## 3 Simulation Experiments
### Model Implementation  
In this experiment, categorical cross-entropy was adopted as the performance evaluation metric for the model. Categorical cross-entropy is a commonly used loss function for multi-class classification tasks and is designed to measure the divergence between the predicted probability distribution and the actual target distribution. The formulation is expressed as follows:  
\[L=-\frac{1}{N}\sum_{i=1}^{N}\sum_{j=1}^{C}y_{ij}\log(y_{ij}^{\ast}) \tag{10}\]  
where \(N\) represents the total number of samples, \(C\) is the total number of classes, \(y_{ij}\) denotes the true label for sample \(i\) belonging to class \(j\) (1 for belonging and 0 for not belonging), and \(y_{ij}^{\ast}\) denotes the normalized predicted probability distribution for the same. By minimizing the categorical cross-entropy loss, the model predictions can be made closer to the true distribution, thereby improving classification accuracy. The experimental results of the models were evaluated and analyzed using Precision, Recall, and F1 Score as evaluation metrics. These metrics provide a comprehensive assessment of model performance from different perspectives. Precision measures the proportion of true positive predictions among all samples predicted as positive by the model. It reflects the accuracy of the model, indicating its reliability in correctly identifying positive samples. A higher Precision value demonstrates that the model makes fewer false positive predictions. Recall evaluates the proportion of true positive predictions among all actual positive samples. It reflects the sensitivity or coverage of the model, indicating its ability to correctly identify as many positive samples as possible. A higher Recall value signifies that the model misses fewer actual positive cases. The F1 Score represents the harmonic mean of Precision and Recall, providing a balanced metric that considers both false positives and false negatives. It represents a comprehensive indicator that is particularly useful when there is an imbalance between the number of positive and negative samples. A higher F1 Score represents that the model achieves a better trade-off between Precision and Recall. \[Precision=\frac{TP}{TP+FP} \tag{11}\]  
\[Recall=\frac{TP}{TP+FN} \tag{12}\]  
\[F1=2\times\frac{Precision\times Recall}{Precision+Recall} \tag{13}\]  
In these equations, _TP_ (true positive) represents the number of samples correctly predicted as positive and _FP_ (false positive) represents the number of samples incorrectly predicted as positive. To optimize the model's performance, a systematic adjustment and evaluation of the hyperparameters were conducted, which significantly enhances the model's accuracy and generalization ability while avoiding overfitting and underfitting. To ensure improved accuracy and generalization capability for complex time-series data, this study employed an automated hyperparameter tuning approach based on the Optuna optimization framework to systematically optimize the key hyperparameters of the TCN-BiLSTM model [22, 23]. The detailed optimization process is as follows:  
* Hyperparameter Selection: Critical hyperparameters for both the TCN and BiLSTM layers were identified, including kernel size, dilation factor, number of hidden layer units, learning rate, dropout rate, and activation function type. These hyperparameters significantly influence the learning capacity and performance of the model. For instance, the kernel size and dilation factor determine the receptive field of the TCN, while the number of hidden units and dropout rate affect the BiLSTM's ability to model long-term dependencies and the model's resistance to overfitting. * Automated Optimization: Using the Optuna framework, automated search and tuning of the aforementioned hyperparameters were conducted. A target function was created (i.e., the loss value on the validation set), and Bayesian optimization was employed to dynamically adjust the search space during each iteration.