PSI - Issue 78

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

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Fig. 1. Scheme of the methodology

(d) Simulation of structural responses: the calibrated FE model is used to simulate the structural response for each parameter set. The resulting input-output pairs constitute the training dataset for the BNN. (e) BNN training and optimization: the BNN is trained on the simulated dataset. Bayesian optimization is employed to explore di ff erent network architectures, activation functions, and prior distributions for the weights, with the aim of maximizing prediction accuracy and uncertainty quantification capabilities. 2. Online phase: the trained BNN is deployed for real-time analysis of the structural health using incoming sensor data. This phase involves: (a) Real-Time data acquisition: sensor data are continuously collected from the monitored structure. These readings, corresponding to the damage-sensitive parameters identified in the o ffl ine phase, are used as inputs for the BNN. (b) Sti ff ness prediction using the BNN: leveraging the relationships learned during training, the BNN predicts the sti ff ness distribution of structural elements. Unlike deterministic models, the BNN provides a full probability distribution for each prediction, o ff ering a robust quantification of uncertainty. (c) Damage scenario identification and analysis: the predicted sti ff ness distributions are compared against baseline distributions from the healthy state. Significant deviations may indicate potential damage. Thresh olds are defined to assess the probability of exceedance, enabling quantification of damage severity with varying tolerance levels. The probabilistic output of the BNN supports a more comprehensive and reliable damage assessment framework.

3. The real case study: prestressed concrete box girder bridge

The proposed methodology is applied to a real-world post-tensioned concrete box girder bridge, constructed in 1984 [Galassi Sconocchia et al. (2024); Meoni et al. (2024); Mariani et al. (2024)]. The bridge spans a total length of approximately 630 meters and comprises ten spans: the end spans measure 35 meters each, while the intermediate spans are 70 meters long. The bridge’s prestressing system includes three distinct sets of cables integrated into the girder. The first set, located between the webs and the upper slab, consists of over 600 cables. The second set, embed ded within the upper slab, consists of 160 cables. The third set, positioned in the lower slab, comprises 180 cables. The