PSI - Issue 84

Laura Ierimonti et al. / Procedia Structural Integrity 84 (2026) 959–966

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planning, allowing them to focus attention on the most likely damaged regions. Because the framework combines efficient surrogate models with rigorous statistical selection criteria, it is well suited for continuous monitoring and

near real-time structural assessment. 3. BIC-based model class selection

Damage hypotheses are represented through a collection of model classes, denominated as candidates SM k . The paper employs Bayesian model class selection to identify which of these candidates is most consistent with the observed system response. Within SHM applications, candidate models frequently differ in their parameter structures, each reflecting a different type of potential deterioration. Bayesian model class selection leverages Bayesian inference (Hernández-González and García-Macías, 2024) to update belief in each model by merging prior knowledge with measurement data. For efficient comparison, the BIC is used as a practical tool for determining the model which best fits the data: BIC(SM )= − 2 ∙ log( ∗ ( ∣ ∗ (SM ))+ ∙ log , (1) where the term k corresponds to the number of the parameters within the model, n represents the number of available measurements, ∗ ( ∣ ∗ (SM )) denotes the maximized value ( ∗ are the values of updating parameters that maximize the likelihood function for model SM ) of the likelihood function ( ∣ (SM )) that quantifies how closely the model’s predictions align with the observed data . The function ( ∣ (SM )) , assuming a Gaussian distribution of the error between the model and experimental data, can be written as: ( ∣ (SM ))= ∑ ∑ √2 1 2 exp (− ( , − ˆ ( ( SM )) ) 2 2 2 ) =1 =1 , (2) where is the -th experimental frequency, ˆ ( (SM )) is the predicted frequency from the surrogate model SM , is the standard deviation associated with the -th frequency. The BIC formulation balances these elements by rewarding explanatory accuracy and penalizing unnecessary complexity. Within BMCS, the preferred model is the one yielding the smallest BIC score, as it best reconciles fidelity and parsimony. 4. The case study 4.1. Description of the real bridge The Volumni is a real bridge located in Perugia, in the Umbria region of Italy, and consists of five spans made of prestressed concrete. Overall, the structure extends for about 340 m. The deck is composed by a continuous post tensioned multi-cell box girder in prestressed concrete. The first and last spans are 42.5 m long, whereas each of the three central spans measures 85 m. Support is provided by four rectangular reinforced-concrete piers on deep foundations. Their heights vary due to the sloping ground conditions; the third pier is the tallest at approximately 12.8 m, the two adjacent piers are around 10 m, and the first pier is substantially shorter. All piers rest on deep pile foundations composed of reinforced-concrete piles. As part of the SHM programme initiated by ANAS S.p.A. (2025), the Bridge was equipped in 2023 with an extensive network of sensors consisting of a combination of one triaxial accelerometer, four biaxial accelerometers, and thirty uniaxial MEMS accelerometers, installed along the structure (Figure 2).