PSI - Issue 77

Douaa Benhaddouche et al. / Procedia Structural Integrity 77 (2026) 152–160 Douaa BENHADDOUCHE/ Structural Integrity Procedia 00 (2026) 000 – 000

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Overall, while minor fluctuations in KS values are expected between consecutive states as in the afternoon, the general trend of KS statistic across dates still reflects the gradual evolution of degradation. The maximum KS value across morning, afternoon and evening periods is considered to capture the worst-case condition. For instance, the GHI reached 6% in March (late winter), increased slightly to 13% in April (spring), and rose sharply to 53% in June (early summer). This progression highlights how seasonal or operational factors can amplify discrepancies between undamaged and damaged states. It should be noted that this index does not quantify the absolute level of physical damage but rather reflects the extent to which the damaged state deviates from the baseline state, thus serving as a practical severity measure for structural health assessment. 4. Conclusion In this paper, an unsupervised deep learning approach was introduced for structural damage detection and condition assessment. The method integrates a GCN-LSTM neural network, combining a graph convolutional layer with LSTM units to forecast future structural responses. The graph structure is built using dynamic time warping (DTW) distance, a similarity metric widely applied in time-series analysis. The sensor graph and the sensor signals are used to learn the spatio-temporal features and predict future sensor data. The forecasting errors expressed in terms of Mean Squared Error (MSE) are then exploited to track degradation and assess structural condition. Monitoring data from a large-scale cable-stayed bridge were used to validate the approach. The results show that the method can reliably identify damage through a forecasting error-based cumulative indicator. In addition, the Kolmogorov – Smirnov (KS) statistic applied to error distributions from undamaged and damaged states, proved to be a suitable tool for global condition assessment. Future research may focus on refining the graph construction strategy through adaptive similarity measures, and on incorporating attention mechanisms to further enhance the forecasting capacity of the model. References Dang, V.-H., Le-Nguyen, K., Nguyen, T.-T., 2023. Semi-supervised vibration-based structural health monitoring via deep graph learning and contrastive learning. Structures 51, 158 – 170. https://doi.org/10.1016/j.istruc.2023.03.011 Deng, A., Hooi, B., 2021. Graph Neural Network-Based Anomaly Detection in Multivariate Time Series. Entezami, A., Sarmadi, H., Mariani, S., 2020. An Unsupervised Learning Approach for Early Damage Detection by Time Series Analysis and Deep Neural Network to Deal with Output-Only (Big) Data, in: 7th International Electronic Conference on Sensors and Applications. Presented at the Preface: International Electronic Conference on Sensors and Applications, MDPI, p. 17. https://doi.org/10.3390/ecsa-7-08281 Frank, J., MASSEY, J., 1951. The Kolmogorov-Smirnov Test for Goodness of Fit. Journal of the American Statistical Association,, Vol. 46, No. 253 68 – 78. Fu, L., Tang, Q., Gao, P., Xin, J., Zhou, J., 2021. Damage Identification of Long-Span Bridges Using the Hybrid of Convolutional Neural Network and Long Short-Term Memory Network 20. Gers, F.A., Schmidhuber, j, Cummins, F., 2000. . Learning to Forget: Continual Prediction with LSTM. Neural Computation, 12, 2451 – 2471. Hung, D.V., Hung, H.M., Anh, P.H., Thang, N.T., 2020. Structural damage detection using hybrid deep learning algorithm. STCE 14, 53 – 64. https://doi.org/10.31814/stce.nuce2020-14(2)-05 Jiang, K., Han, Q., Du, X., Ni, P., 2021. A decentralized unsupervised structural condition diagnosis approach using deep auto‐encoders. Computer‐Aided Civil and Infrastructure Engineering 36, 711 – 732. https://doi.org/10.1111/mice.12641 Ma, X., Lin, Y., Nie, Z., Ma, H., 2020. Structural damage identification based on unsupervised feature-extraction via Variational Auto-encoder. Measurement 160, 107811. https://doi.org/10.1016/j.measurement.2020.107811 Ma, X., Wu, J., Xue, S., Yang, J., Zhou, C., Sheng, Q.Z., Xiong, H., Akoglu, L., 2021. A Comprehensive Survey on Graph Anomaly Detection with Deep Learning. IEEE Trans. Knowl. Data Eng. 1 – 1. https://doi.org/10.1109/TKDE.2021.3118815 Meruane, V., 2016. Online Sequential Extreme Learning Machine for Vibration-Based Damage Assessment Using Transmissibility Data. J. Comput. Civ. Eng. 30, 04015042. https://doi.org/10.1061/(ASCE)CP.1943-