## 5 Results
### Comparison Experiments  
When evaluating the performance of the WOA-CatBoost model, we conducted comparisons with other machine learning models, including CatBoost, Extra Trees, random forest, Logistic Regression, and SVM, all utilizing default parameters. For the WOA-CatBoost model, we experimented with setting the whale population size in the range from 0 to 50 at intervals of 10. Multiple experimental results indicated that the whale population size had a negligible impact on the model's classification accuracy, as the whales consistently moved toward the optimal position, leading the entire population to converge to the best location. However, increasing the number of whales significantly extended the program's runtime. Consequently, we set the whale population size to 10 in subsequent experiments. By training each model on the training set and making classification predictions on the test set, we obtained evaluation metrics such as accuracy, precision, recall, and F1. The results of the comparison related to these four metrics are depicted in Figure 11a. The WOA-CatBoost algorithm demonstrated the highest accuracy, indicated by the red bar, providing intuitive evidence that the WOA-CatBoost model outperforms other classifiers in terms of identification performance. Figure 10: Fitness value curves for the WOA-CatBoost model. Secondly, the QAR data of a specific route were used to identify the turbulence occurring on the route from Sanya to Jinan by training the model as shown in Figure 11b, and the corresponding turbulence segments were identified by using label 1 to represent the time segment where turbulence occurred, and label 0 to represent that no turbulence occurred. The trained model was then used on the test dataset (Chongqing to Jinan route) and each time segment where turbulence occurred was labelled as shown in Figure 11c. Evaluation metrics values are listed in Table 3. WOA-CatBoost achieved the highest accuracy of 0.96, precision of 0.96, recall of 0.90, and F1 of 0.93. These results demonstrated the superior performance of WOA-CatBoost compared to CatBoost, Extra Trees, random forest, Logistic Regression, and SVM. Simultaneously, the correctly classified values (TP + TN) and misclassified values (FP + FN) of WOA-CatBoost indicated that the proposed model outperformed the other five models. Additionally, based on the confusion matrix (a) and (c) in Figure 12, the overall accuracy for the training and testing data was 99% and 96%, respectively. The WOA-CatBoost classifier generated a 90% TPR and 10% FPR for the testing dataset. These results effectively validated the proficiency of the hybrid model based on WOA-CatBoost in turbulence identification and classification. Figure 11: Model performance comparison and turbulence identification on training and testing datasets. (**a**) Model evaluation metric comparison; (**b**) turbulence identification from Sanya to Jinan; (**c**) turbulence identification from Chongqing to Jinan. To further compare and assess the stability and robustness of the evaluation models, the QAR dataset was subjected to additional algorithms (CatBoost, Extra Trees, random forest, Logistic Regression, SVM), and a corresponding fusion ROC curve was applied to CatBoost for comparison. From Figure 12b, it is observed that these popular algorithms exhibited good performance in the QAR data classification task on the training dataset. However, in Figure 12d, significant differences are apparent in the testing dataset, indicating poorer performance for these popular algorithms. The Logistic Regression classifier had the minimum AUC value of 0.68, while other algorithms surpassed it. WOA-CatBoost achieved the highest AUC value of 0.98, suggesting that the proposed WOA-CatBoost outperformed other classifiers. On the other hand, other machine learning algorithms exhibited better performance on the training set but poorer performance on the testing set, indicating the weaker robustness of these popular algorithms.