## Case Study
### Network Determination and Training
#### 4.2.3 The Size of Training Dataset  
The prediction accuracy of an LSTM network model is usually affected by many factors, including the structure of the neural network, network parameters, training sample size, and so on. As descripted in Section 4.2.2, the neural network model with 2 LSTM layers and 128 neurons can achieve relatively good prediction accuracy. On this basis, this section further discusses the influence of the size of training dataset on the prediction accuracy. The detailed information of the applied datasets, i.e., A to E, can be found in Table 1.  
The evaluation metrics of the predicted bridge displacements across datasets A to E are illustrated in Figure 13. The results demonstrate consistently high levels of Pearson correlation coefficient and for all datasets, indicating a robust correlation between predicted displacement and theoretical values. Moreover, the influence of individual samples appears negligible. The APVE is consistently maintained between 0.5% and 2.5%, suggesting low peak error levels. Additionally, all dimensional metrics, including WMAE, RMSE, and WRMSE, range from 0.004 to 0.012 mm, further indicating excellent prediction accuracy.  
Figure 11: Theoretical and predicted bridge responses using neural network structure ‘2-128’.  
Figure 12: The PSD of predicted bridge responses using neural network structure ‘2-128’.  
The evaluation metrics of the predicted bridge acceleration responses across datasets A to E are illustrated in Figure 14. As shown in the figure, the Pearson correlation coefficient and \(\text{R}_{\text{W}}^{2}\) ranged from 0.3 to 0.95. This shows that the prediction accuracy of acceleration is more sensitive than that of displacement. At the same time, the APVE ranges between 10% and 35%, indicating a larger error level of the acceleration than that of the displacement. The dimensional parameters including WMAE, RMSE, and WRMSE range between 4 mm/s\({}^{2}\) and 14 mm/s\({}^{2}\). When the size of the training dataset increases from 25 to 100, the evaluation metrics demonstrate a gradual improvement in prediction accuracy. However, as the size of the training dataset further increases from 100 to 200, the change in each evaluation metrics becomes less apparent, and, in some cases, even tends to increase. This observation suggests that increasing the number of training samples does not consistently enhance the prediction effectiveness of the model.  
This phenomenon may be attributed to the quality of the dataset. An examination of Table 1 reveals significant differences in working conditions between dataset A (25 samples), dataset B (50 samples), and dataset C (100 samples). However, dataset D (150 samples) and dataset E (200 samples) exhibit relatively minor variations in working conditions compared to dataset C. Specifically, the changes in working conditions for dataset D and dataset E are minimal, with only slight adjustments in sampling frequency and train fixed wheel  
Figure 14: The impact of training sample quantity on acceleration prediction accuracy.  
Figure 13: The impact of training sample quantity on displacement prediction accuracy.  
Indeed, despite the increased size of datasets D and E, the quality enhancement of these datasets is not readily apparent due to the repetition or similarity of working conditions. Consequently, the improvement in model prediction effectiveness is not evident and, in some cases, may even decrease. Therefore, when constructing the dataset, it is crucial to gather a wide range of potential working conditions while avoiding the collection of repeated or similar working conditions. This approach ensures the development of a high-quality training dataset. By doing so, the LSTM network model can undergo comprehensive training and learning, ultimately enhancing the predictive effectiveness of the model.