PSI - Issue 84

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

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Fig. 5. Transfer learning of the NN on the data of the target bridge. (a) Frequency training and validation loss; (b) mode shape training and validation loss; (c) comparison between predicted frequencies ̂ and FEM reference values and (d) MAC values computed between the predicted mode shapes ̂ and the FEM mode shapes for each sample in the validation dataset. The FEM of the target bridge was parameterized using the same discretization scheme adopted for the source bridge, as depicted in Fig. 2. Each stiffness multiplier was independently sampled within the interval [0.80,1.05] using a LHS strategy, yielding a target training dataset of 256 samples. To ensure consistency with the source SM and maximize information transfer, the output space was not limited to the sensor layout of the target bridge. Instead, mode shapes were extracted at all nodal locations corresponding to the accelerometer positions of the source bridge, resulting in mode shape vectors with 30 components, as depicted in Fig. 2(b). This choice preserves compatibility with the source representation while enriching the informational content of the target outputs. To rigorously assess generalization, an independent validation dataset containing 1024 samples was generated using the same LHS-based methodology. The relatively small training set was intentionally selected to avoid overfitting and preserve the pretrained knowledge embedded in the source model, while the larger validation set enabled a robust evaluation of transfer performance. TL was implemented through fine-tuning, starting from the source SM. The general feature-extraction layers were frozen, and only the specialized output branches for frequencies and mode shapes were retrained using the target dataset. Fine-tuning was carried out for 1000 epochs, with 20% of the samples reserved for internal validation. To reduce loss fluctuations during early training, the scaling parameter was reduced to 2. A mini-batch size of 4 and data shuffling at each epoch were adopted to enhance convergence and generalization. The results of the TL via fine tuning are depicted in Figs. 5(a, b). Finally, as shown in Figs. 5(c, d), the transferred surrogate model achieves excellent predictive performance for all eight modes, with coefficients of determination exceeding 2 =0.99 and MAC values consistently above 0.99. These results confirm the effectiveness of the proposed TL strategy and demonstrate the strong generalization capability of the surrogate model across structurally

similar bridges. 4. Conclusions

This paper has presented a model-driven methodology for network-scale bridge Structural Health Monitoring based on surrogate modeling and transfer learning. The proposed framework leverages neural-network-based surrogate