PSI - Issue 84

Elisa Tomassini et al. / Procedia Structural Integrity 84 (2026) 288–295

290

Fig. 1. Architecture of the proposed neural network.

dedicated to predicting the modal displacements of a single mode shape. This modular design, similar to the one proposed by García-Macías et al. (2025), enables effective learning of the spatial and physical diversity of modal components, allowing the SM to accurately reproduce both natural frequencies and mode shapes based on changes in stiffness distribution. The training process of the FNN is governed by the following loss function: ̂ =arg min ℒ ( ) = arg min (ℒ ( )+ ℒ ( ) ) (2) where the loss function combines frequency- and mode-shape-based contributions, defined respectively as ℒ ( ) and ℒ ( ). The FNN is first trained on a source dataset to construct the source surrogate model, while TL is subsequently performed by freezing the first layers connected to the input one, and fine-tuning only the layers of the specialized branches using a smaller target dataset, with the requirement that the source dataset size exceeds that of the target. This strategy preserves general knowledge learned from the source structure while adapting the model to target specific features, enabling rapid construction of the target SM with minimal additional computational effort. For TL to be effective, structural similarity between source and target systems must be ensured. Two criteria are adopted: (i) geometrical similarity , primarily related to the number of spans, while differences in dimensions are accommodated through the non-dimensional damage parameters; and (ii) consistency in damage parameter distribution , requiring the same number, relative position, and extent of damaged regions, which is particularly important for transferring mode shape information. Under these conditions, the proposed architecture is highly generalizable and supports learning of shared damage mechanisms across populations of similar structures. Finally, the modular output structure allows selective activation of frequency and mode-shape branches, facilitating transfer between models with different numbers of modes. Differences in sensor layouts are addressed by constructing the TL space using the full set of modal displacements from the source model, while continuous damage assessment is performed using the actual sensor configuration of the target structure. 3. Results and discussion 3.1. Selection of the source and target domains Both the source and target structures are five-span prestressed concrete bridges. The source bridge has a total length of 340 m and consists of a continuous post-tensioned, multi-cell box-girder deck. The span arrangement is non uniform, with the first and last spans measuring 42.5 m and the three central spans 85 m each. The deck is supported