PSI - Issue 64

Marco Pirrò et al. / Procedia Structural Integrity 64 (2024) 661–668 Author name / Structural Integrity Procedia 00 (2019) 000–000

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used to evaluate the training parameters of the AE model, such as: (a) the activation encoder-decoder functions f and g (see Eqs. (1) and (2)); (b) the maximum number of iterations for the optimization method (epochs) and (c) the number of nodes of the hidden layer. The last parameter is extremely important since it quantifies the number of hidden patterns learned by the encoder. Among the matrices of signals collected during the training period, the 75% of the total are used for training purposes and the remaining 25% for validation purposes: during the training, the ADAM algorithm (Kingmaand and Ba, 2015) is adopted to minimize a loss function Z( x n , y n ) between the input and the reconstructed output. However, since some numerical problems may arise during the training procedure that might prevent the convergence of the optimization method (Finotti et al. 2022), it is generally recommended to normalize the input data. In this paper the signal portions are re-scaled in the range [ − 10, 10]. 3.3. Reconstruction of testing data Once trained, the AE is tested using newly collected data − that are measured in unknown structural scenarios − with the main objective of reconstructing the new data. The reconstruction error, between the original input data and the reconstructed output, is the Mean Absolute Error (MAE, measuring the average absolute difference between two sequences): where I is the length of each realization, x ni and y ni are the samples of the n-th input and reconstructed output realizations, respectively, acquired at time i Δ , being Δ the sampling period. If the new signals are collected when the structural condition and the EOV are similar to the ones of training period, the AE is able to well reconstruct the input. Conversely, the AE will fail to reconstruct well the signals from different structural condition, leading to higher reconstruction errors computed using the input and the output data (i.e., higher MAE). To detect abnormal MAE variations, the reconstruction error is represented in a graph, along with the m-th percentile of the values computed within the training dataset. If a persistent and non-negligible occurrence of outliers is detected, a different condition with respect to the normal state can be inferred. 4. Application: KW51 bridge 4.1. The bridge and the monitoring system The KW51 railway bridge (Fig. 2a) is located between Leuven and Brussels (Belgium) and realizes the crossing of the canal Leuven-Mechelen. The bridge, hosting two curved ballasted tracks, is of the bowstring type and has a length of 115 m and a width of 12.4 m. Passenger trains regularly uses the bridge since 2003. From 15/05/2019 to 27/09/2019, the bridge was retrofitted to resolve a construction error that was noticed during inspection. The retrofit consisted of strengthening the connections of the diagonals to the arches and the bridge deck. Figs. 2b and 2c show a typical connection before and after the retrofit: for each diagonal, a steel box was welded around the original bolted connection at the intersection with the arches and the bridge deck. A monitoring system has been installed on the bridge in September 2018 (Maes and Lombaert 2021) which included, beyond strains sensors, several accelerometers disposed on the bridge deck along the lateral and vertical direction, as well as on the arches along the lateral direction. Furthermore, the surface temperature and the relative humidity below the deck are measured with two sensors. Only the four vertical accelerometers of the bridge deck and the environmental measurements (Fig. 3) from 10/10/2018 to 15/01/2020 are herein considered. For every day within the monitoring period, ambient accelerations are provided for a period of 5 min within the 1st, 5th, 9th, 13th, 17th, and 21st hour. The ambient accelerations might include either a free decay (after a train passage) or the vibration associated to wind effects and vehicle passages under the bridge. Furthermore, the hourly-average temperature and humidity measurements are provided (Fig. 4). (3)