# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 4 Dataset Construction
### Data Collection and Labeling
#### 4.2.3 Automatic Data Labeling  
The primary objectives of the automatic labeling process mirrored those of the manual labeling phase; in addition, it encompasses the following functions:  
* Filtering out excessively noisy signal blocks that could not be corrected through preprocessing;
* Automatically segmenting the pre-labeled 60 s data block into 251-point segments and assigning these the corresponding state identifier; \((F_{i},P_{j},S_{k})\)
* Reducing the time and manual effort required for labeling. To achieve these objectives, the 60 s pre-labeled acceleration data, as discussed in the previous section, were divided into atomic blocks of 251 sampled data points using a sliding window technique. This approach ensured that the signal blocks were efficiently processed and labeled according to their corresponding states. Figure 8 illustrates the deep learning model designed for automatic labeling, which was specifically trained to recognize patterns within the acceleration signals and accurately apply the pre-defined state labels. Figure 8 incorporate 1D convolutional layers and a transformer encoder with an attention mechanism. The left part of the figure illustrates the model architecture during the training phase, while the right part depicts the model's operation during the automatic labeling phase. The model was trained using binary cross-entropy loss. To train the model shown in Figure 8, 50% of the manually labeled 251-point acceleration signal data segments were used in training, while the remaining 50% of the manually labeled data were used in the validation dataset. This division ensured that the model was not only able to learn from the labeled data, but also evaluated unseen data to ensure its generalization performance. Furthermore, the dataset was augmented by adding Gaussian noise to 35% of the manually labeled data. This noisy data was split into 15% for training, 15% for validation, and the remaining 70% was used as the test dataset. This augmentation process helped to increase the robustness of the model by exposing it to variations in the acceleration signals. In Figure 9, 251-point acceleration data segments and corresponding noisy augmented data are illustrated. The segmented 251-point atomic data was processed through 1D convolutional layers, which were designed to detect local patterns in the acceleration signals. This was followed by a transformer encoder block, which employed the attention mechanism to capture  
Figure 7: Labeled acceleration signal segments. long-term dependencies in the sequential 1D data and identify broader patterns within the dataset. The model was trained using the binary cross-entropy loss function, and classification and automatic labeling were subsequently performed based on the learned patterns from the training phase. After the model was trained for a specific state \((F_{i},P_{j},S_{k})\), it was employed to automatically label the remaining data corresponding to that same state. For each subsequent state, the model's weights were reset, and the training and labeling process was repeated for the new state. Figure 8: Deep learning model for automatic labeling. Figure 9: The 251-point data segments and corresponding noisy augmented segments for \((F_{i},P_{j},S_{k})\). Figure 10 presents the confusion matrix, illustrating the performance of the 1D CNN and transformer encoder-based deep learning model on the test data for automatic acceleration data labeling, specifically for the state (150 kg, 70 km/h, 200 kPa). The model was trained using the Adam optimization algorithm with a learning rate of \(1\times 10^{-4}\). Since the labeling task is inherently a classification problem, binary cross-entropy was employed as the loss function. The model was trained for a total of 500 epochs. True Positive (TP) and True Negative (TN) signal examples, along with their respective heatmaps, are shown in Figure 11 and Figure 12, respectively, which are generated by the model's attention mechanism, highlighting the key areas contributing to the correct classification.