PSI - Issue 84

596 Laura Dieci et al. / Procedia Structural Integrity 84 (2026) 591–598 . These parameters are chosen due to their marked influence on the global stiffness and mass distribution of the deck, as well as on the boundary restraint conditions, all of which have a significant impact on both modal properties and static deflections. To determine the optimal values of these parameters, the numerical results are compared against a set of target quantities derived from experimental data. In particular, the values used as reference targets for the dynamic behaviour are the frequencies of the first bending mode and the first torsional mode. The adoption of only the first two natural modes for model calibration is motivated by the following consideration. These are the only modes that can be clearly and reliably associated with the corresponding numerical modes. In contrast, establishing a consistent correspondence between the numerical modes and the higher experimental modes is considerably more challenging. This difficulty arises because the sensors were primarily installed along the main span; therefore, for higher-order modes, the available measurements are insufficient to ensure an unambiguous matching with the numerical results. Therefore, to avoid introducing additional uncertainties into the calibration process, only the first two modes are taken into account. For the static behavior, the calibration relies on the vertical deflections at midspan and at the Gerber saddles. Specifically, the experimental displacements measured on both sides of the bridge are averaged to estimate the displacement along the bridge centerline, which is then compared with the displacements predicted by the numerical model. The calibration problem is formulated as an optimization problem, involving the weighted sum of different objectives following the classic framework proposed in the literature for FE model updating. The two objectives are defined as the residuals between experimental and numerical quantities in the frequency and displacement domains. Let = [ , , ] (1) be the vector of calibration parameters. The optimization problem reads: { { ( ), ( )} ∈ (2) where ⊂ℝ 3 denotes the set of admissible parameter values, represents the frequency residual, and the displacement residual. The frequency objective quantifies the relative error between numerical and experimental natural frequencies of the first bending and torsional modes: =∑ ( − ) 2 = 1 (3) Similarly, the static objective measures the relative difference between numerical and experimental vertical deflections under the reference load condition, evaluated at midspan and at the Gerber saddles: =∑ ( − ) 2 = 1 (4) The problem is solved by combining the two objectives into a single objective function using a weighted sum approach: ( ) = ( ) + (1 − ) ( ) (5) where α∈ [0,1] is a weighting factor expressing the relative importance of the frequency residual versus the displacement residual. Different values of α are employed to explore the Pareto front and evaluate the trade-off between the dynamic and static objectives. Following Ponsi et al. (2021), the preferred solution is chosen as the point