PSI - Issue 78

Marco Pirrò et al. / Procedia Structural Integrity 78 (2026) 1641–1648

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• DMG3, involving a full cut to a vertical truss member at 5/8ths of the span length, on the same side of accelerometer A4. It is important to highlight that: (a) the cuts were introduced to replicate damage patterns typically resulting from corrosion or excessive loading, and (b) in the RCV condition, a jack was employed to reduce the gap in the severed member prior to welding the steel components, although a complete retu rn to the bridge’s original, undamaged state was not ensured (Kim et al. 2021). Each case scenario included several test repetitions. In the INT condition (Kim et al. 2021), vehicle speeds ranged between 30 and 50 km/h. Due to minor variations in signal durations between tests, the initial 40 seconds of data were consistently used for analysis.

Fig. 2. Old ADA bridge: (a) sensor layout and damage locations; (b) damage scenarios (adapted from Kim et al. 2021).

5.2. Training of the SAE

A total of 26 acceleration matrices (each consisting of 8000×8 elements, where each column represents an individual acceleration measurement) were gathered under the INT scenario and employed for both training and testing purposes. Specifically, 19 of these matrices – approximately 75% of the dataset – were allocated for training, while the remaining 7 matrices – roughly 25% – were used for validation. The optimal configuration of the SAE parameters was determined through a grid search approach, as described by Yang and Shami (2020). The selected setup included: (a) sigmoid activation for the encoder and linear activation for the decoder; (b) training over 500 epochs; and (c) a compression rate set at 30% of the original signal length. To enhance the stability of the ADAM optimization algorithm (Kingma and Ba 2015) during convergence, each acceleration sequence was normalized within the range [−1, +1]. The training process took approximately 20 minutes on a personal computer equipped with 16 GB of RAM and a 2.7 GHz Intel Core i5 dual-core CPU. After determining the SAE parameters, the acceleration matrices from the remaining scenarios (namely DMG1, DMG2, RCV, and DMG3) are input into the network. As mentioned earlier, the metric used to assess the quality of data reconstruction is the MAE calculated between the input and output sequences. It is anticipated that, for data originating from DMG1, DMG2, and DMG3 scenarios, the network will struggle to accurately reconstruct the acceleration sequences, resulting in higher MAE values compared to those observed for the INT scenario. Conversely, the MAE values for the RCV scenario are expected to be similar to those of the INT condition. Figure 3 presents the reconstructed sequences from both the INT validation set and the DMG2 scenario. These results confirm that the trained network can effectively reconstruct time series data from an undamaged (intact) condition, while it fails to do so when the input data corresponds to a damaged state. 5.3. Testing of the SAE and discussions