Figure 7 Histogram of importance of model hyperparameters
Figure 7 illustrates the importance of the eight hyperparameters on the loss of the CBi-GRU model after 80 experimental runs. As shown in Figure 7, the dropout rate for the CNN network (cnn_dropout) has the most significant impact on model accuracy, accounting for 31.0%. This is followed by the number of units in the first layer of the Bi-GRU network (bigru_units_layer0), the dropout rate for the Bi-GRU network (bigru_dropout), and the learning rate (learning_rate), with impacts of 10.0%, 8.0%, and 7.0%, respectively. The term ”first layer units (bigru_units_layer0)” refers to the number of units in the first layer within the searched interval [1,4] for the number of layers (bigru_num_layers). Subsequently, the dropout rate for the final layer of the Bi-GRU network (bigru_dropout_final) and the number of units in the final layer (bigru_unit_final) impact the model by 5.0% and 4.0%, respectively. The number of units in the CNN network (cnn_unit) and the number of layers in the Bi-GRU network (bigru_num_layers) have the smallest impact, each accounting for 3.0%.
The detailed breakdown of the hyperparameters and their respective impacts on the model’s performance underscores the critical elements influencing the CBi-GRU model’s accuracy and provides a clear path for targeted optimization. This analysis emphasizes the significance of fine-tuning dropout rates and layer configurations to enhance predictive performance effectively.
The total experimental duration was 21 hours, 35 minutes, and 55 seconds, significantly reducing the time required compared to manual trials. The major advantage of automated hyperparameter optimization lies in its efficiency and accuracy. Utilizing the Bayesian optimization algorithm based on Tree-Structured Parzen Estimator (TPE), parameter adjustments during the experimental process are completed in a shorter timeframe with more precise results. Compared to manual experimentation, the automated optimization method significantly improves experimental efficiency, reduces resource wastage, and facilitates easier replication and adjustment. This automated approach not only accelerates research progress but also enhances the reliability of experimental results, thereby providing strong support for scientific research and engineering applications.
Through the analysis of 80 trials, the results are shown in Figure 8. The highest value of 96.00% was achieved in the 51st experiment, indicating the highest fitting degree between the predicted curve and the actual values. Therefore, the hyperparameter combination with an value of 96.00% was selected to build the model, with the parameter combination detailed in Table 5. Figure 9 shows the loss curves of the training and validation sets for the selected hyperparameter combination, demonstrating that the errors for both the training and validation sets are below 0.1, indicating a well-fitted model.