PSI - Issue 77

156 Douaa Benhaddouche et al. / Procedia Structural Integrity 77 (2026) 152–160 Author name / Structural Integrity Procedia 00 (2026) 000 – 000 5 1951). Formally, if F ( ) and F ( ) denote the empirical CDFs of the healthy and damaged state respectively, the index is defined as: = | ( )− ( )| × 100 The symbol denotes the supremum over all values of x, which means taking the largest vertical distance between the two empirical CDFs at any point along the error axis. The resulting statistic therefore captures the maximum discrepancy between the undamaged and damaged error distributions. For ease of interpretation, the KS statistic is rescaled and expressed as a percentage-based indicator by multiplying it by 100. Since the KS statistic is inherently bounded between 0 and 1, this transformation provides a relative measure of severity, where small value of indicates that the structure is likely undamaged, while a large value implies a pronounced shift in error behavior, indicating a severe structural degradation. 3. Results and discussion To validate the effectiveness of the proposed method The Tianjin Yonghe Bridge monitoring data are used. Tianjin Yonghe Bridge, illustrated in Figure 2.a, features a main span of 260 meters, flanked by two side spans measuring 25.15 meters and 99.85 meters respectively. After 19 years of service, some cracks and corrosion were discovered in the bridge. After repair and rehabilitation in 2007, an SHM system was designed and implemented to monitor the bridge vibrations. 14 uniaxial accelerometers across the bridge deck were installed. The placement of these sensors is represented in Figure 2. Inspections in August 2008 revealed two major damage patterns: significant cracking in the side spans and pier damage. To study this degradation, we consider five dates of monitoring data 17/01/2008, 27/01/2008, 03/02/2008, 19/03/2008, 10/04/2008 and 06/06/2008. Data from 17/01/2008, 27/01/2008, 03/02/2008 are considered for training and validation ( ≈600 000 samples) and the remaining dates are used for test ( ≈150 000) . Data collected by sensors 3 and 10 were determined to be uninformative and were therefore excluded from our analysis.

Fig. 1. View of Tianjin Bridge.

Fig. 2. Placement of the accelerometer network.

Since daytime periods may be influenced by heavier traffic or temperature changes, and nighttime data might reflect more stable structural responses, we trained the model separately on three periods: morning, afternoon, and evening from 1h to 23h. By training models on these distinct patterns, the overall system becomes more sensitive and robust to time-dependent anomalies or damage. In addition, a same fixed 3-minute slice was chosen from each hour where data are smoothest, enabling the model to focus on structural patterns and learn consistently from the same structural state. In the graph data constructed based on monitoring data, each sensor is treated as a node and the DTW distance is calculated to measure the similarities between sensors. The values of DTW distance between sensors for the three periods are above 150 across 430 000-time steps, showing a very high degree of similarity in the structural response measured by the respective sensors, suggesting a strong spatial correlation and the sensors are experiencing similar operational and environmental conditions in each daytime.