# Accelerometer-Based Pavement Classification for Vehicle Dynamics Analysis Using Neural Networks
## 4 Discussion
### Neural Network Classifier  
A 3-layer neural network was used to classify the pavement. Table 2 presents the structure of the neural network, but Figure 9 presents the scheme of data processing and learning process using a neural network for pavement identification. Table 2 illustrates the outcomes of the deep neural network architecture, focusing on the configuration of the network layers and their impact on the final classification results. The output of the first dense layer, including 15 neurons with softsign activation, indicates that this layer effectively regulates substantial input levels. The softsign activation function normalizes values between \(-1\) and \(1\), mitigating significant volatility and enhancing  
the stability of the learning process. The softsign function was used to emphasize the differences resulting from the application of aggregation of the results obtained after quantile standardization. Consequently, the network enhances its ability to identify diverse data patterns, leading to more reliable and consistent outcomes. The second dense layer, including 10 neurons with ReLU activation, conveys significant insights into neuronal activity since ReLU eliminates negative values and permits only positive values to affect the output. This method is significant since it preserves network simplicity, decreases computing complexity, and enhances accuracy. The ReLU function enhances the network's learning velocity, facilitating expedited convergence. The final output layer, using softmax activation, delivers the network's ultimate predictions: seven probabilities indicating the extent to which a data point is associated with a certain class. The probabilistic outcomes of this layer facilitate the interpretation of the model's performance and enable the assessment of the classifier's accuracy based on the network's recognition of each class. The network produces 567 parameters, enabling the model to execute intricate classification tasks while preserving an optimal balance between accuracy and processing efficiency. The total number of parameters of the neural network is 567. The number of training epochs is 200. Validation was also applied during learning in each epoch. In each epoch, the batch was divided into a training set, containing 90% of the batch, and a validation set, containing 10% of the batch. Cross-entropy was selected as the quality function for the classification model based on the neural network, and the accuracy was chosen as a verification metric. Figure 10 shows the cross-entropy and accuracy values during the neural network training. The cross-entropy graph illustrates the reduction in the loss function for both the training and validation datasets. Initially, the cross-entropy is high (about 2.0), indicating that the model starts learning with poor precision and misclassifies the data. Nonetheless, with the passage of time, particularly after the first 50 epochs, the entropy value markedly diminishes, and both curves consistently decline towards a near-zero value. This indicates that the model increasingly improves its efficiency in minimizing mistakes and refining categorization for both training and validation datasets. The cross-entropy stabilization \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer (type)** & **Output Shape** & **Parameters** & **Activation** \\ \hline Input Layer & \((1,21)\) & 0 & \\ Dense 1 & \((1,15)\) & 330 & _softsign_ \\ Dense 2 & \((1,10)\) & 160 & _relu_ \\ Output Dense & \((1,7)\) & 77 & _softsmax_ \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Confusion matrix for classifier performance evaluation. Figure 9: The data processing scheme and learning process using a neural network for pavement identification. indicates that the model is not in significant danger of overfitting and effectively generalizes the findings. Figure 10 depicting category accuracy demonstrates an upward trend. Initially, the training accuracy escalates swiftly, reaching about 100% after around 50 epochs.