PSI - Issue 84

Prajwal Giri et al. / Procedia Structural Integrity 84 (2026) 1119–1126

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Table 1 summarizes global bending modes and the first torsional mode before and after calibration, while Figure 4(b–e) compares the corresponding experimental and numerical mode shapes.

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(d)

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Fig. 4. (a) 3D FEM of the bridge; (b) to (d) comparison between the first three experimental and numerical mode shapes.

5. Definition of Damage Classes This study defines representative damage scenarios reflecting the most probable deterioration mechanisms in prestressed concrete bridge girders, forming the basis for multi-class damage classification. The scenarios capture localized sti ff ness degradation and prestress force loss, which are key indicators of structural deterioration in prestressed systems. As illustrated in Figure 5, five damage classes (DS-0 to DS-4) are examined. DS-0 indicates the undamaged reference state, while DS-1 models a 10% localized sti ff ness reduction over a 5 m section near the ends of the girder. DS-2 presents a 15% sti ff ness reduction over a 10 m midspan segment. DS-3 shows a global 15% sti ff ness loss across the full 20 m span, and DS-4 simulates a 20% reduction in the prestressing force of the post tensioned tendons, with one tendon in each of the two external beams, representing the long-term e ff ects of prestress losses due to creep, shrinkage, or relaxation. To generate physically representative datasets, sti ff ness and force multipliers (E , F) were introduced and randomly perturbed within ± 3% of their nominal values using E , F = 1 + (rand(N , 1) × 0 . 06 − 0 . 03), where N is the number of samples and rand(N , 1) is uniformly distributed in [0 , 1]. For DS-0, E ∈ [0 . 97 , 1 . 03] represents minor material variability. DS-1 corresponds to a 10% sti ff ness reduction (0 . 9E ∈ [0 . 87 , 0 . 93]), DS-2 and DS-3 to 15% sti ff ness losses (0 . 85E ∈ [0 . 82 , 0 . 88]), and DS-4 to a 20% prestress loss (0 . 8F ∈ [0 . 77 , 0 . 83]). For each damage class, 500 realizations were generated, each comprising 29 features (21 modal features and 8 static rotation features), yielding 2500 samples in total (Figure 5a). To emulate measurement uncertainty, class-specific noise was introduced according to noisy data = noise free + (rand(data size) − 0 . 5) × 2 × (level / 100), where rand is uniformly distributed in [0 , 1], producing noise values in [ − level / 100 , + level / 100], and level denotes the noise percentage for each class. Training noise levels were set to 3 . 0%, 2 . 8%, 2 . 5%, 2 . 0%, and 1 . 5% for DS-0 to DS-4, respectively. The dataset was stratified into an 80:20 training–validation split (2000 / 500 samples). An independent test set of 100 samples per class (500 total) was