the piers sustain damage during a seismic event. As typically observed in such cases, damage is localized at the base of the piers, with reductions in elastic modulus varying between 5% and 15%. The BNN successfully captures both the location and severity of these damages, underscoring its ability to generalize to unseen but physically plausible structural conditions.

7. Results: probabilistic damage detection

Following the evaluation of the BNN’s predictive performance, the advantages of a probabilistic framework are further highlighted through an analysis of the statistical properties of the predicted distributions. Figure 7 presents the same damage scenarios introduced in Figure 6, focusing on the pier bases. In this figure, two thresholds are defined to represent reductions in the nominal elastic modulus of concrete: a 5% reduction indicating minor degradation, and a 10% reduction marking a significant deterioration. These thresholds divide the value range into three regions: (from top to bottom) ordinary degradation due to aging, sensitive damage requiring ongoing monitoring, and critical damage