PSI - Issue 64

Bowen Meng et al. / Procedia Structural Integrity 64 (2024) 774–783 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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models. This decision was based on the observation that including the dropout layer adversely affects the predictive accuracy of these models. For training, 90% of the total signal data derived from the FE model was utilized, reserving 10% for validation. This validation aids in determining the appropriate number of training epochs and monitoring overfitting. Once the models are trained, on-site strain signal measurements were employed to evaluate each model's performance. Specifically, two typical trains with distinct stress histories during the passages were selected to test the models' generality. The results are shown in Fig. 7. On the left column of Fig. 7, the predicted stress response ̂ 7 using 5 from each model is depicted for two different train passages. The measured stress response of 7 is represented by blue lines, while the yellow lines denote the output from the local response function method. All deep learning models exhibit comparable accuracy, with R-squared scores exceeding 0.9, to the local response function method for the three train signals. However, for train type 2 in Fig. 7(b), the local response function method and MLP model tend to underestimate stress fluctuations caused by train passage. In contrast, LSTM, TCN, and the hybrid models slightly overestimate the peak and trough magnitudes.

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Fig. 7. Predicted stress response of ̂ 7 derived from 5 (left column) and 2 (right column). Fig. 7(c) and Fig. 7(d) contrast the predictions of ̂ 7 using 2 from deep learning models. Given the challenges in approximating the time-dependent correlation with the local response function method, only the results from the deep learning models are presented. All models successfully captured the overall trend of signal variations compared to the true stress response in blue. Except for the MLP model, the other models generally provided amplitudes close to or slightly above the actual measurements. However, the results for train type 1, reveal deviations from the actual response, including two unexpected signal peaks and troughs. Potential causes may include discrepancies in the modeled versus actual axle distance of trains, variations in train speed, and measurement errors from the strain gauges. In fact, the imperfect FEM model can hardly replicate the behaviors of the bridge and thus cause deviations in stress correlations. Furthermore, the axle distance of the train and train speed will influence the time-dependency of stress variations. The trained model with inconsistent loading conditions and biased mapping between stress histories will not give precise predictions. Currently, the FEM model only employs a simple loading condition