PSI - Issue 78

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

1644

1 I ∑| I k=1

n,k (i) |

(i) –y

(i) =

(3)

MAE n

x n,k

(i) and y

n,k (i) are, respectively, the samples of the input and reconstructed output

where I is the length of the signals, x n,k

from channel i , recorded at time k  t , being  t the sampling period. If the test data reflects structural patterns similar to those encountered during training, the network is expected to reproduce the input accurately. However, when the structural characteristics differ from the training conditions, the SAE may fail to reconstruct the input precisely, resulting in elevated MAE values. A test sequence is classified as an outlier if its reconstruction error exceeds the m th percentile (typically between the 95th and 99th percentiles) of the training error distribution. A high frequency of such anomalies may signal the emergence of abnormal structural behavior. A typical method for evaluating experimental outcomes against a known set of ground truth labels (when available) involves identifying the following counts: (a) normal instances accurately identified as such (true negatives, TN); (b) normal instances incorrectly flagged as anomalies (false positives, FP); (c) anomalous instances correctly detected (true positives, TP); and (d) anomalous instances mistakenly classified as normal (false negatives, FN). Based on these values, several performance metrics can be derived: ACC = (TP+TN)/(TP+FP+TN+FN) (4.1) FAR = FP/(FP+TN) (4.3) where: (a) Accuracy (ACC), representing the proportion of correctly classified samples out of the total; (b) Detection Rate (DR), indicating the percentage of anomalies that were correctly identified; and (c) False Alarm Rate (FAR), which quantifies the fraction of normal samples wrongly labeled as anomalies. 5. The Old ADA bridge 5.1. Description of the bridge and the test scenarios Vibration data resulting from both vehicle loads, and ambient sources were collected on the Old ADA steel truss bridge in Japan, as reported by Kim et al. (2021). As illustrated in Fig. 2a, this simply supported structure spans 59.2 meters and features a deck width of 3.6 meters. Having served for over five decades, the bridge was slated for demolition in 2012. Prior to its dismantling, dynamic testing was conducted over two days – March 1st and 2nd, 2012 – between 10:00 a.m. and 5:00 p.m., during which artificial damage was intentionally introduced. Acceleration data were captured at a frequency of 200 Hz using eight vertically oriented uniaxial accelerometers installed on the bridge deck (see Fig. 2a). Although both ambient and vehicle-induced vibrations were recorded, this study focuses exclusively on the latter. The test vehicle was a two-axle Nissan Serena (manufactured by Nissan Motor Co. Ltd.) weighing 21 kN, and no other traffic was permitted on the bridge throughout the testing period. For comprehensive information on the experimental procedures, readers are encouraged to consult Kim et al. (2021). Figure 2b outlines the five scenarios that were implemented for the vibration experiments: • INT, with no human-induced damage; • DMG1, which involves a half-cut performed on a vertical truss member at the midspan of the bridge, on the same side of accelerometer A3; • DMG2, involving a full cut to the same vertical truss member at midspan, in the neighborhood of sensor A3; • RCV (recovery state), wherein the full cut of the midspan member was repaired; DR = TP/(TP+FN) (4.2)